Connor Colombe

The Johnson system of distributions provides a flexible framework for modeling continuous random variables through monotonic transformations of the standard normal distribution. Recently Bickel [2026] proposed a novel formulation of the Johnson system based on power series expansions of the Johnson quantile functions (JPSE). Their paper conjectured conditions for the monotonicity of the SL and SB JPSE distributions-namely, that the corresponding power series must be truncated to odd powers only. In this paper we rigorously prove those conjectures, putting the JPSE systems on a more grounded mathematical footing.

Quantile-parameterized distributions (QPDs) are widely used in decision analysis because expert judgments are naturally expressed in terms of quantiles. Existing QPD families such as the Metalog offer considerable flexibility but lack analytic monotonicity guarantees, requiring ex post numerical repair. This paper introduces the QFlex distribution, a new QPD system constructed entirely from monotone transformations of valid quantile functions. QFlex interleaves powers of exponential, reflected-exponential, and centered-uniform quantile bases, yielding a flexible expansion that remains monotone under simple coefficient conditions. We show that QFlex has a full-rank design matrix under mild assumptions, can interpolate any finite set of quantile assessments, and converges to the target quantile function as the number of terms increases. When all coefficients are nonnegative, QFlex is strictly increasing and unimodal; additional modes arise only in a structured and controllable manner. A comprehensive comparison across approximately 3,500 Pearson-system distributions demonstrates that QFlex generally matches or exceeds the accuracy of the Metalog distribution at moderate orders while offering explicit analytic monotonicity conditions. A synthetic example illustrates QFlex’s practical advantage: valid fits can be enforced directly through simple coefficient constraints, avoiding the complex post-fit monotonicity repair required by the Metalog distribution.

Model-based deep decarbonization scenarios tend to envision significant deployment of carbon capture (CC) in sectors such as electricity and heavy industries. Through its 45Q tax credits, the United States federal government provides a subsidy payment for each ton of carbon dioxide (CO2) that firms capture. In this paper, we develop and analyze a Stackelberg game model featuring a social-welfare-maximizing government as the leader and a profit-maximizing firm as the follower. The government sets the CC subsidy level and the firm responds by jointly choosing whether to invest in CC technology and its production level. In the case with perfect information, we analytically derive the optimal CC subsidy and establish the conditions under which subsidizing CC will actually increase CO2 emissions. We then consider an extension where the firm’s CC investment cost is uncertain from the government’s perspective. In this case, we show that uncertainty can raise or lower the optimal subsidy depending on parameters. Lastly, we apply our model to a numerical case study of a coal-fired power plant. We find that, under perfect information, it is optimal for the government to subsidize CC just enough to make it profitable for the firm to adopt, or not at all. Our case study results suggest that the current 45Q level of $85/tCO2 for geological storage applications may be quite close to the optimal subsidy amount. While we show that a CC subsidy can theoretically increase CO2 emissions, our case study results demonstrate why this is unlikely to occur in practical applications.

Many model-based decarbonization pathways include substantial carbon capture, utilization, and storage (CCUS), and engineering cost estimates suggest that these technologies should be profitable to deploy under current incentives, such as the 45Q tax credits in the United States. However, CCUS investments have been slow to materialize. In this paper, we investigate the extent to which policy uncertainty and investor risk aversion may explain the limited buildout of CCUS infrastructure to date. To do so, we develop a two-stage stochastic programming model for optimal CCUS infrastructure network design that incorporates policy uncertainty and risk aversion as novel features. We then apply it to an empirically parameterized case study of the Texas-Louisiana Gulf Coast region. Our results show that the current 45Q incentive levels make a fair number of CCUS projects profitable even if they were to be discontinued after ten years. Moreover, while future policy uncertainty and risk aversion reduce CCUS development, the maximum effect size is only a 16% decline in expected total CO2 captured. We find policy uncertainty plays a more important role than investor risk aversion in the development of CCUS infrastructure, with increased uncertainty leading to reduced CO2 capture and investment.

In this paper, we investigate the resilience of alternative electric grid configurations by adopting a stylized approach based on graph theory, probabilistic analysis, and simulation. We consider two alternative classes of electricity network topology: binary trees and rectangular lattices. For each topology, we find the probabilities that customers located at various nodes in the network will continue to have power following a disaster, depending on the locations of resources (e.g., generators, storage units) in the network. Then, these probabilities are incorporated into the problem of optimally placing resources throughout the network. This is a cost–benefit problem that weighs the benefits of placing resources closer to customers – that is, pursuing a distributed resilience strategy – against the higher total cost of deploying a greater number of smaller resource units. Our analytical and numerical results thus shed light on the general circumstances in which centralized or distributed resilience strategies are preferable. While optimal resource placements depend on various assumptions, such as the probability that power lines fail and the strength of economies of scale, we find that distributed resilience strategies are more often preferred in the binary tree topology than in the rectangular lattice topology. Rectangular lattices feature greater redundancy in terms of paths between nodes in the network, enabling the system to be fairly resilient even with centralized resources.

We describe the first strongly subquadratic time algorithm with subexponential approximation ratio for approximately computing the Fr}’echet distance between two polygonal chains. Specifically, let \P and \Q be two polygonal chains with \n vertices in \d\-dimensional Euclidean space, and let {}alpha }in [}sqrt{n}, n]\. Our algorithm deterministically finds an Ø(}alpha)\-approximate Fr}’echet correspondence in time Ø((n^3 / }alpha^2) }log n)\. In particular, we get an Ø(n)\-approximation in near-linear Ø(n }log n) time, a vast improvement over the previously best know result, a linear time \2^{O(n)}\-approximation. As part of our algorithm, we also describe how to turn any approximate decision procedure for the Fr}’echet distance into an approximate optimization algorithm whose approximation ratio is the same up to arbitrarily small constant factors. The transformation into an approximate optimization algorithm increases the running time of the decision procedure by only an Ø(}log n) factor.