arXiv subjects

David Steinberg

Publications and source records attributed to David Steinberg.

3 recordsLinked to original sources

arXiv2024

Investigation of the Nonlinear Optical Frequency Conversion in Ultrathin Franckeite Heterostructures

Layered franckeite is a natural superlattice composed of two alternating layers of different compositions, SnS$_2$- and PbS-like. This creates incommensurability between the two species along the planes of the layers, resulting in spontaneous symmetry-break periodic ripples in the \textit{a}-axis orientation. Nevertheless, natural franckeite heterostructure has shown potential for optoelectronic applications mostly because it is a semiconductor with 0.7 eV bandgap, air-stable, and can be easily exfoliated down to ultrathin thicknesses. Here, we demonstrate that few-layer franckeite shows a highly anisotropic nonlinear optical response due to its lattice structure, which allow for the identification of the ripple axis. Moreover, we find that the highly anisotropic third-harmonic emission strongly varies with material thickness. These features are further corroborated by a theoretical nonlinear susceptibility model and the nonlinear transfer matrix method. Overall, our findings help to understand this material and propose a characterization method that could be used in other layered materials and heterostructures to assign their characteristic axes.

physics.optics↗

arXiv2019

Early Detection of Long Term Evaluation Criteria in Online Controlled Experiments

A common dilemma encountered by many upon implementing an optimization method or experiment, whether it be a reinforcement learning algorithm, or A/B testing, is deciding on what metric to optimize for. Very often short-term metrics, which are easier to measure are chosen over long term metrics which have undesirable time considerations and often a more complex calculation. In this paper, we argue the importance of choosing a metrics that focuses on long term effects. With this comes the necessity in the ability to measure significant differences between groups relatively early. We present here an efficient methodology for early detection of lifetime differences between groups based on bootstrap hypothesis testing of the lifetime forecast of the response. We present an application of this method in the domain of online advertising and we argue that approach not only allows one to focus on the ultimate metric of importance but also provides a means of accelerating the testing period.

stat.AP↗

arXiv2014

Curve-counting invariants for crepant resolutions

We construct curve counting invariants for a Calabi-Yau threefold $Y$ equipped with a dominant birational morphism $π:Y \to X$. Our invariants generalize the stable pair invariants of Pandharipande and Thomas which occur for the case when $π:Y\to Y$ is the identity. Our main result is a PT/DT-type formula relating the partition function of our invariants to the Donaldson-Thomas partition function in the case when $Y$ is a crepant resolution of $X$, the coarse space of a Calabi-Yau orbifold $\mathcal{X}$ satisfying the hard Lefschetz condition. In this case, our partition function is equal to the Pandharipande-Thomas partition function of the orbifold $\mathcal{X}$. Our methods include defining a new notion of stability for sheaves which depends on the morphism $π$. Our notion generalizes slope stability which is recovered in the case where $π$ is the identity on $Y$. Our proof is a generalization of Bridgeland's proof of the PT/DT correspondence via the Hall algebra and Joyce's integration map.

math.AG↗