12,082 research outputs found
Normalisation Control in Deep Inference via Atomic Flows
We introduce `atomic flows': they are graphs obtained from derivations by
tracing atom occurrences and forgetting the logical structure. We study simple
manipulations of atomic flows that correspond to complex reductions on
derivations. This allows us to prove, for propositional logic, a new and very
general normalisation theorem, which contains cut elimination as a special
case. We operate in deep inference, which is more general than other syntactic
paradigms, and where normalisation is more difficult to control. We argue that
atomic flows are a significant technical advance for normalisation theory,
because 1) the technique they support is largely independent of syntax; 2)
indeed, it is largely independent of logical inference rules; 3) they
constitute a powerful geometric formalism, which is more intuitive than syntax
Behavioral Communities and the Atomic Structure of Networks
We develop a theory of `behavioral communities' and the `atomic structure' of
networks. We define atoms to be groups of agents whose behaviors always match
each other in a set of coordination games played on the network. This provides
a microfoundation for a method of detecting communities in social and economic
networks. We provide theoretical results characterizing such behavior-based
communities and atomic structures and discussing their properties in large
random networks. We also provide an algorithm for identifying behavioral
communities. We discuss applications including: a method of estimating
underlying preferences by observing behavioral conventions in data, and
optimally seeding diffusion processes when there are peer interactions and
homophily. We illustrate the techniques with applications to high school
friendship networks and rural village networks
âDo Not Kill Guinea Pig before Setting up Apparatusâ: The Kymograph's Lost Educational Context
The objects of science education are transformed, degraded and disappeared for many reasons, and sometimes take other things with them when they go. This close reading of an undergraduate physiology laboratory report demonstrates how the kymograph was never a stand-alone instrument, but intertwined with conceptual frameworks and technical skills, laboratory amenities, materials, animal supply, technicians. Replacing the obsolete kymograph entails changing all of that, though our usual stories are focussed on progress associated with better measurements with fewer complications, not complications themselves. Such interconnectedness between progress and demise raises uncomfortable challenges for laboratory pedagogy, and for museum practice: what is laboratory education really about, and what kinds of heritage should museums, libraries and archives preserve to document it
Contrasting Views of Complexity and Their Implications For Network-Centric Infrastructures
There exists a widely recognized need to better understand
and manage complex âsystems of systems,â ranging from
biology, ecology, and medicine to network-centric technologies.
This is motivating the search for universal laws of highly evolved
systems and driving demand for new mathematics and methods
that are consistent, integrative, and predictive. However, the theoretical
frameworks available today are not merely fragmented
but sometimes contradictory and incompatible. We argue that
complexity arises in highly evolved biological and technological
systems primarily to provide mechanisms to create robustness.
However, this complexity itself can be a source of new fragility,
leading to ârobust yet fragileâ tradeoffs in system design. We
focus on the role of robustness and architecture in networked
infrastructures, and we highlight recent advances in the theory
of distributed control driven by network technologies. This view
of complexity in highly organized technological and biological systems
is fundamentally different from the dominant perspective in
the mainstream sciences, which downplays function, constraints,
and tradeoffs, and tends to minimize the role of organization and
design
Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs
We introduce a new approach to computing an approximately maximum s-t flow in
a capacitated, undirected graph. This flow is computed by solving a sequence of
electrical flow problems. Each electrical flow is given by the solution of a
system of linear equations in a Laplacian matrix, and thus may be approximately
computed in nearly-linear time.
Using this approach, we develop the fastest known algorithm for computing
approximately maximum s-t flows. For a graph having n vertices and m edges, our
algorithm computes a (1-\epsilon)-approximately maximum s-t flow in time
\tilde{O}(mn^{1/3} \epsilon^{-11/3}). A dual version of our approach computes a
(1+\epsilon)-approximately minimum s-t cut in time
\tilde{O}(m+n^{4/3}\eps^{-8/3}), which is the fastest known algorithm for this
problem as well. Previously, the best dependence on m and n was achieved by the
algorithm of Goldberg and Rao (J. ACM 1998), which can be used to compute
approximately maximum s-t flows in time \tilde{O}(m\sqrt{n}\epsilon^{-1}), and
approximately minimum s-t cuts in time \tilde{O}(m+n^{3/2}\epsilon^{-3})
Mathematics and the Internet: A Source of Enormous Confusion and Great Potential
Graph theory models the Internet mathematically, and a number of plausible mathematically intersecting network models for the Internet have been developed and studied. Simultaneously, Internet researchers have developed methodology to use real data to validate, or invalidate, proposed Internet models. The authors look at these parallel developments, particularly as they apply to scale-free network models of the preferential attachment type
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