12,646 research outputs found
An Efficient Local Search for Partial Latin Square Extension Problem
A partial Latin square (PLS) is a partial assignment of n symbols to an nxn
grid such that, in each row and in each column, each symbol appears at most
once. The partial Latin square extension problem is an NP-hard problem that
asks for a largest extension of a given PLS. In this paper we propose an
efficient local search for this problem. We focus on the local search such that
the neighborhood is defined by (p,q)-swap, i.e., removing exactly p symbols and
then assigning symbols to at most q empty cells. For p in {1,2,3}, our
neighborhood search algorithm finds an improved solution or concludes that no
such solution exists in O(n^{p+1}) time. We also propose a novel swap
operation, Trellis-swap, which is a generalization of (1,q)-swap and
(2,q)-swap. Our Trellis-neighborhood search algorithm takes O(n^{3.5}) time to
do the same thing. Using these neighborhood search algorithms, we design a
prototype iterated local search algorithm and show its effectiveness in
comparison with state-of-the-art optimization solvers such as IBM ILOG CPLEX
and LocalSolver.Comment: 17 pages, 2 figure
Neural Connectivity with Hidden Gaussian Graphical State-Model
The noninvasive procedures for neural connectivity are under questioning.
Theoretical models sustain that the electromagnetic field registered at
external sensors is elicited by currents at neural space. Nevertheless, what we
observe at the sensor space is a superposition of projected fields, from the
whole gray-matter. This is the reason for a major pitfall of noninvasive
Electrophysiology methods: distorted reconstruction of neural activity and its
connectivity or leakage. It has been proven that current methods produce
incorrect connectomes. Somewhat related to the incorrect connectivity
modelling, they disregard either Systems Theory and Bayesian Information
Theory. We introduce a new formalism that attains for it, Hidden Gaussian
Graphical State-Model (HIGGS). A neural Gaussian Graphical Model (GGM) hidden
by the observation equation of Magneto-encephalographic (MEEG) signals. HIGGS
is equivalent to a frequency domain Linear State Space Model (LSSM) but with
sparse connectivity prior. The mathematical contribution here is the theory for
high-dimensional and frequency-domain HIGGS solvers. We demonstrate that HIGGS
can attenuate the leakage effect in the most critical case: the distortion EEG
signal due to head volume conduction heterogeneities. Its application in EEG is
illustrated with retrieved connectivity patterns from human Steady State Visual
Evoked Potentials (SSVEP). We provide for the first time confirmatory evidence
for noninvasive procedures of neural connectivity: concurrent EEG and
Electrocorticography (ECoG) recordings on monkey. Open source packages are
freely available online, to reproduce the results presented in this paper and
to analyze external MEEG databases
- …