Forecasting consumer products using prediction markets

Thesis (M. Eng. in Logistics)--Massachusetts Institute of Technology, Engineering Systems Division, 2009.Includes bibliographical references (leaves 105-106).Prediction Markets hold the promise of improving the forecasting process. Research has shown that Prediction Markets can develop more accurate forecasts than polls or experts. Our research concentrated on analyzing Prediction Markets for business decision-making. We configured a Prediction Market to gather primary data, sent out surveys to gauge participant views and conducted in-depth interviews to explain trader behavior. Our research was conducted with 169 employees from General Mills who participated in Prediction Markets that lasted from two to ten weeks. Our research indicates that short term forecasting Prediction Markets are no more accurate than conventional forecasting methods. It also presents and addresses three interesting contradictions. First, the Sales Organization won the majority of the Prediction Markets, yet the overall performance of Sales as a group was worse than that of other groups. Second, Prediction Markets were able to gain access to more information than General Mills' current process, yet the impact on forecast accuracy was not significant. Third, with a MAPE of 11% for promotional Prediction Markets, it would seem that promotional demand was well understood up-front, yet when we dissected the promotional forecasts we discovered that participants changed their minds over time degrading overall forecast accuracy. We believe that we have extended the current body of work on Prediction Markets in ways that will increase the utilization in business environments.by Kai Trepte and Rajaram Narayanaswamy.M.Eng.in Logistic

How good are recent density functionals for ground and excited states of one-electron systems?

Sun et al. [J. Chem. Phys. 144, 191101 (2016)] suggested that common density functional approximations (DFAs) should exhibit large energy errors for excited states as a necessary consequence of orbital nodality. Motivated by self-interaction corrected density functional calculations on many-electron systems, we continue their study with the exactly solvable 1s, 2p, and 3d states of 36 hydrogenic one-electron ions (H-Kr35+) and demonstrate with self-consistent calculations that state-of-the-art DFAs indeed exhibit large errors for the 2p and 3d excited states. We consider 56 functionals at the local density approximation (LDA), generalized gradient approximation (GGA) as well as meta-GGA levels, also including several hybrid functionals like the recently proposed machine-learned DM21 local hybrid functional. The best non-hybrid functional for the 1s ground state is revTPSS. The 2p and 3d excited states are more difficult for DFAs as Sun et al. predicted, and LDA functionals turn out to yield the most systematic accuracy for these states amongst non-hybrid functionals. The best performance for the three states overall is observed with the BHandH global hybrid GGA functional, which contains 50% Hartree-Fock exchange and 50% LDA exchange. The performance of DM21 is found to be inconsistent, yielding good accuracy for some states and systems and poor accuracy for others. Based on these results, we recommend including a variety of one-electron cations in future training of machine-learned density functionals. (C) 2022 Author(s).Peer reviewe

Bond formation insights into the Diels-Alder reaction: A bond perception and self-interaction perspective

The behavior of electrons during bond formation and breaking cannot commonly be accessed from experiments. Thus, bond perception is often based on chemical intuition or rule-based algorithms. Utilizing computational chemistry methods, we present intrinsic bond descriptors for the Diels-Alder reaction, allowing for an automatic bond perception. We show that these bond descriptors are available from localized orbitals and self-interaction correction calculations, e.g., from Fermi-orbital descriptors. The proposed descriptors allow a sparse, simple, and educational inspection of the Diels-Alder reaction from an electronic perspective. We demonstrate that bond descriptors deliver a simple visual representation of the concerted bond formation and bond breaking, which agrees with Lewis' theory of bonding.Comment: 10 pages, 7 figures, supplementary material can be found under ancillary file

Lead candidates for high-performance organic photovoltaics from high-throughput quantum chemistry – the Harvard Clean Energy Project

The virtual high-throughput screening framework of the Harvard Clean Energy Project allows for the computational assessment of candidate structures for organic electronic materials – in particular photovoltaics – at an unprecedented scale. We report the most promising compounds that have emerged after studying 2.3 million molecular motifs by means of 150 million density functional theory calculations. Our top candidates are analyzed with respect to their structural makeup in order to identify important building blocks and extract design rules for efficient materials. An online database of the results is made available to the community.Engineering and Applied Science

Stretched or noded orbital densities and self-interaction correction in density functional theory

Semilocal approximations to the density functional for the exchange-correlation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semilocal approximation makes that approximation exact for all one-electron ground- or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semilocal approximations satisfy, suggesting the need for a generalized SIC. These conclusions are supported by calculations for one-electron densities and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGAs) and meta-GGAs, it reduces and often worsens the atomization energies of molecules. Thus, PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here, in particular, to the strongly constrained and appropriately normed (SCAN) meta-GGA, for which the correlation part is already self-interaction-free. This property makes SCAN a natural first candidate for a generalized SIC. Published under license by AIP Publishing.Peer reviewe

Electronic magnetism and magnetic shielding in metal-organic frameworks

In this dissertation, investigations regarding magnetism within metal-organic frameworks (MOFs) based on calculations in the framework of density functional theory (DFT) were carried out. On the one hand, the intrinsic magnetic properties within the MOF DUT-8(Ni) were studied (DUT -- Dresden University of Technology). This MOF is flexible, thus it can exist in two crystal structures named DUT-8(Ni)ppen and DUT-8(Ni)closed. A transition from one structure to the other can be achieved via e.g. gas adsorption, leading to a volume increase of approximately 260 %. The magnetic properties originate from spin-spin interactions between the unpaired electrons at the Ni centers. The magnetic coupling between the Ni ions was found to be low-spin (antiferromagnetic). Considering that MOFs tend to have rather large unit cells (> 100 atoms), model systems (< 30 atoms) were generated. Such models can qualitatively as well as quantitatively describe the coupling inside the crystal structure while drastically reducing computational time. Furthermore, the model systems can be easily altered e.g. to introduce defects. The influence of these alterations on the magnetic coupling was studied. In addition, the metal centers have been exchanged by other 3d-metals to analyze the coupling constant with respect to different magnetic centers. On the other hand, the magnetic shielding of Xe adsorbed into the MOFs UiO-66 and UiO-67 was investigated (UiO -- University of Oslo). Based on high-pressure nuclear magnetic resonance (NMR) measurements, which showed a decrease of the total chemical shift when going from the smaller MOF (UiO-66) to the larger one (UiO-67), a thorough theoretical analysis was carried out. For this purpose the ansatz of Ito and Fraissard, i.e. the chemical shift of Xe being a sum of different contributions, was employed. Accordingly, model systems which describe the influences of the MOFs and adjacent Xe atoms on the magnetic shielding were contructed. After equilibrating the Xe positions using molecular dynamics simulations, these model systems were taken to study the chemical shift of all Xe atoms individually. Thus, an analysis of the chemical shift inside each pore of the MOFs was carried out. This allows a description of different influences (Xe-surface, Xe-Xe) on the chemical shift, explaining the experimental behavior at an atomistic level

Electronic magnetism and magnetic shielding in metal-organic frameworks

In this dissertation, investigations regarding magnetism within metal-organic frameworks (MOFs) based on calculations in the framework of density functional theory (DFT) were carried out. On the one hand, the intrinsic magnetic properties within the MOF DUT-8(Ni) were studied (DUT -- Dresden University of Technology). This MOF is flexible, thus it can exist in two crystal structures named DUT-8(Ni)ppen and DUT-8(Ni)closed. A transition from one structure to the other can be achieved via e.g. gas adsorption, leading to a volume increase of approximately 260 %. The magnetic properties originate from spin-spin interactions between the unpaired electrons at the Ni centers. The magnetic coupling between the Ni ions was found to be low-spin (antiferromagnetic). Considering that MOFs tend to have rather large unit cells (> 100 atoms), model systems (< 30 atoms) were generated. Such models can qualitatively as well as quantitatively describe the coupling inside the crystal structure while drastically reducing computational time. Furthermore, the model systems can be easily altered e.g. to introduce defects. The influence of these alterations on the magnetic coupling was studied. In addition, the metal centers have been exchanged by other 3d-metals to analyze the coupling constant with respect to different magnetic centers. On the other hand, the magnetic shielding of Xe adsorbed into the MOFs UiO-66 and UiO-67 was investigated (UiO -- University of Oslo). Based on high-pressure nuclear magnetic resonance (NMR) measurements, which showed a decrease of the total chemical shift when going from the smaller MOF (UiO-66) to the larger one (UiO-67), a thorough theoretical analysis was carried out. For this purpose the ansatz of Ito and Fraissard, i.e. the chemical shift of Xe being a sum of different contributions, was employed. Accordingly, model systems which describe the influences of the MOFs and adjacent Xe atoms on the magnetic shielding were contructed. After equilibrating the Xe positions using molecular dynamics simulations, these model systems were taken to study the chemical shift of all Xe atoms individually. Thus, an analysis of the chemical shift inside each pore of the MOFs was carried out. This allows a description of different influences (Xe-surface, Xe-Xe) on the chemical shift, explaining the experimental behavior at an atomistic level