30,235 research outputs found
Modulated phases in magnetic models frustrated by long-range interactions
We study an Ising model in one dimension with short range ferromagnetic and
long range (power law) antiferromagnetic interactions. We show that the zero
temperature phase diagram in a (longitudinal) field H involves a sequence of up
and down domains whose size varies continuously with H, between -H_c and H_c
which represent the edge of the ferromagnetic up and down phases. The
implications of long range interaction in many body systems are discussed.Comment: 5 pages, 3 figure
Almost direct summands
In this short note, we point out how some new cases of Hochster's direct
summand conjecture can be deduced from fundamental theorems in p-adic Hodge
theory due to Faltings. The cases tackled include the ones when the
ramification of the map being considered lies entirely in characteristic p.Comment: 5 pages, comments welcome
Between Sense and Sensibility: Declarative narrativisation of mental models as a basis and benchmark for visuo-spatial cognition and computation focussed collaborative cognitive systems
What lies between `\emph{sensing}' and `\emph{sensibility}'? In other words,
what kind of cognitive processes mediate sensing capability, and the formation
of sensible impressions ---e.g., abstractions, analogies, hypotheses and theory
formation, beliefs and their revision, argument formation--- in domain-specific
problem solving, or in regular activities of everyday living, working and
simply going around in the environment? How can knowledge and reasoning about
such capabilities, as exhibited by humans in particular problem contexts, be
used as a model and benchmark for the development of collaborative cognitive
(interaction) systems concerned with human assistance, assurance, and
empowerment?
We pose these questions in the context of a range of assistive technologies
concerned with \emph{visuo-spatial perception and cognition} tasks encompassing
aspects such as commonsense, creativity, and the application of specialist
domain knowledge and problem-solving thought processes. Assistive technologies
being considered include: (a) human activity interpretation; (b) high-level
cognitive rovotics; (c) people-centred creative design in domains such as
architecture & digital media creation, and (d) qualitative analyses geographic
information systems. Computational narratives not only provide a rich cognitive
basis, but they also serve as a benchmark of functional performance in our
development of computational cognitive assistance systems. We posit that
computational narrativisation pertaining to space, actions, and change provides
a useful model of \emph{visual} and \emph{spatio-temporal thinking} within a
wide-range of problem-solving tasks and application areas where collaborative
cognitive systems could serve an assistive and empowering function.Comment: 5 pages, research statement summarising recent publication
- …