4,838 research outputs found
An constructive proof for the Umemura polynomials for the third Painlev\'e equation
We are concerned with the Umemura polynomials associated with the third
Painlev\'e equation. We extend Taneda's method, which was developed for the
Yablonskii--Vorob'ev polynomials associated with the second Painlev\'e
equation, to give an algebraic proof that the rational functions generated by
the nonlinear recurrence relation satisfied by Umemura polynomials are indeed
polynomials. Our proof is constructive and gives information about the roots of
the Umemura polynomials.Comment: 20 pages, 3 figure
2D Qubit Placement of Quantum Circuits using LONGPATH
In order to achieve speedup over conventional classical computing for finding
solution of computationally hard problems, quantum computing was introduced.
Quantum algorithms can be simulated in a pseudo quantum environment, but
implementation involves realization of quantum circuits through physical
synthesis of quantum gates. This requires decomposition of complex quantum
gates into a cascade of simple one qubit and two qubit gates. The
methodological framework for physical synthesis imposes a constraint regarding
placement of operands (qubits) and operators. If physical qubits can be placed
on a grid, where each node of the grid represents a qubit then quantum gates
can only be operated on adjacent qubits, otherwise SWAP gates must be inserted
to convert non-Linear Nearest Neighbor architecture to Linear Nearest Neighbor
architecture. Insertion of SWAP gates should be made optimal to reduce
cumulative cost of physical implementation. A schedule layout generation is
required for placement and routing apriori to actual implementation. In this
paper, two algorithms are proposed to optimize the number of SWAP gates in any
arbitrary quantum circuit. The first algorithm is intended to start with
generation of an interaction graph followed by finding the longest path
starting from the node with maximum degree. The second algorithm optimizes the
number of SWAP gates between any pair of non-neighbouring qubits. Our proposed
approach has a significant reduction in number of SWAP gates in 1D and 2D NTC
architecture.Comment: Advanced Computing and Systems for Security, SpringerLink, Volume 1
An algebraic proof for the Umemura polynomials for the third Painlevé equation
We are concerned with the Umemura polynomials associated with the third Painlev\'e equation. We extend Taneda's method, which was developed for the Yablonskii-Vorob'ev polynomials associated with the second Painlev\'e equation, to give an algebraic proof that the rational functions generated by the nonlinear recurrence relation satisfied by Umemura polynomials are indeed polynomials
Poly[(μ6-benzene-1,3,5-tricarboxylato-κ6 O 1:O 1′:O 3:O 3′:O 5:O 5′)tris(N,N-dimethylformamide-κO)tris(μ3-formato-κ2 O:O′)trimagnesium(II)]
The title complex, [Mg3(CHO2)3(C9H3O6)(C3H7NO)3]n, exhibits a two-dimensional structure parallel to (001), which is built up from the MgII atoms and bridging carboxylate ligands (3 symmetry). The MgII atom is six-coordinated by one O atom from a dimethylformamide molecule, two O atoms from two μ6-benzene-1,3,5-tricarboxylate ligands and three O atoms from three μ3-formate ligands in a distorted octahedral geometry
Distributed Training Large-Scale Deep Architectures
Scale of data and scale of computation infrastructures together enable the
current deep learning renaissance. However, training large-scale deep
architectures demands both algorithmic improvement and careful system
configuration. In this paper, we focus on employing the system approach to
speed up large-scale training. Via lessons learned from our routine
benchmarking effort, we first identify bottlenecks and overheads that hinter
data parallelism. We then devise guidelines that help practitioners to
configure an effective system and fine-tune parameters to achieve desired
speedup. Specifically, we develop a procedure for setting minibatch size and
choosing computation algorithms. We also derive lemmas for determining the
quantity of key components such as the number of GPUs and parameter servers.
Experiments and examples show that these guidelines help effectively speed up
large-scale deep learning training
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