320,352 research outputs found
Logics of Finite Hankel Rank
We discuss the Feferman-Vaught Theorem in the setting of abstract model
theory for finite structures. We look at sum-like and product-like binary
operations on finite structures and their Hankel matrices. We show the
connection between Hankel matrices and the Feferman-Vaught Theorem. The largest
logic known to satisfy a Feferman-Vaught Theorem for product-like operations is
CFOL, first order logic with modular counting quantifiers. For sum-like
operations it is CMSOL, the corresponding monadic second order logic. We
discuss whether there are maximal logics satisfying Feferman-Vaught Theorems
for finite structures.Comment: Appeared in YuriFest 2015, held in honor of Yuri Gurevich's 75th
birthday. The final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-23534-9_1
Route Planning in Transportation Networks
We survey recent advances in algorithms for route planning in transportation
networks. For road networks, we show that one can compute driving directions in
milliseconds or less even at continental scale. A variety of techniques provide
different trade-offs between preprocessing effort, space requirements, and
query time. Some algorithms can answer queries in a fraction of a microsecond,
while others can deal efficiently with real-time traffic. Journey planning on
public transportation systems, although conceptually similar, is a
significantly harder problem due to its inherent time-dependent and
multicriteria nature. Although exact algorithms are fast enough for interactive
queries on metropolitan transit systems, dealing with continent-sized instances
requires simplifications or heavy preprocessing. The multimodal route planning
problem, which seeks journeys combining schedule-based transportation (buses,
trains) with unrestricted modes (walking, driving), is even harder, relying on
approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4,
previously published by Microsoft Research. This work was mostly done while
the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at
Microsoft Research Silicon Valle
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
Isotropic-nematic phase transition in suspensions of filamentous virus and the neutral polymer Dextran
We present an experimental study of the isotropic-nematic phase transition in
an aqueous mixture of charged semi-flexible rods (fd virus) and neutral polymer
(Dextran). A complete phase diagram is measured as a function of ionic strength
and polymer molecular weight. At high ionic strength we find that adding
polymer widens the isotropic-nematic coexistence region with polymers
preferentially partitioning into the isotropic phase, while at low ionic
strength the added polymer has no effect on the phase transition. The nematic
order parameter is determined from birefringence measurements and is found to
be independent of polymer concentration (or equivalently the strength of
attraction). The experimental results are compared with the existing
theoretical predictions for the isotropic-nematic transition in rods with
attractive interactions.Comment: 8 Figures. To be published in Phys. Rev. E. For more information see
http://www.elsie.brandeis.ed
Complexity of Restricted and Unrestricted Models of Molecular Computation
In [9] and [2] a formal model for molecular computing was
proposed, which makes focused use of affinity purification.
The use of PCR was suggested to expand the range of
feasible computations, resulting in a second model. In this
note, we give a precise characterization of these two models
in terms of recognized computational complexity classes,
namely branching programs (BP) and nondeterministic
branching programs (NBP) respectively. This allows us to
give upper and lower bounds on the complexity of desired
computations. Examples are given of computable and
uncomputable problems, given limited time
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