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