7,469 research outputs found
Inverse Optimization: Closed-form Solutions, Geometry and Goodness of fit
In classical inverse linear optimization, one assumes a given solution is a
candidate to be optimal. Real data is imperfect and noisy, so there is no
guarantee this assumption is satisfied. Inspired by regression, this paper
presents a unified framework for cost function estimation in linear
optimization comprising a general inverse optimization model and a
corresponding goodness-of-fit metric. Although our inverse optimization model
is nonconvex, we derive a closed-form solution and present the geometric
intuition. Our goodness-of-fit metric, , the coefficient of
complementarity, has similar properties to from regression and is
quasiconvex in the input data, leading to an intuitive geometric
interpretation. While is computable in polynomial-time, we derive a
lower bound that possesses the same properties, is tight for several important
model variations, and is even easier to compute. We demonstrate the application
of our framework for model estimation and evaluation in production planning and
cancer therapy
Spectroscopic Constants and Vibrational Frequencies for l-C3H+ and Isotopologues from Highly-Accurate Quartic Force Fields: The Detection of l-C3H+ in the Horsehead Nebula PDR Questioned
Very recently, molecular rotational transitions observed in the
photon-dominated region of the Horsehead nebula have been attributed to l-C3H+.
In an effort to corroborate this finding, we employed state-of-the art and
proven high-accuracy quantum chemical techniques to compute spectroscopic
constants for this cation and its isotopologues. Even though the B rotational
constant from the fit of the observed spectrum and our computations agree to
within 20 MHz, a typical level of accuracy, the D rotational constant differs
by more than 40%, while the H rotational constant differs by three orders of
magnitude. With the likely errors in the rotational transition energies
resulting from this difference in D on the order of 1 MHz for the lowest
observed transition (J = 4 <- 3) and growing as J increases, the assignment of
the observed rotational lines from the Horsehead nebula to l-C3H+ is
questionable
The Possible Interstellar Anion CH2CN-: Spectroscopic Constants, Vibrational Frequencies, and Other Considerations
It is hypothesized that the A ^1B_1 <- X ^1A' excitation into the
dipole-bound state of the cyanomethyl anion (CH2CN-) is proposed as the carrier
for one diffuse interstellar band. However, this particular molecular system
has not been detected in the interstellar medium even though the related
cyanomethyl radical and the isoelectronic ketenimine molecule have been found.
In this study we are employing the use of proven quartic force fields and
second-order vibrational perturbation theory to compute accurate spectroscopic
constants and fundamental vibrational frequencies for ^1A' CH2CN- in order to
assist in laboratory studies and astronomical observations
The Failure of Correlation to Describe Out-of-Plane Carbon=Carbon Bending
Carbon-carbon multiply bonded systems are improperly described with standard correlation methods and basis sets. For computations of vibrational modes, the out-of- plane bends can be reported as imaginary at worst or simply too low at best. Utilizing the simplest of aromatic structures (cyclopropenylidene) and various levels of theory, this work diagnoses this known behavior for the first time. A combined 1-particle and n-particle basis set effect conspire to produce these non-physical results. When moving from sp2 to sp3 hybridization in the carbon atoms, the larger number of basis functions overcorrects the energy. This is exacerbated by correlation methods. These allow for occupation of the and orbitals in the expanded wave function that combine with the hydrogen s orbitals. As a result, the improperly described space can be further and non-physically stabilized by post-Hartree-Fock correlation. This represents a fundamental problem with at least Hartree-Fock based methods of all flavors in describing carbon. Beyond being a flaw in quantum chemical theory, other repercussions will be present in computations regarding spectroscopy as well as energy and environmental studies where highly-accurate hydrocabon vibrational transitions or thermochemical data are needed
Nearly Deterministic Bell Measurement for Multiphoton Qubits and Its Application to Quantum Information Processing
We propose a Bell measurement scheme by employing a logical qubit in
Greenberger-Horne-Zeilinger (GHZ) entanglement with an arbitrary number of
photons. Remarkably, the success probability of the Bell measurement as well as
teleportation of the GHZ entanglement can be made arbitrarily high using only
linear optics elements and photon on-off measurements as the number of photons
increases. Our scheme outperforms previous proposals using single photon qubits
when comparing the success probabilities in terms of the average photon usages.
It has another important advantage for experimental feasibility that it does
not require photon number resolving measurements. Our proposal provides an
alternative candidate for all-optical quantum information processing.Comment: 7 pages (including supplementary material), 2 figures, to be
published in Phys. Rev. Let
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