443 research outputs found
Deciding first-order properties of nowhere dense graphs
Nowhere dense graph classes, introduced by Nesetril and Ossona de Mendez,
form a large variety of classes of "sparse graphs" including the class of
planar graphs, actually all classes with excluded minors, and also bounded
degree graphs and graph classes of bounded expansion.
We show that deciding properties of graphs definable in first-order logic is
fixed-parameter tractable on nowhere dense graph classes. At least for graph
classes closed under taking subgraphs, this result is optimal: it was known
before that for all classes C of graphs closed under taking subgraphs, if
deciding first-order properties of graphs in C is fixed-parameter tractable,
then C must be nowhere dense (under a reasonable complexity theoretic
assumption).
As a by-product, we give an algorithmic construction of sparse neighbourhood
covers for nowhere dense graphs. This extends and improves previous
constructions of neighbourhood covers for graph classes with excluded minors.
At the same time, our construction is considerably simpler than those. Our
proofs are based on a new game-theoretic characterisation of nowhere dense
graphs that allows for a recursive version of locality-based algorithms on
these classes. On the logical side, we prove a "rank-preserving" version of
Gaifman's locality theorem.Comment: 30 page
Multi Layered Multi Task Marker Based Interaction in Information Rich Virtual Environments
Simple and cheap interaction has a key role in the operation and exploration of any Virtual Environment (VE). In this paper, we propose an interaction technique that provides two different ways of interaction (information and control) on complex objects in a simple and computationally cheap way. The interaction is based on the use of multiple embedded markers in a specialized manner. The proposed marker like an interaction peripheral works just like a touch paid which can perform any type of interaction in a 3D VE. The proposed marker is not only used for interaction with Augmented Reality (AR), but also with Mixed Reality. A biological virtual learning application is developed which is used for evaluation and experimentation. We conducted our experiments in two phases. First, we compared a simple VE with the proposed layered VE. Second, a comparative study is conducted between the proposed marker, a simple layered marker, and multiple single markers. We found the proposed marker with improved learning, easiness in interaction, and comparatively less task execution time. The results gave improved learning for layered VE as compared to simple VE
Impaired haematopoietic stem cell differentiation and enhanced skewing towards myeloid progenitors in aged caspase-2-deficient mice
The apoptotic cysteine protease caspase-2 has been shown to suppress tumourigenesis in mice and its reduced expression correlates with poor prognosis in some human malignancies. Caspase-2-deficient mice develop normally but show ageing-related traits and, when challenged by oncogenic stimuli or certain stress, show enhanced tumour development, often accompanied by extensive aneuploidy. As stem cells are susceptible to acquiring age-related functional defects because of their self-renewal and proliferative capacity, we examined whether loss of caspase-2 promotes such defects with age. Using young and aged Casp2−/− mice, we demonstrate that deficiency of caspase-2 results in enhanced aneuploidy and DNA damage in bone marrow (BM) cells with ageing. Furthermore, we demonstrate for the first time that caspase-2 loss results in significant increase in immunophenotypically defined short-term haematopoietic stem cells (HSCs) and multipotent progenitors fractions in BM with a skewed differentiation towards myeloid progenitors with ageing. Caspase-2 deficiency leads to enhanced granulocyte macrophage and erythroid progenitors in aged mice. Colony-forming assays and long-term culture-initiating assay further recapitulated these results. Our results provide the first evidence of caspase-2 in regulating HSC and progenitor differentiation, as well as aneuploidy, in vivo.Swati Dawar, Nur Hezrin Shahrin, Nikolina Sladojevic, Richard J D, Andrea, Loretta Dorstyn, Devendra K Hiwase and Sharad Kuma
The pebbling comonad in finite model theory
Pebble games are a powerful tool in the study of finite model theory, constraint satisfaction and database theory. Monads and comonads are basic notions of category theory which are widely used in semantics of computation and in modern functional programming. We show that existential k-pebble games have a natural comonadic formulation. Winning strategies for Duplicator in the k-pebble game for structures A and B are equivalent to morphisms from A to B in the coKleisli category for this comonad. This leads on to comonadic characterisations of a number of central concepts in Finite Model Theory: - Isomorphism in the co-Kleisli category characterises elementary equivalence in the k-variable logic with counting quantifiers. - Symmetric games corresponding to equivalence in full k-variable logic are also characterized. - The treewidth of a structure A is characterised in terms of its coalgebra number: the least k for which there is a coalgebra structure on A for the k-pebbling comonad. - Co-Kleisli morphisms are used to characterize strong consistency, and to give an account of a Cai-F\"urer-Immerman construction. - The k-pebbling comonad is also used to give semantics to a novel modal operator. These results lay the basis for some new and promising connections between two areas within logic in computer science which have largely been disjoint: (1) finite and algorithmic model theory, and (2) semantics and categorical structures of computation
Reconfiguration on sparse graphs
A vertex-subset graph problem Q defines which subsets of the vertices of an
input graph are feasible solutions. A reconfiguration variant of a
vertex-subset problem asks, given two feasible solutions S and T of size k,
whether it is possible to transform S into T by a sequence of vertex additions
and deletions such that each intermediate set is also a feasible solution of
size bounded by k. We study reconfiguration variants of two classical
vertex-subset problems, namely Independent Set and Dominating Set. We denote
the former by ISR and the latter by DSR. Both ISR and DSR are PSPACE-complete
on graphs of bounded bandwidth and W[1]-hard parameterized by k on general
graphs. We show that ISR is fixed-parameter tractable parameterized by k when
the input graph is of bounded degeneracy or nowhere-dense. As a corollary, we
answer positively an open question concerning the parameterized complexity of
the problem on graphs of bounded treewidth. Moreover, our techniques generalize
recent results showing that ISR is fixed-parameter tractable on planar graphs
and graphs of bounded degree. For DSR, we show the problem fixed-parameter
tractable parameterized by k when the input graph does not contain large
bicliques, a class of graphs which includes graphs of bounded degeneracy and
nowhere-dense graphs
Image, brand and price info: do they always matter the same?
We study attention processes to brand, price and visual information about products in online retailing websites, simultaneously considering the effects of consumers’ goals, purchase category and consumers’ statements. We use an intra-subject experimental design, simulated web stores and a combination of observational eye-tracking data and declarative measures. Image information about the product is the more important stimulus, regardless of the task at hand or the store involved. The roles of brand and price information are dependent on the product category and the purchase task involved. Declarative measures of relative brand importance are found to be positively related with its observed importance
Compact Labelings For Efficient First-Order Model-Checking
We consider graph properties that can be checked from labels, i.e., bit
sequences, of logarithmic length attached to vertices. We prove that there
exists such a labeling for checking a first-order formula with free set
variables in the graphs of every class that is \emph{nicely locally
cwd-decomposable}. This notion generalizes that of a \emph{nicely locally
tree-decomposable} class. The graphs of such classes can be covered by graphs
of bounded \emph{clique-width} with limited overlaps. We also consider such
labelings for \emph{bounded} first-order formulas on graph classes of
\emph{bounded expansion}. Some of these results are extended to counting
queries
Randomisation and Derandomisation in Descriptive Complexity Theory
We study probabilistic complexity classes and questions of derandomisation
from a logical point of view. For each logic L we introduce a new logic BPL,
bounded error probabilistic L, which is defined from L in a similar way as the
complexity class BPP, bounded error probabilistic polynomial time, is defined
from PTIME. Our main focus lies on questions of derandomisation, and we prove
that there is a query which is definable in BPFO, the probabilistic version of
first-order logic, but not in Cinf, finite variable infinitary logic with
counting. This implies that many of the standard logics of finite model theory,
like transitive closure logic and fixed-point logic, both with and without
counting, cannot be derandomised. Similarly, we present a query on ordered
structures which is definable in BPFO but not in monadic second-order logic,
and a query on additive structures which is definable in BPFO but not in FO.
The latter of these queries shows that certain uniform variants of AC0
(bounded-depth polynomial sized circuits) cannot be derandomised. These results
are in contrast to the general belief that most standard complexity classes can
be derandomised. Finally, we note that BPIFP+C, the probabilistic version of
fixed-point logic with counting, captures the complexity class BPP, even on
unordered structures
On Second-Order Monadic Monoidal and Groupoidal Quantifiers
We study logics defined in terms of second-order monadic monoidal and
groupoidal quantifiers. These are generalized quantifiers defined by monoid and
groupoid word-problems, equivalently, by regular and context-free languages. We
give a computational classification of the expressive power of these logics
over strings with varying built-in predicates. In particular, we show that
ATIME(n) can be logically characterized in terms of second-order monadic
monoidal quantifiers
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