Guillermo Gallego
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View article: A prophet inequality based approach to the adaptive ProbeTop$$\varvec{K}$$ problem
A prophet inequality based approach to the adaptive ProbeTop$$\varvec{K}$$ problem Open
In the adaptive ProbeTop $$K$$ problem, given a collection of mutually independent random variables $$X_1, \ldots , X_n$$ , our goal is to design an adaptive probing policy to sample these variables in a sequence of T stages, …
View article: Multiplicative Higgs bundles and involutions
Multiplicative Higgs bundles and involutions Open
In this paper we generalize the theory of multiplicative G-Higgs bundles over a curve to pairs (G,θ), where G is a reductive algebraic group and θ is an involution of G. This generalization involves the notion of a multiplicative Higgs bun…
View article: Multiplicative Higgs bundles and involutions
Multiplicative Higgs bundles and involutions Open
In this paper we generalize the theory of multiplicative $G$-Higgs bundles over a curve to pairs $(G,θ)$, where $G$ is a reductive algebraic group and $θ$ is an involution of $G$. This generalization involves the notion of a multiplicative…
View article: A Cost-Agnostic Model to Identify Infrastructure Projects to Improve Rain-flow Allocations in a Growing Demand Environment
A Cost-Agnostic Model to Identify Infrastructure Projects to Improve Rain-flow Allocations in a Growing Demand Environment Open
Climate change has led to the redistribution of water resources in many regions due to changes in global and regional water cycles. Sustainable water management is essential to ensure further socioeconomic development in the fastest-growin…
View article: A Constructive Prophet Inequality Approach to The Adaptive ProbeMax Problem
A Constructive Prophet Inequality Approach to The Adaptive ProbeMax Problem Open
In the adaptive ProbeMax problem, given a collection of mutually-independent random variables $X_1, \ldots, X_n$, our goal is to design an adaptive probing policy for sequentially sampling at most $k$ of these variables, with the objective…
View article: The Limits of Personalization in Assortment Optimization
The Limits of Personalization in Assortment Optimization Open
To study the limits of personalization, we introduce the notion of a clairvoyant firm that can read the mind of consumers and sell them the highest revenue product that they are willing to buy. We show how to compute the expected revenue o…
View article: Higgs bundles twisted by a vector bundle
Higgs bundles twisted by a vector bundle Open
In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We defin…
View article: The Refined Assortment Optimization Problem
The Refined Assortment Optimization Problem Open
We introduce the refined assortment optimization problem where a firm may decide to make some of its products harder to get instead of making them unavailable as in the traditional assortment optimization problem. Airlines, for example, of…
View article: Limits of Personalization: Prophet Inequalities for Revenue-Ordered Assortments
Limits of Personalization: Prophet Inequalities for Revenue-Ordered Assortments Open
Consider a clairvoyant firm that knows the products' valuations of each arriving consumer and offers them only the most profitable product they are willing to buy. How much more can such a firm make relative to a firm that offers all consu…