41950213
Holographic algorithms: From art to science
We develop the theory of holographic algorithms initiated by Leslie Valiant. First we define a basis manifold. Then we characterize algebraic varieties of realizable symmetric generators and recognizers on the basis manifold, and give a polynomial time decision algorithm for the simultaneous realizability problem. These results enable one to decide whether suitable signatures for a holographic algorithm are realizable, and if so, to find a suitable linear basis to realize these signatures by an efficient algorithm. Using the general machinery we are able to give unexpected holographic algorithms for some counting problems, modulo certain Mersenne type integers. These counting problems are #P-complete without the moduli. Going beyond symmetric signatures, we define d-admissibility and d-realizability for general signatures, and give a characterization of 2-admissibility and some general constructions of admissible and realizable families.
11584914
A Relation of Primal-Dual Lattices and the Complexity of Shortest Lattice Vector Problem
We give a simplified proof of a theorem of Lagarias, Lenstra and Schnorr [17] that the problem of approximating the length of the shortest lattice vector within a factor of Cn, for an appropriate constant C, cannot be NP-hard, unless NP = coNP. We also prove that the problem of finding a n14-unique shortest lattice vector is not NP-hard under polynomial time many-one reductions, unless the polynomial time hierarchy collapses. © 1998—Elsevier Science B.V. All rights reserved
11342779
On Proving Circuit Lower Bounds against the Polynomial-Time Hierarchy: Positive and Negative Results
We consider the problem of proving circuit lower bounds against the polynomial-time hierarchy. We give both positive and negative results. For the positive side, for any fixed integer k > 0, we give an explicit Σ2p language, acceptable by a Σ2p-machine with running time O(nk2+k), that requires circuit size > nk. For the negative side, we propose a new stringent notion of relativization, and prove under this stringent relativization that every language in the polynomial-time hierarchy has polynomial circuit size. (For technical details, see also [CW03].)
7471594
The resolution of a Hartmanis conjecture
Building on the recent breakthrough by M. Ogihara (1995), we resolve a conjecture made by J. Hartmanis (1978) regarding the (non) existence of sparse sets complete for P under logspace many-one reductions. We show that if there exists a sparse hard set for P under logspace many-one reductions, then P=LOGSPACE. We further prove that if P has a sparse hard set under many-one reductions computable in NC/sup 1/, then P collapses to NC/sup 1/.
15088558
Some Results on Matchgates and Holographic Algorithms
We establish a 1-1 correspondence between Valiant's character theory of matchgate/matchcircuit [14] and his signature theory of planar-matchgate/matchgrid [16], thus unifying the two theories in expressibility. In [3], we had established a complete characterization of general matchgates, in terms of a set of useful Grassmann-Plucker identities. With this correspondence, we give a corresponding set of identities which completely characterizes planar-matchgates and their signatures. Applying this characterization we prove some negative results for holographic algorithms. On the positive side, we also give a polynomial time algorithm for a simultaneous node-edge deletion problem, using holographic algorithms. Finally we give characterizations of symmetric signatures realizable in the Hadamard basis.
27123977
Classifying G-protein coupled receptors with bagging classification tree
G-protein coupled receptors (GPCRs) play a key role in different biological processes, such as regulation of growth, death and metabolism of cells. They are major therapeutic targets of numerous prescribed drugs. However, the ligand specificity of many receptors is unknown and there is little structural information available. Bioinformatics may offer one approach to bridge the gap between sequence data and functional knowledge of a receptor. In this paper, we use a bagging classification tree algorithm to predict the type of the receptor based on its amino acid composition. The prediction is performed for GPCR at the sub-family and sub-sub-family level. In a cross-validation test, we achieved an overall predictive accuracy of 91.1% for GPCR sub-family classification, and 82.4% for sub-sub-family classification. These results demonstrate the applicability of this relative simple method and its potential for improving prediction accuracy.
12735579
The enumeration of rooted nonseparable nearly cubic maps
Abstract This paper provides the functional equations satisfied by the generating functions for enumerating rooted nonseparable near-cubic planar maps with the size and the valency of root-vertex and/or root-face of the maps as parameters. Moreover, explicit expressions of these functions are also derived. Two of them are summation-free.
44495329
Enumeration on Nonseparable Planar Maps
Abstract This paper provides some functional equations satisfied by the generating functions for nonseparable rooted planar maps with the valency of root-vertex, the number of edges and the valency of root-faces of the maps as three parameters. But the solutions of these equations can only be obtained indirectly by considering some relations between nonseparable and general rooted planar maps. One of them is an answer to the open problem 6.1 in Liu (1983, Comb. Optim. CORR83-26, University of Waterloo).
5733190
Automating the drug scheduling of cancer chemotherapy via evolutionary computation
This paper presents the optimal control of drug scheduling in cancer chemotherapy using a distributed evolutionary computing software. Unlike conventional methods that often require gradient information or hybridization of different approaches in drug scheduling, the proposed evolutionary optimization methodology is simple and capable of automatically finding the near-optimal solutions for complex cancer chemotherapy problems. It is shown that different number of variable pairs in evolutionary representation for drug scheduling can be easily implemented via the software, since the computational workload is shared and distributed among multiple computers over the Internet. Simulation results show that the proposed evolutionary approach produces excellent control of drug scheduling in cancer chemotherapy, which are competitive or equivalent to the best solutions published in literature.