43665408
Resolution of Hartmanis' Conjecture for NL-Hard Sparse Sets
We resolve a conjecture of Hartmanis from 1978 about sparse hard sets for nondeterministic logspace (NL). We show that there exists a sparse hard set S for NL under logspace many-one reductions if and only if NL = L (deterministic logspace).
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.
6323016
Valiant's Holant Theorem and matchgate tensors
We propose matchgate tensors as a natural and proper language to develop Valiant’s new theory of Holographic Algorithms. We give a treatment of the central theorem in this theory— the Holant Theorem—in terms of matchgate tensors. Some generalizations are presented.
474133
On Block-Wise Symmetric Signatures for Matchgates
In a tank having an internal float there is a standpipe coupled through the tank. The standpipe conducts liquid into the tank. Equipment for controlling the level of liquid in the tank includes a valve. This valve is operated by the float. A conduit depends from the valve. This conduit is longer than the valve and conducts liquid thereto. Also included is a pliable seal which mounted on the conduit at an end opposite the valve. This seal engages an interior surface of the conduit. The seal also has a bore sized to encircle and seal the standpipe. Thus, the standpipe may telescope into the conduit.
28522023
Essentially Every Unimodular Matrix Defines an Expander 


AbstractAbstract. We generalize the construction of Gabber and Galil to essentially every unimodular matrix in SL2 (Z). It is shown that every parabolic or hyperbolic fractional linear transformation explicitly defines an expander of bounded degree and constant expansion. Thus all but a vanishingly small fraction of unimodular matrices define expanders.

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].)
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.
38252080
A New Transference Theorem in the Geometry of Numbers
We prove a new transference theorem in the geometry of numbers, giving optimal bounds relating the successive minima of a lattice with the minimal length of generating vectors of its dual. It generalizes the transference theorem due to Banaszczyk. The theorem is motivated by our efforts to improve Ajtai's connection factors in the connection of average-case to worst-case complexity of the shortest lattice vector problem. Our proofs are non-constructive, based on methods from harmonic analysis.
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.
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.