Inventory model of deteriorating items on non-periodic discrete-time domains

In this paper, we demonstrate how to model a discrete-time dynamic process on a non-periodic time domain with applications to operations research. We introduce a discrete-time model of inventory with deterioration on domains where time points may be unevenly spaced over a time interval. We formalize the average cost function composed of storage, depreciation and back-ordering costs. The optimal condition is given to locate the optimal point that minimizes the average cost function. Finally, we present simulations to demonstrate how a manager can use this model to make inventory decisions.     

Accuracy-Risk Trade-Off Due to Social Learning in Crowd-Sourced Financial Predictions

A critical question relevant to the increasing importance of crowd-sourced-based finance is how to optimize collective information processing and decision-making. Here, we investigate an often under-studied aspect of the performance of online traders: beyond focusing on just accuracy, what gives rise to the trade-off between risk and accuracy at the collective level? Answers to this question will lead to designing and deploying more effective crowd-sourced financial platforms and to minimizing issues stemming from risk such as implied volatility. To investigate this trade-off, we conducted a large online Wisdom of the Crowd study where 2037 participants predicted the prices of real financial assets (S&P 500, WTI Oil and Gold prices). Using the data collected, we modeled the belief update process of participants using models inspired by Bayesian models of cognition. We show that subsets of predictions chosen based on their belief update strategies lie on a Pareto frontier between accuracy and risk, mediated by social learning. We also observe that social learning led to superior accuracy during one of our rounds that occurred during the high market uncertainty of the Brexit vote.     

DNA computation: a photochemically controlled AND gate

DNA computation is an emerging field that enables the assembly of complex circuits based on defined DNA logic gates. DNA-based logic gates have previously been operated through purely chemical means, controlling logic operations through DNA strands or other biomolecules. Although gates can operate through this manner, it limits temporal and spatial control of DNA-based logic operations. A photochemically controlled AND gate was developed through the incorporation of caged thymidine nucleotides into a DNA-based logic gate. By using light as the logic inputs, both spatial control and temporal control were achieved. In addition, design rules for light-regulated DNA logic gates were derived. A step-response, which can be found in a controller, was demonstrated. Photochemical inputs close the gap between DNA computation and silicon-based electrical circuitry, since light waves can be directly converted into electrical output signals and vice versa. This connection is important for the further development of an interface between DNA logic gates and electronic devices, enabling the connection of biological systems with electrical circuits.     

Zeolite synthesis in fluoride media: structure direction toward ITW by small methylimidazolium cations

Pure silica ITW zeolite can be synthesized using 1,2,3-trimethylimidazolium and 1,3-dimethylimidazolium cations and fluoride anions as structure-directing agents (SDAs). Similarly to the previously reported 1,3,4-trimethylimidazolium, the dimethyl cation can also produce the zeolite TON, but this higher framework density phase finally transforms in situ into ITW. The structures of the as-made and calcined phases prepared with the new cations show a unit cell doubling along z, and the refined structures are reported. Periodic Density Functional Theory calculations provide the energies of the six SDA-ITW and SDA-TON zeolites, and their relative stabilities fully agree with the experimental observations. Structure-direction in this system is discussed from experimental and theoretical results that give strong support to the idea that strained silica frameworks are made possible in fluoride media by decreasing the covalent character of the Si-O bond. This decreased covalency is enhanced with the 1,2,3-trimethyl isomer, which is shown to be the strongest SDA for ITW and, at the same time, is the more hydrophilic of the three SDAs tested. Our observations with the three SDAs agree with the so-called Villaescusa's rule, i.e., the low framework density phase is favored at higher concentrations, but at the same time question the supersaturation hypothesis that has been proposed to explain this rule, since here the low-density phase is the most stable one.     

Polarons, bipolarons, and side-by-side polarons in reduction of oligofluorenes

The nature of charge carriers in conjugated polymers was elucidated through optical spectroscopy following single- and multielectron reduction of 2,7-(9,9-dihexylfluorene) oligomers, F(n), n = 1-10, yielding spectra with the two bands typical of polarons upon single reduction. For short oligomers addition of a second electron gave a single band demonstrating the classic polaron-bipolaron transition. However, for long oligomers double reductions yielded spectra with two bands, better described as two polarons, possibly residing side-by-side in the F(n) chains. The singly reduced anions do not appear to delocalize over the entire length of the longer conjugated systems; instead they are polarons occupying approximately four fluorene repeat units. The polarons of F(3) and F(4) display sharp absorption bands, but for longer oligomers the bands broaden, possibly due to fluctuations of the lengths of these unconfined polarons. DFT calculations with long-range-corrected functionals were fully consistent with the experiments describing polarons in anions, bipolarons in dianions of short oligomers, and side-by-side polarons in dianions of long oligomers, while results from standard functionals were not compatible with the experimental results. The computations found F(10)(2-), for example, to be an open-shell singlet ( ≈ 1), with electrons in two side-by-side orbitals, while dianions of shorter oligomers experienced a gradual transition to bipolarons with states of intermediate character at intermediate lengths. The energies and extinction coefficients of each anionic species were measured by ultraviolet-visible-near-infrared absorption spectroscopy with chemical reduction and pulse radiolysis. Reduction potentials determined from equilibria mirrored oxidation potentials reported by Chi and Wegner. Anions of oligomers four or more units in length contained vestigial neutral (VN) absorption bands that arise from neutral parts of the chain. Energies of the VN bands correspond to those of oligomers shorter by four units.     

Double-pass self-spectral-calibration of a polarization state analyzer

We present a new method that allows efficient spectral calibration for a polarization state analyzer. The procedure does not require any additional polarization optical element other than the polarization state analyzer itself. It uses a double-pass technique that can be achieved up to a very good precision. The method is illustrated using real measurements done at several wavelengths with a rotating wave plate polarization state analyzer. Alignment of axis as well as true retardation at a specific wavelength are easily obtained by a standard function fitting.     

On sets of directions determined by subsets of ℝ<Superscript><Emphasis Type="Italic">d</Emphasis></Superscript>

Given E ? ? ^d , d ≥ 2, define

$D(E) \equiv \left\{ {{{x - y} \over {\left| {x - y} \right|}}:x,y \in E} \right\} \subset {S^{d - 1}}$

to be the set of directions determined by E. We prove that if the Hausdorff dimension of E is greater than d ? 1, then σ(D(E)) > 0, where σ denotes the surface measure on S ^d?1. In the process, we prove some tight upper and lower bounds for the maximal function associated with the Radon-Nikodym derivative of the natural measure on D. This result is sharp, since the conclusion fails to hold if E is a (d ? 1)-dimensional hyper-plane. This result can be viewed as a continuous analog of a recent result of Pach, Pinchasi, and Sharir ([22, 23]) on directions determined by finite subsets of ? ^d . We also discuss the case when the Hausdorff dimension of E is precisely d ? 1, where some interesting counter-examples have been obtained by Simon and Solomyak ([25]) in the planar case. In response to the conjecture stated in this paper, T. Orponen and T. Sahlsten ([20]) have recently proved that if the Hausdorff dimension of E equals d ? 1 and E is rectifiable and is not contained in a hyper-pane, the Lebesgue measure of the set of directions is still positive. Finally, we show that our continuous results can be used to recover and, in some cases, improve the exponents for the corresponding results in the discrete setting for large classes of finite point sets. In particular, we prove that a finite point set P ? ? ^d , d ≥ 3, satisfying a certain discrete energy condition (Definition 3.1) determines ? #P distinct directions.

     

Metrizability of Clifford topological semigroups

We prove that a countably compact Clifford topological semigroup S is metrizable if and only if the set E={e∈S:ee=e} of idempotents of S is a metrizable G _δ -set in S.