1,150 research outputs found
Eigenvalue problem for radial potentials in space with SU(2) fuzziness
The eigenvalue problem for radial potentials is considered in a space whose
spatial coordinates satisfy the SU(2) Lie algebra. As the consequence, the
space has a lattice nature and the maximum value of momentum is bounded from
above. The model shows interesting features due to the bound, namely, a
repulsive potential can develop bound-states, or an attractive region may be
forbidden for particles to propagate with higher energies. The exact radial
eigen-functions in momentum space are given by means of the associated
Chebyshev functions. For the radial stepwise potentials the exact energy
condition and the eigen-functions are presented. For a general radial potential
it is shown that the discrete energy spectrum can be obtained in desired
accuracy by means of given forms of continued fractions.Comment: 1+20 pages, 2 figs, LaTe
Incremental Consistency Guarantees for Replicated Objects
Programming with replicated objects is difficult. Developers must face the
fundamental trade-off between consistency and performance head on, while
struggling with the complexity of distributed storage stacks. We introduce
Correctables, a novel abstraction that hides most of this complexity, allowing
developers to focus on the task of balancing consistency and performance. To
aid developers with this task, Correctables provide incremental consistency
guarantees, which capture successive refinements on the result of an ongoing
operation on a replicated object. In short, applications receive both a
preliminary---fast, possibly inconsistent---result, as well as a
final---consistent---result that arrives later.
We show how to leverage incremental consistency guarantees by speculating on
preliminary values, trading throughput and bandwidth for improved latency. We
experiment with two popular storage systems (Cassandra and ZooKeeper) and three
applications: a Twissandra-based microblogging service, an ad serving system,
and a ticket selling system. Our evaluation on the Amazon EC2 platform with
YCSB workloads A, B, and C shows that we can reduce the latency of strongly
consistent operations by up to 40% (from 100ms to 60ms) at little cost (10%
bandwidth increase, 6% throughput drop) in the ad system. Even if the
preliminary result is frequently inconsistent (25% of accesses), incremental
consistency incurs a bandwidth overhead of only 27%.Comment: 16 total pages, 12 figures. OSDI'16 (to appear
Progressive Transactional Memory in Time and Space
Transactional memory (TM) allows concurrent processes to organize sequences
of operations on shared \emph{data items} into atomic transactions. A
transaction may commit, in which case it appears to have executed sequentially
or it may \emph{abort}, in which case no data item is updated.
The TM programming paradigm emerged as an alternative to conventional
fine-grained locking techniques, offering ease of programming and
compositionality. Though typically themselves implemented using locks, TMs hide
the inherent issues of lock-based synchronization behind a nice transactional
programming interface.
In this paper, we explore inherent time and space complexity of lock-based
TMs, with a focus of the most popular class of \emph{progressive} lock-based
TMs. We derive that a progressive TM might enforce a read-only transaction to
perform a quadratic (in the number of the data items it reads) number of steps
and access a linear number of distinct memory locations, closing the question
of inherent cost of \emph{read validation} in TMs. We then show that the total
number of \emph{remote memory references} (RMRs) that take place in an
execution of a progressive TM in which concurrent processes perform
transactions on a single data item might reach , which
appears to be the first RMR complexity lower bound for transactional memory.Comment: Model of Transactional Memory identical with arXiv:1407.6876,
arXiv:1502.0272
On The Robustness of a Neural Network
With the development of neural networks based machine learning and their
usage in mission critical applications, voices are rising against the
\textit{black box} aspect of neural networks as it becomes crucial to
understand their limits and capabilities. With the rise of neuromorphic
hardware, it is even more critical to understand how a neural network, as a
distributed system, tolerates the failures of its computing nodes, neurons, and
its communication channels, synapses. Experimentally assessing the robustness
of neural networks involves the quixotic venture of testing all the possible
failures, on all the possible inputs, which ultimately hits a combinatorial
explosion for the first, and the impossibility to gather all the possible
inputs for the second.
In this paper, we prove an upper bound on the expected error of the output
when a subset of neurons crashes. This bound involves dependencies on the
network parameters that can be seen as being too pessimistic in the average
case. It involves a polynomial dependency on the Lipschitz coefficient of the
neurons activation function, and an exponential dependency on the depth of the
layer where a failure occurs. We back up our theoretical results with
experiments illustrating the extent to which our prediction matches the
dependencies between the network parameters and robustness. Our results show
that the robustness of neural networks to the average crash can be estimated
without the need to neither test the network on all failure configurations, nor
access the training set used to train the network, both of which are
practically impossible requirements.Comment: 36th IEEE International Symposium on Reliable Distributed Systems 26
- 29 September 2017. Hong Kong, Chin
The Weakest Failure Detector for Eventual Consistency
In its classical form, a consistent replicated service requires all replicas
to witness the same evolution of the service state. Assuming a message-passing
environment with a majority of correct processes, the necessary and sufficient
information about failures for implementing a general state machine replication
scheme ensuring consistency is captured by the {\Omega} failure detector. This
paper shows that in such a message-passing environment, {\Omega} is also the
weakest failure detector to implement an eventually consistent replicated
service, where replicas are expected to agree on the evolution of the service
state only after some (a priori unknown) time. In fact, we show that {\Omega}
is the weakest to implement eventual consistency in any message-passing
environment, i.e., under any assumption on when and where failures might occur.
Ensuring (strong) consistency in any environment requires, in addition to
{\Omega}, the quorum failure detector {\Sigma}. Our paper thus captures, for
the first time, an exact computational difference be- tween building a
replicated state machine that ensures consistency and one that only ensures
eventual consistency
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