915 research outputs found
Two-stage stochastic minimum s − t cut problems: Formulations, complexity and decomposition algorithms
We introduce the two‐stage stochastic minimum s − t cut problem. Based on a classical linear 0‐1 programming model for the deterministic minimum s − t cut problem, we provide a mathematical programming formulation for the proposed stochastic extension. We show that its constraint matrix loses the total unimodularity property, however, preserves it if the considered graph is a tree. This fact turns out to be not surprising as we prove that the considered problem is NP-hard in general, but admits a linear time solution algorithm when the graph is a tree. We exploit the special structure of the problem and propose a tailored Benders decomposition algorithm. We evaluate the computational efficiency of this algorithm by solving the Benders dual subproblems as max-flow problems. For many tested instances, we outperform a standard Benders decomposition by two orders of magnitude with the Benders decomposition exploiting the max-flow structure of the subproblems
An integrated fuzzy-stochastic model for revenue management: The hospitality industry case
Revenue management aims at improving the performance of an organization by selling the right product/service to the right customer at the right time. This task is very dependent on uncontrollable external factors. In the hospitality industry, rooms of the hotel represent perishable assets and fixed capacities at the same time. Therefore, in the case of a stochastic process for customers calling in reservations prior to a particular booking date, a common problem for hotels is to devise a policy for maximizing the total expected profit conditional on the set of bookings. We propose a fuzzy model for the hotel revenue management under an uncertain and vague environment. Fuzziness of objective and constraint functions have been incorporated into a stochastic booking model considering multiple-day stays to show the effect of uncertainty on the optimal demand. By changing the relaxation parameters of the objective function, we have found a set of optimal solutions with, in most of the cases, a value of the objective function equal to the optimal solution of the stochastic model, providing several alternative optimal room allocations
Frequency dependent specific heat of viscous silica
We apply the Mori-Zwanzig projection operator formalism to obtain an
expression for the frequency dependent specific heat c(z) of a liquid. By using
an exact transformation formula due to Lebowitz et al., we derive a relation
between c(z) and K(t), the autocorrelation function of temperature fluctuations
in the microcanonical ensemble. This connection thus allows to determine c(z)
from computer simulations in equilibrium, i.e. without an external
perturbation. By considering the generalization of K(t) to finite wave-vectors,
we derive an expression to determine the thermal conductivity \lambda from such
simulations. We present the results of extensive computer simulations in which
we use the derived relations to determine c(z) over eight decades in frequency,
as well as \lambda. The system investigated is a simple but realistic model for
amorphous silica. We find that at high frequencies the real part of c(z) has
the value of an ideal gas. c'(\omega) increases quickly at those frequencies
which correspond to the vibrational excitations of the system. At low
temperatures c'(\omega) shows a second step. The frequency at which this step
is observed is comparable to the one at which the \alpha-relaxation peak is
observed in the intermediate scattering function. Also the temperature
dependence of the location of this second step is the same as the one of the
peak, thus showing that these quantities are intimately connected to
each other. From c'(\omega) we estimate the temperature dependence of the
vibrational and configurational part of the specific heat. We find that the
static value of c(z) as well as \lambda are in good agreement with experimental
data.Comment: 27 pages of Latex, 8 figure
On the Power of Robust Solutions in Two-Stage Stochastic and Adaptive Optimization Problems
We consider a two-stage mixed integer stochastic optimization problem and show that a static robust solution is a good approximation to the fully adaptable two-stage solution for the stochastic problem under fairly general assumptions on the uncertainty set and the probability distribution. In particular, we show that if the right-hand side of the constraints is uncertain and belongs to a symmetric uncertainty set (such as hypercube, ellipsoid or norm ball) and the probability measure is also symmetric, then the cost of the optimal fixed solution to the corresponding robust problem is at most twice the optimal expected cost of the two-stage stochastic problem. Furthermore, we show that the bound is tight for symmetric uncertainty sets and can be arbitrarily large if the uncertainty set is not symmetric. We refer to the ratio of the optimal cost of the robust problem and the optimal cost of the two-stage stochastic problem as the stochasticity gap. We also extend the bound on the stochasticity gap for another class of uncertainty sets referred to as positive.
If both the objective coefficients and right-hand side are uncertain, we show that the stochasticity gap can be arbitrarily large even if the uncertainty set and the probability measure are both symmetric. However, we prove that the adaptability gap (ratio of optimal cost of the robust problem and the optimal cost of a two-stage fully adaptable problem) is at most four even if both the objective coefficients and the right-hand side of the constraints are uncertain and belong to a symmetric uncertainty set. The bound holds for the class of positive uncertainty sets as well. Moreover, if the uncertainty set is a hypercube (special case of a symmetric set), the adaptability gap is one under an even more general model of uncertainty where the constraint coefficients are also uncertain.National Science Foundation (U.S.) (NSF Grant DMI-0556106)National Science Foundation (U.S.) (NSF Grant EFRI-0735905
Universal conductance fluctuations in three dimensional metallic single crystals of Si
In this paper we report the measurement of conductance fluctuations in single
crystals of Si made metallic by heavy doping (n \approx 2-2.5n_c, n_c being
critical composition at Metal-Insulator transition). Since all dimensions (L)
of the samples are much larger than the electron phase coherent length L_\phi
(L/L_\phi \sim 10^3), our system is truly three dimensional. Temperature and
magnetic field dependence of noise strongly indicate the universal conductance
fluctuations (UCF) as predominant source of the observed magnitude of noise.
Conductance fluctuations within a single phase coherent region of L_\phi^3 was
found to be saturated at \approx (e^2/h)^2. An accurate
knowledge of the level of disorder, enables us to calculate the change in
conductance \delta G_1 due to movement of a single scatterer as \delta G_1 \sim
e^2/h, which is \sim 2 orders of magnitude higher than its theoretically
expected value in 3D systems.Comment: Text revised version. 4 eps figs unchange
Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks
This paper considers the nonparametric maximum likelihood estimator (MLE) for
the joint distribution function of an interval censored survival time and a
continuous mark variable. We provide a new explicit formula for the MLE in this
problem. We use this formula and the mark specific cumulative hazard function
of Huang and Louis (1998) to obtain the almost sure limit of the MLE. This
result leads to necessary and sufficient conditions for consistency of the MLE
which imply that the MLE is inconsistent in general. We show that the
inconsistency can be repaired by discretizing the marks. Our theoretical
results are supported by simulations.Comment: 27 pages, 4 figure
Shifting a Quantum Wire through a Disordered Crystal: Observation of Conductance Fluctuations in Real Space
A quantum wire is spatially displaced by suitable electric fields with
respect to the scatterers inside a semiconductor crystal. As a function of the
wire position, the low-temperature resistance shows reproducible fluctuations.
Their characteristic temperature scale is a few hundred millikelvin, indicating
a phase-coherent effect. Each fluctuation corresponds to a single scatterer
entering or leaving the wire. This way, scattering centers can be counted one
by one.Comment: 4 pages, 3 figure
Spin-boson models for quantum decoherence of electronic excitations of biomolecules and quantum dots in a solvent
We give a theoretical treatment of the interaction of electronic excitations
(excitons) in biomolecules and quantum dots with the surrounding polar solvent.
Significant quantum decoherence occurs due to the interaction of the electric
dipole moment of the solute with the fluctuating electric dipole moments of the
individual molecules in the solvent. We introduce spin boson models which could
be used to describe the effects of decoherence on the quantum dynamics of
biomolecules which undergo light-induced conformational change and on
biomolecules or quantum dots which are coupled by Forster resonant energy
transfer.Comment: More extended version, to appear in Journal of Physics: Condensed
Matter. 13 pages, 3 figure
Excited states of linear polyenes
We present density matrix renormalisation group calculations of the Pariser-
Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation.
We calculate the vertical and relaxed transition energies, and relaxed
geometries for various excitations on long chains. The triplet (3Bu+) and even-
parity singlet (2Ag+) states have a 2-soliton and 4-soliton form, respectively,
both with large relaxation energies. The dipole-allowed (1Bu-) state forms an
exciton-polaron and has a very small relaxation energy. The relaxed energy of
the 2Ag+ state lies below that of the 1Bu- state. We observe an attraction
between the soliton-antisoliton pairs in the 2Ag+ state. The calculated
excitation energies agree well with the observed values for polyene oligomers;
the agreement with polyacetylene thin films is less good, and we comment on the
possible sources of the discrepencies. The photoinduced absorption is
interpreted. The spin-spin correlation function shows that the unpaired spins
coincide with the geometrical soliton positions. We study the roles of
electron-electron interactions and electron-lattice coupling in determining the
excitation energies and soliton structures. The electronic interactions play
the key role in determining the ground state dimerisation and the excited state
transition energies.Comment: LaTeX, 15 pages, 9 figure
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