25,944 research outputs found
Strong Equivalence Relations for Iterated Models
The Iterated Immediate Snapshot model (IIS), due to its elegant geometrical
representation, has become standard for applying topological reasoning to
distributed computing. Its modular structure makes it easier to analyze than
the more realistic (non-iterated) read-write Atomic-Snapshot memory model (AS).
It is known that AS and IIS are equivalent with respect to \emph{wait-free
task} computability: a distributed task is solvable in AS if and only if it
solvable in IIS. We observe, however, that this equivalence is not sufficient
in order to explore solvability of tasks in \emph{sub-models} of AS (i.e.
proper subsets of its runs) or computability of \emph{long-lived} objects, and
a stronger equivalence relation is needed. In this paper, we consider
\emph{adversarial} sub-models of AS and IIS specified by the sets of processes
that can be \emph{correct} in a model run. We show that AS and IIS are
equivalent in a strong way: a (possibly long-lived) object is implementable in
AS under a given adversary if and only if it is implementable in IIS under the
same adversary. %This holds whether the object is one-shot or long-lived.
Therefore, the computability of any object in shared memory under an
adversarial AS scheduler can be equivalently investigated in IIS
The solvability of consensus in iterated models extended with safe-consensus
The safe-consensus task was introduced by Afek, Gafni and Lieber (DISC'09) as
a weakening of the classic consensus. When there is concurrency, the consensus
output can be arbitrary, not even the input of any process. They showed that
safe-consensus is equivalent to consensus, in a wait-free system. We study the
solvability of consensus in three shared memory iterated models extended with
the power of safe-consensus black boxes. In the first model, for the -th
iteration, processes write to the memory, invoke safe-consensus boxes and
finally they snapshot the memory. We show that in this model, any wait-free
implementation of consensus requires safe-consensus black-boxes
and this bound is tight. In a second iterated model, the processes write to
memory, then they snapshot it and finally they invoke safe-consensus boxes. We
prove that in this model, consensus cannot be implemented. In the last iterated
model, processes first invoke safe-consensus, then they write to memory and
finally they snapshot it. We show that this model is equivalent to the previous
model and thus consensus cannot be implemented.Comment: 49 pages, A preliminar version of the main results appeared in the
SIROCCO 2014 proceeding
Relating L-Resilience and Wait-Freedom via Hitting Sets
The condition of t-resilience stipulates that an n-process program is only
obliged to make progress when at least n-t processes are correct. Put another
way, the live sets, the collection of process sets such that progress is
required if all the processes in one of these sets are correct, are all sets
with at least n-t processes.
We show that the ability of arbitrary collection of live sets L to solve
distributed tasks is tightly related to the minimum hitting set of L, a minimum
cardinality subset of processes that has a non-empty intersection with every
live set. Thus, finding the computing power of L is NP-complete.
For the special case of colorless tasks that allow participating processes to
adopt input or output values of each other, we use a simple simulation to show
that a task can be solved L-resiliently if and only if it can be solved
(h-1)-resiliently, where h is the size of the minimum hitting set of L.
For general tasks, we characterize L-resilient solvability of tasks with
respect to a limited notion of weak solvability: in every execution where all
processes in some set in L are correct, outputs must be produced for every
process in some (possibly different) participating set in L. Given a task T, we
construct another task T_L such that T is solvable weakly L-resiliently if and
only if T_L is solvable weakly wait-free
Iterated filtering methods for Markov process epidemic models
Dynamic epidemic models have proven valuable for public health decision
makers as they provide useful insights into the understanding and prevention of
infectious diseases. However, inference for these types of models can be
difficult because the disease spread is typically only partially observed e.g.
in form of reported incidences in given time periods. This chapter discusses
how to perform likelihood-based inference for partially observed Markov
epidemic models when it is relatively easy to generate samples from the Markov
transmission model while the likelihood function is intractable. The first part
of the chapter reviews the theoretical background of inference for partially
observed Markov processes (POMP) via iterated filtering. In the second part of
the chapter the performance of the method and associated practical difficulties
are illustrated on two examples. In the first example a simulated outbreak data
set consisting of the number of newly reported cases aggregated by week is
fitted to a POMP where the underlying disease transmission model is assumed to
be a simple Markovian SIR model. The second example illustrates possible model
extensions such as seasonal forcing and over-dispersion in both, the
transmission and observation model, which can be used, e.g., when analysing
routinely collected rotavirus surveillance data. Both examples are implemented
using the R-package pomp (King et al., 2016) and the code is made available
online.Comment: This manuscript is a preprint of a chapter to appear in the Handbook
of Infectious Disease Data Analysis, Held, L., Hens, N., O'Neill, P.D. and
Wallinga, J. (Eds.). Chapman \& Hall/CRC, 2018. Please use the book for
possible citations. Corrected typo in the references and modified second
exampl
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