Incentivizing Exploration with Heterogeneous Value of Money

Recently, Frazier et al. proposed a natural model for crowdsourced exploration of different a priori unknown options: a principal is interested in the long-term welfare of a population of agents who arrive one by one in a multi-armed bandit setting. However, each agent is myopic, so in order to incentivize him to explore options with better long-term prospects, the principal must offer the agent money. Frazier et al. showed that a simple class of policies called time-expanded are optimal in the worst case, and characterized their budget-reward tradeoff. The previous work assumed that all agents are equally and uniformly susceptible to financial incentives. In reality, agents may have different utility for money. We therefore extend the model of Frazier et al. to allow agents that have heterogeneous and non-linear utilities for money. The principal is informed of the agent's tradeoff via a signal that could be more or less informative. Our main result is to show that a convex program can be used to derive a signal-dependent time-expanded policy which achieves the best possible Lagrangian reward in the worst case. The worst-case guarantee is matched by so-called "Diamonds in the Rough" instances; the proof that the guarantees match is based on showing that two different convex programs have the same optimal solution for these specific instances. These results also extend to the budgeted case as in Frazier et al. We also show that the optimal policy is monotone with respect to information, i.e., the approximation ratio of the optimal policy improves as the signals become more informative.Comment: WINE 201

Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space

We obtain upper and lower bounds for Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space. A very general upper bound is proved, which depends only on the geometry of the fixed boundary and on the measure of the interior. Sharp lower bounds are given for hypersurfaces of revolution with connected boundary: We prove that each eigenvalue is uniquely minimized by the ball. We also observe that each surface of revolution with connected boundary is Steklov isospectral to the disk

The dynamical tides of spinning Newtonian stars

We carefully develop the framework required to model the dynamical tidal response of a spinning neutron star in an inspiralling binary system, in the context of Newtonian gravity, making sure to include all relevant details and connections to the existing literature. The tidal perturbation is decomposed in terms of the normal oscillation modes, used to derive an expression for the effective Love number which is valid for any rotation rate. In contrast to previous work on the problem, our analysis highlights subtle issues relating to the orthogonality condition required for the mode-sum representation of the dynamical tide and shows how the prograde and retrograde modes combine to provide the overall tidal response. Utilising a slow-rotation expansion, we show that the dynamical tide (the effective Love number) is corrected at first order in rotation, whereas in the case of the static tide (the static Love number) the rotational corrections do not enter until second order.PP acknowledges support from the María Zambrano Fellowship Programme (ZAMBRANO21), funded by the Spanish Ministry of Universities and the University of Alicante through the European Union’s “Next Generation EU” package, as well as from the grant PID2021-127495NBI00, funded by MCIN/AEI/10.13039/501100011033 and by the European Union, from the Astrophysics and High Energy Physics programme of the Generalitat Valenciana ASFAE/2022/026, funded by the Spanish Ministry of Science and Innovation (MCIN) and the European Union’s “Next Generation EU” package (PRTR-C17.I1), and from the Prometeo 2023 excellence programme grant CIPROM/2022/13, funded by the Ministry of Innovation, Universities, Science, and Digital Society of the Generalitat Valenciana. This work was also supported by the “Ministero dell’istruzione, dell’università e della ricerca" (MIUR) PRIN 2017 programme (CUP: B88D19001440001), from the Amaldi Research Center, funded by the MIUR programme “Dipartimento di Eccellenza" (CUP: B81I18001170001), and from the EU Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie Grant Agreement N. 101007855. FG, NA, and DIJ are grateful for support from STFC via grant numbers ST/R00045X/1 and ST/V000551/1

Bistable molecular conductors with a field-switchable dipole group

A class of bistable "stator-rotor" molecules is proposed, where a stationary bridge (stator) connects the two electrodes and facilitates electron transport between them. The rotor part, which has a large dipole moment, is attached to an atom of the stator via a single sigma bond. Hydrogen bonds formed between the rotor and stator make the symmetric orientation of the dipole unstable. The rotor has two potential minima with equal energy for rotation about the sigma bond. The dipole orientation, which determines the conduction state of the molecule, can be switched by an external electric field that changes the relative energy of the two potential minima. Both orientation of the rotor correspond to asymmetric current-voltage characteristics that are the reverse of each other, so they are distinguishable electrically. Such bistable stator-rotor molecules could potentially be used as parts of molecular electronic devices.Comment: 8 pages, 7 figure

Controlling microenvironments and modifying anion binding selectivities using core functionalised hyperbranched polymers

An isophthalamide anion binding site has been incorporated into hyperbranched polymers resulting in a change in the selectivity of the receptor from chloride to bromide

Dynamic Models of Reputation and Competition in Job-Market Matching

A fundamental decision faced by a firm hiring employees - and a familiar one to anyone who has dealt with the academic job market, for example - is deciding what caliber of candidates to pursue. Should the firm try to increase its reputation by making offers to higher-quality candidates, despite the risk that the candidates might reject the offers and leave the firm empty-handed? Or should it concentrate on weaker candidates who are more likely to accept the offer? The question acquires an added level of complexity once we take into account the effect one hiring cycle has on the next: hiring better employees in the current cycle increases the firm's reputation, which in turn increases its attractiveness for higher-quality candidates in the next hiring cycle. These considerations introduce an interesting temporal dynamic aspect to the rich line of research on matching models for job markets, in which long-range planning and evolving reputational effects enter into the strategic decisions made by competing firms. We develop a model based on two competing firms to try capturing as cleanly as possible the elements that we believe constitute the strategic tension at the core of the problem: the trade-off between short-term recruiting success and long-range reputation-building; the inefficiency that results from underemployment of people who are not ranked highest; and the influence of earlier accidental outcomes on long-term reputations. Our model exhibits all these phenomena in a stylized setting, governed by a parameter q that captures the difference in strength between the two top candidates in each hiring cycle. We show that when q is relatively low the efficiency of the job market is improved by long-range reputational effects, but when q is relatively high, taking future reputations into account can sometimes reduce the efficiency

Incoherent dynamics of vibrating single-molecule transistors

We study the tunneling conductance of nano-scale quantum ``shuttles'' in connection with a recent experiment (H. Park et al., Nature, 407, 57 (2000)) in which a vibrating C^60 molecule was apparently functioning as the island of a single electron transistor (SET). While our calculation starts from the same model of previous work (D. Boese and H. Schoeller, Europhys. Lett. 54, 66(2001)) we obtain quantitatively different dynamics. Calculated I-V curves exhibit most features present in experimental data with a physically reasonable parameter set, and point to a strong dependence of the oscillator's potential on the electrostatics of the island region. We propose that in a regime where the electric field due to the bias voltage itself affects island position, a "catastrophic" negative differential conductance (NDC) may be realized. This effect is directly attributable to the magnitude of overlap of final and initial quantum oscillator states, and as such represents experimental control over quantum transitions of the oscillator via the macroscopically controllable bias voltage.Comment: 6 pages, LaTex, 6 figure