392 research outputs found
Database Analysis to Support Nutrient Criteria Development (Phase II)
The intent of this publication of the Arkansas Water Resources Center is to provide a location whereby a final report on water research to a funding agency can be archived. The Texas Commission on Environmental Quality (TCEQ) contracted with University of Arkansas researchers for a multiple year project titled “Database Analysis to Support Nutrient Criteria Development”. This publication covers the second of three phases of that project and has maintained the original format of the report as submitted to TCEQ. This report can be cited either as an AWRC publication (see below) or directly as the final report to TCEQ
Approximating the Termination Value of One-Counter MDPs and Stochastic Games
One-counter MDPs (OC-MDPs) and one-counter simple stochastic games (OC-SSGs)
are 1-player, and 2-player turn-based zero-sum, stochastic games played on the
transition graph of classic one-counter automata (equivalently, pushdown
automata with a 1-letter stack alphabet). A key objective for the analysis and
verification of these games is the termination objective, where the players aim
to maximize (minimize, respectively) the probability of hitting counter value
0, starting at a given control state and given counter value. Recently, we
studied qualitative decision problems ("is the optimal termination value = 1?")
for OC-MDPs (and OC-SSGs) and showed them to be decidable in P-time (in NP and
coNP, respectively). However, quantitative decision and approximation problems
("is the optimal termination value ? p", or "approximate the termination value
within epsilon") are far more challenging. This is so in part because optimal
strategies may not exist, and because even when they do exist they can have a
highly non-trivial structure. It thus remained open even whether any of these
quantitative termination problems are computable. In this paper we show that
all quantitative approximation problems for the termination value for OC-MDPs
and OC-SSGs are computable. Specifically, given a OC-SSG, and given epsilon >
0, we can compute a value v that approximates the value of the OC-SSG
termination game within additive error epsilon, and furthermore we can compute
epsilon-optimal strategies for both players in the game. A key ingredient in
our proofs is a subtle martingale, derived from solving certain LPs that we can
associate with a maximizing OC-MDP. An application of Azuma's inequality on
these martingales yields a computable bound for the "wealth" at which a "rich
person's strategy" becomes epsilon-optimal for OC-MDPs.Comment: 35 pages, 1 figure, full version of a paper presented at ICALP 2011,
invited for submission to Information and Computatio
Phase separation and stripe formation in the 2D t-J model: a comparison of numerical results
We make a critical analysis of numerical results for and against phase
separation and stripe formation in the t-J model. We argue that the frustrated
phase separation mechanism for stripe formation requires phase separation at
too high a doping for it to be consistent with existing numerical studies of
the t-J model. We compare variational energies for various methods, and
conclude that the most accurate calculations for large systems appear to be
from the density matrix renormalization group. These calculations imply that
the ground state of the doped t-J model is striped, not phase separated.Comment: This version includes a revised, more careful comparison of numerical
results between DMRG and Green's function Monte Carlo. In particular, for the
original posted version we were accidentally sent obsolete data by Hellberg
and Manousakis; their new results, which are what were used in their Physical
Review Letter, are more accurate because a better trial wavefunction was use
Phase Separation Based on U(1) Slave-boson Functional Integral Approach to the t-J Model
We investigate the phase diagram of phase separation for the hole-doped two
dimensional system of antiferromagnetically correlated electrons based on the
U(1) slave-boson functional integral approach to the t-J model. We show that
the phase separation occurs for all values of J/t, that is, whether or with J, the Heisenberg coupling constant and t, the hopping
strength. This is consistent with other numerical studies of hole-doped two
dimensional antiferromagnets. The phase separation in the physically
interesting J region, is examined by introducing
hole-hole (holon-holon) repulsive interaction. We find from this study that
with high repulsive interaction between holes the phase separation boundary
tends to remain robust in this low region, while in the high J region, J/t
> 0.4, the phase separation boundary tends to disappear.Comment: 4 pages, 2 figures, submitted to Phys. Rev.
The breakdown of the Nagaoka phase in the 2D t-J model
In the limit of weak exchange, J, at low hole concentration, the ground state
of the 2D t-J model is believed to be ferromagnetic. We study the leading
instability of this Nagaoka state, which emerges with increasing J. Both exact
diagonalization of small clusters, and a semiclassical analytical calculation
of larger systems show that above a certain critical value of the exchange,
Nagaoka's state is unstable to phase separation. In a finite-size system a
bubble of antiferromagnetic Mott insulator appears in the ground state above
this threshold. The size of this bubble depends on the hole concentration and
scales as a power of the system size, N
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