1,569 research outputs found
On Backtracking in Real-time Heuristic Search
Real-time heuristic search algorithms are suitable for situated agents that
need to make their decisions in constant time. Since the original work by Korf
nearly two decades ago, numerous extensions have been suggested. One of the
most intriguing extensions is the idea of backtracking wherein the agent
decides to return to a previously visited state as opposed to moving forward
greedily. This idea has been empirically shown to have a significant impact on
various performance measures. The studies have been carried out in particular
empirical testbeds with specific real-time search algorithms that use
backtracking. Consequently, the extent to which the trends observed are
characteristic of backtracking in general is unclear. In this paper, we present
the first entirely theoretical study of backtracking in real-time heuristic
search. In particular, we present upper bounds on the solution cost exponential
and linear in a parameter regulating the amount of backtracking. The results
hold for a wide class of real-time heuristic search algorithms that includes
many existing algorithms as a small subclass
Factorisation of Macdonald polynomials
We discuss the problem of factorisation of the symmetric Macdonald
polynomials and present the obtained results for the cases of 2 and 3
variables.Comment: 13 pages, LaTex, no figure
Eigenproblem for Jacobi matrices: hypergeometric series solution
We study the perturbative power-series expansions of the eigenvalues and
eigenvectors of a general tridiagonal (Jacobi) matrix of dimension d.
The(small) expansion parameters are being the entries of the two diagonals of
length d-1 sandwiching the principal diagonal, which gives the unperturbed
spectrum.
The solution is found explicitly in terms of multivariable (Horn-type)
hypergeometric series of 3d-5 variables in the generic case, or 2d-3 variables
for the eigenvalue growing from a corner matrix element. To derive the result,
we first rewrite the spectral problem for a Jacobi matrix as an equivalent
system of cubic equations, which are then resolved by the application of the
multivariable Lagrange inversion formula. The corresponding Jacobi determinant
is calculated explicitly. Explicit formulae are also found for any monomial
composed of eigenvector's components.Comment: Latex, 20 pages; v2: corrected typos, added section with example
Perturbation of spectra and spectral subspaces
We consider the problem of variation of spectral subspaces for linear
self-adjoint operators under off-diagonal perturbations. We prove a number of
new optimal results on the shift of the spectrum and obtain (sharp) estimates
on the norm of the difference of two spectral projections
On a Subspace Perturbation Problem
We discuss the problem of perturbation of spectral subspaces for linear
self-adjoint operators on a separable Hilbert space. Let and be bounded
self-adjoint operators. Assume that the spectrum of consists of two
disjoint parts and such that . We show that the norm of the difference of the spectral projections
\EE_A(\sigma) and \EE_{A+V}\big (\{\lambda | \dist(\lambda, \sigma)
for and is less then one whenever either (i)
or (ii) and certain assumptions on the
mutual disposition of the sets and are satisfied
Q-operator and factorised separation chain for Jack polynomials
Applying Baxter's method of the Q-operator to the set of Sekiguchi's
commuting partial differential operators we show that Jack polynomials
P(x_1,...,x_n) are eigenfunctions of a one-parameter family of integral
operators Q_z. The operators Q_z are expressed in terms of the
Dirichlet-Liouville n-dimensional beta integral. From a composition of n
operators Q_{z_k} we construct an integral operator S_n factorising Jack
polynomials into products of hypergeometric polynomials of one variable. The
operator S_n admits a factorisation described in terms of restricted Jack
polynomials P(x_1,...,x_k,1,...,1). Using the operator Q_z for z=0 we give a
simple derivation of a previously known integral representation for Jack
polynomials.Comment: 26 page
Heterogeneous biomedical database integration using a hybrid strategy: a p53 cancer research database.
Complex problems in life science research give rise to multidisciplinary collaboration, and hence, to the need for heterogeneous database integration. The tumor suppressor p53 is mutated in close to 50% of human cancers, and a small drug-like molecule with the ability to restore native function to cancerous p53 mutants is a long-held medical goal of cancer treatment. The Cancer Research DataBase (CRDB) was designed in support of a project to find such small molecules. As a cancer informatics project, the CRDB involved small molecule data, computational docking results, functional assays, and protein structure data. As an example of the hybrid strategy for data integration, it combined the mediation and data warehousing approaches. This paper uses the CRDB to illustrate the hybrid strategy as a viable approach to heterogeneous data integration in biomedicine, and provides a design method for those considering similar systems. More efficient data sharing implies increased productivity, and, hopefully, improved chances of success in cancer research. (Code and database schemas are freely downloadable, http://www.igb.uci.edu/research/research.html.)
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