229,820 research outputs found
Model Order Reduction of Non-Linear Magnetostatic Problems Based on POD and DEI Methods
In the domain of numerical computation, Model Order Reduction approaches are more and more frequently applied in mechanics and have shown their efficiency in terms of reduction of computation time and memory storage requirements. One of these approaches, the Proper Orthogonal Decomposition (POD), can be very efficient in solving linear problems but encounters limitations in the non-linear case. In this paper, the Discret Empirical Interpolation Method coupled with the POD method is presented. This is an interesting alternative to reduce large-scale systems deriving from the discretization of non-linear magnetostatic problems coupled with an external electrical circuit
Efficient and long-lived quantum memory with cold atoms inside a ring cavity
Quantum memories are regarded as one of the fundamental building blocks of
linear-optical quantum computation and long-distance quantum communication. A
long standing goal to realize scalable quantum information processing is to
build a long-lived and efficient quantum memory. There have been significant
efforts distributed towards this goal. However, either efficient but
short-lived or long-lived but inefficient quantum memories have been
demonstrated so far. Here we report a high-performance quantum memory in which
long lifetime and high retrieval efficiency meet for the first time. By placing
a ring cavity around an atomic ensemble, employing a pair of clock states,
creating a long-wavelength spin wave, and arranging the setup in the
gravitational direction, we realize a quantum memory with an intrinsic spin
wave to photon conversion efficiency of 73(2)% together with a storage lifetime
of 3.2(1) ms. This realization provides an essential tool towards scalable
linear-optical quantum information processing.Comment: 6 pages, 4 figure
A Computationally Efficient Limited Memory CMA-ES for Large Scale Optimization
We propose a computationally efficient limited memory Covariance Matrix
Adaptation Evolution Strategy for large scale optimization, which we call the
LM-CMA-ES. The LM-CMA-ES is a stochastic, derivative-free algorithm for
numerical optimization of non-linear, non-convex optimization problems in
continuous domain. Inspired by the limited memory BFGS method of Liu and
Nocedal (1989), the LM-CMA-ES samples candidate solutions according to a
covariance matrix reproduced from direction vectors selected during the
optimization process. The decomposition of the covariance matrix into Cholesky
factors allows to reduce the time and memory complexity of the sampling to
, where is the number of decision variables. When is large
(e.g., > 1000), even relatively small values of (e.g., ) are
sufficient to efficiently solve fully non-separable problems and to reduce the
overall run-time.Comment: Genetic and Evolutionary Computation Conference (GECCO'2014) (2014
Cache-Oblivious Peeling of Random Hypergraphs
The computation of a peeling order in a randomly generated hypergraph is the
most time-consuming step in a number of constructions, such as perfect hashing
schemes, random -SAT solvers, error-correcting codes, and approximate set
encodings. While there exists a straightforward linear time algorithm, its poor
I/O performance makes it impractical for hypergraphs whose size exceeds the
available internal memory.
We show how to reduce the computation of a peeling order to a small number of
sequential scans and sorts, and analyze its I/O complexity in the
cache-oblivious model. The resulting algorithm requires
I/Os and time to peel a random hypergraph with edges.
We experimentally evaluate the performance of our implementation of this
algorithm in a real-world scenario by using the construction of minimal perfect
hash functions (MPHF) as our test case: our algorithm builds a MPHF of
billion keys in less than hours on a single machine. The resulting data
structure is both more space-efficient and faster than that obtained with the
current state-of-the-art MPHF construction for large-scale key sets
Spatial mode storage in a gradient echo memory
Three-level atomic gradient echo memory (lambda-GEM) is a proposed candidate
for efficient quantum storage and for linear optical quantum computation with
time-bin multiplexing. In this paper we investigate the spatial multimode
properties of a lambda-GEM system. Using a high-speed triggered CCD, we
demonstrate the storage of complex spatial modes and images. We also present an
in-principle demonstration of spatial multiplexing by showing selective recall
of spatial elements of a stored spin wave. Using our measurements, we consider
the effect of diffusion within the atomic vapour and investigate its role in
spatial decoherence. Our measurements allow us to quantify the spatial
distortion due to both diffusion and inhomogeneous control field scattering and
compare these to theoretical models.Comment: 11 pages, 9 figure
Improved Deterministic Connectivity in Massively Parallel Computation
A long line of research about connectivity in the Massively Parallel Computation model has culminated in the seminal works of Andoni et al. [FOCS\u2718] and Behnezhad et al. [FOCS\u2719]. They provide a randomized algorithm for low-space MPC with conjectured to be optimal round complexity O(log D + log log_{m/n} n) and O(m) space, for graphs on n vertices with m edges and diameter D. Surprisingly, a recent result of Coy and Czumaj [STOC\u2722] shows how to achieve the same deterministically. Unfortunately, however, their algorithm suffers from large local computation time.
We present a deterministic connectivity algorithm that matches all the parameters of the randomized algorithm and, in addition, significantly reduces the local computation time to nearly linear.
Our derandomization method is based on reducing the amount of randomness needed to allow for a simpler efficient search. While similar randomness reduction approaches have been used before, our result is not only strikingly simpler, but it is the first to have efficient local computation. This is why we believe it to serve as a starting point for the systematic development of computation-efficient derandomization approaches in low-memory MPC
Arya: Nearly linear-time zero-knowledge proofs for correct program execution
There have been tremendous advances in reducing interaction, communication and verification time in zero-knowledge proofs but it remains an important challenge to make the prover efficient. We construct the first zero-knowledge proof of knowledge for the correct execution of a program on public and private inputs where the prover computation is nearly linear time. This saves a polylogarithmic factor in asymptotic performance compared to current state of the art proof systems.
We use the TinyRAM model to capture general purpose processor computation. An instance consists of a TinyRAM program and public inputs. The witness consists of additional private inputs to the program. The prover can use our proof system to convince the verifier that the program terminates with the intended answer within given time and memory bounds. Our proof system has perfect completeness, statistical special honest verifier zero-knowledge, and computational knowledge soundness assuming linear-time computable collision-resistant hash functions exist. The main advantage of our new proof system is asymptotically efficient prover computation. The prover’s running time is only a superconstant factor larger than the program’s running time in an apples-to-apples comparison where the prover uses the same TinyRAM model. Our proof system is also efficient on the other performance parameters; the verifier’s running time and the communication are sublinear in the execution time of the program and we only use a log-logarithmic number of rounds
Incremental Control Synthesis in Probabilistic Environments with Temporal Logic Constraints
In this paper, we present a method for optimal control synthesis of a plant
that interacts with a set of agents in a graph-like environment. The control
specification is given as a temporal logic statement about some properties that
hold at the vertices of the environment. The plant is assumed to be
deterministic, while the agents are probabilistic Markov models. The goal is to
control the plant such that the probability of satisfying a syntactically
co-safe Linear Temporal Logic formula is maximized. We propose a
computationally efficient incremental approach based on the fact that temporal
logic verification is computationally cheaper than synthesis. We present a
case-study where we compare our approach to the classical non-incremental
approach in terms of computation time and memory usage.Comment: Extended version of the CDC 2012 pape
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