5,719 research outputs found
Defining Recursive Predicates in Graph Orders
We study the first order theory of structures over graphs i.e. structures of
the form () where is the set of all
(isomorphism types of) finite undirected graphs and some vocabulary. We
define the notion of a recursive predicate over graphs using Turing Machine
recognizable string encodings of graphs. We also define the notion of an
arithmetical relation over graphs using a total order on the set
such that () is isomorphic to
().
We introduce the notion of a \textit{capable} structure over graphs, which is
one satisfying the conditions : (1) definability of arithmetic, (2)
definability of cardinality of a graph, and (3) definability of two particular
graph predicates related to vertex labellings of graphs. We then show any
capable structure can define every arithmetical predicate over graphs. As a
corollary, any capable structure also defines every recursive graph relation.
We identify capable structures which are expansions of graph orders, which are
structures of the form () where is a partial order. We
show that the subgraph order i.e. (), induced subgraph
order with one constant i.e. () and an expansion
of the minor order for counting edges i.e. ()
are capable structures. In the course of the proof, we show the definability of
several natural graph theoretic predicates in the subgraph order which may be
of independent interest. We discuss the implications of our results and
connections to Descriptive Complexity
Observation of a uniform temperature dependence in the electrical resistance across the structural phase transition in thin film vanadium oxide ()
An electrical study of thin films in the vicinity of the structural
phase transition at shows (a) that the electrical resistance
follows over the -range,
covering both sides of the structural transition, and (b) a history dependent
hysteresis loop in upon thermal cycling. These features are attributed here
to transport through a granular network.Comment: 3 pages, 3 color figure
Entropic Test of Quantum Contextuality
We study the contextuality of a three-level quantum system using classical
conditional entropy of measurement outcomes. First, we analytically construct
the minimal configuration of measurements required to reveal contextuality.
Next, an entropic contextual inequality is formulated, analogous to the
entropic Bell inequalities derived by Braunstein and Caves in [Phys. Rev. Lett.
{\bf 61}, 662 (1988)], that must be satisfied by all non-contextual theories.
We find optimal measurements for violation of this inequality. The approach is
easily extendable to higher dimensional quantum systems and more measurements.
Our theoretical findings can be verified in the laboratory with current
technology.Comment: 4 pages, 4 figure
Induced abortion potential among Indian women
Information on abortion is limited and inaccurate especially in the developing world, which has led to several speculations on the prevalence of abortion in this region. A rise in prevalence of abortion is mostly accounted for in terms of increase in the prevalence of induced abortions, which reflects on the reproductive health of women. With the growing concern for reproductive health of women, the study of abortion phenomenon has drawn serious attention of researchers world wide. In such circumstances, this is an attempt to assess the induced abortion potential among Indian women by utilising information on proportion of unwanted and ill-timed pregnancies obtained through National Family Health Survey, India.
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