103,482 research outputs found
Single-Server Multi-Message Private Information Retrieval with Side Information
We study the problem of single-server multi-message private information
retrieval with side information. One user wants to recover out of
independent messages which are stored at a single server. The user initially
possesses a subset of messages as side information. The goal of the user is
to download the demand messages while not leaking any information about the
indices of these messages to the server. In this paper, we characterize the
minimum number of required transmissions. We also present the optimal linear
coding scheme which enables the user to download the demand messages and
preserves the privacy of their indices. Moreover, we show that the trivial MDS
coding scheme with transmissions is optimal if or .
This means if one wishes to privately download more than the square-root of the
number of files in the database, then one must effectively download the full
database (minus the side information), irrespective of the amount of side
information one has available.Comment: 12 pages, submitted to the 56th Allerton conferenc
th power residue chains of global fields
In 1974, Vegh proved that if is a prime and a positive integer, there
is an term permutation chain of th power residue for infinitely many
primes [E.Vegh, th power residue chains, J.Number Theory, 9(1977), 179-181].
In fact, his proof showed that is an term permutation
chain of th power residue for infinitely many primes. In this paper, we
prove that for any "possible" term sequence , there are
infinitely many primes making it an term permutation chain of th
power residue modulo , where is an arbitrary positive integer [See
Theorem 1.2]. From our result, we see that Vegh's theorem holds for any
positive integer , not only for prime numbers. In fact, we prove our result
in more generality where the integer ring is replaced by any -integer
ring of global fields (i.e. algebraic number fields or algebraic function
fields over finite fields).Comment: 4 page
Incremental learning with respect to new incoming input attributes
Neural networks are generally exposed to a dynamic environment where the training patterns or the input attributes (features) will likely be introduced into the current domain incrementally. This paper considers the situation where a new set of input attributes must be considered and added into the existing neural network. The conventional method is to discard the existing network and redesign one from scratch. This approach wastes the old knowledge and the previous effort. In order to reduce computational time, improve generalization accuracy, and enhance intelligence of the learned models, we present ILIA algorithms (namely ILIA1, ILIA2, ILIA3, ILIA4 and ILIA5) capable of Incremental Learning in terms of Input Attributes. Using the ILIA algorithms, when new input attributes are introduced into the original problem, the existing neural network can be retained and a new sub-network is constructed and trained incrementally. The new sub-network and the old one are merged later to form a new network for the changed problem. In addition, ILIA algorithms have the ability to decide whether the new incoming input attributes are relevant to the output and consistent with the existing input attributes or not and suggest to accept or reject them. Experimental results show that the ILIA algorithms are efficient and effective both for the classification and regression problems
Tolerating Correlated Failures in Massively Parallel Stream Processing Engines
Fault-tolerance techniques for stream processing engines can be categorized
into passive and active approaches. A typical passive approach periodically
checkpoints a processing task's runtime states and can recover a failed task by
restoring its runtime state using its latest checkpoint. On the other hand, an
active approach usually employs backup nodes to run replicated tasks. Upon
failure, the active replica can take over the processing of the failed task
with minimal latency. However, both approaches have their own inadequacies in
Massively Parallel Stream Processing Engines (MPSPE). The passive approach
incurs a long recovery latency especially when a number of correlated nodes
fail simultaneously, while the active approach requires extra replication
resources. In this paper, we propose a new fault-tolerance framework, which is
Passive and Partially Active (PPA). In a PPA scheme, the passive approach is
applied to all tasks while only a selected set of tasks will be actively
replicated. The number of actively replicated tasks depends on the available
resources. If tasks without active replicas fail, tentative outputs will be
generated before the completion of the recovery process. We also propose
effective and efficient algorithms to optimize a partially active replication
plan to maximize the quality of tentative outputs. We implemented PPA on top of
Storm, an open-source MPSPE and conducted extensive experiments using both real
and synthetic datasets to verify the effectiveness of our approach
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