Combinatorial Choice Research Articles

Learning to Rasterize Differentiably

AbstractDifferentiable rasterization changes the standard formulation of primitive rasterization — by enabling gradient flow from a pixel to its underlying triangles — using distribution functions in different stages of rendering, creating a “soft” version of the original rasterizer. However, choosing the optimal softening function that ensures the best performance and convergence to a desired goal requires trial and error. Previous work has analyzed and compared several combinations of softening. In this work, we take it a step further and, instead of making a combinatorial choice of softening operations, parameterize the continuous space of common softening operations. We study meta‐learning tunable softness functions over a set of inverse rendering tasks (2D and 3D shape, pose and occlusion) so it generalizes to new and unseen differentiable rendering tasks with optimal softness.

Combinatorial choice and limited attention

Combinatorial choice and limited attention

Combinatorial Choice with Limited Attention

Combinatorial Choice with Limited Attention

SAT modulo discrete event simulation applied to railway design capacity analysis

This paper proposes a new method of combining SAT with discrete event simulation. This new integration proved useful for designing a solver for capacity analysis in early phase railway construction design. Railway capacity is complex to define and analyze, and existing tools and methods used in practice require comprehensive models of the railway network and its timetables. Design engineers working within the limited scope of construction projects report that only ad-hoc, experience-based methods of capacity analysis are available to them. Designs often have subtle capacity pitfalls which are discovered too late, only when network-wide timetables are made—there is a mismatch between the scope of construction projects and the scope of capacity analysis, as currently practiced. We suggest a language for capacity specifications suited for construction projects, expressing properties such as running time, train frequency, overtaking and crossing. Such specifications can be used as contracts in the interface between construction projects and network-wide capacity analysis. We show how these properties can be verified fully automatically by building a special-purpose solver which splits the problem into two: an abstracted SAT-based dispatch planning, and a continuous-domain dynamics with timing constraints evaluated using discrete event simulation. The two components communicate in a CEGAR loop (counterexample-guided abstraction refinement). This architecture is beneficial because it clearly distinguishes the combinatorial choices on the one hand from continuous calculations on the other, so that the simulation can be extended by relevant details as needed. We describe how loops in the infrastructure can be handled to eliminate repeating dispatch plans, and use case studies based on data from existing infrastructure and ongoing construction projects to show that our method is fast enough at relevant scales to provide agile verification in a design setting. Similar SAT modulo discrete event simulation combinations could also be useful elsewhere where one or both of these methods are already applicable such as in bioinformatics or hardware/software verification.

WARP and combinatorial choice

For combinatorial choice problems, I show that the Irrelevance of Rejected Items condition is equivalent to the Weak Axiom of Revealed Preference (WARP), and is necessary and sufficient for the existence of a complete, reflexive and antisymmetric rationalization of a combinatorial choice function. I also show the equivalence of WARP to path independence and to other classical choice conditions when the choice domain is combinatorial.

Integrating Teaching and Research in Undergraduate Biology Laboratory Education

Integrating Teaching and Research in Undergraduate Biology Laboratory Education

Joint Metering and Conflict Resolution in Air Traffic Control

This paper describes a novel optimization-based approach to conflict resolution in air traffic control, based on geometric programming. A key feature of this approach is its ability to also take into account various metering directives issued by the traffic flow management level, in contrast to most methods that focus purely on aircraft separation issues. Moreover, the proposed methodology can account for some of the nonlinearities present in the formulationsofconflictresolutionproblems,whileincurringonlyasmallpenaltyincomputationtimewithrespectto the fastest linear-programming-based approaches. Integer variables can be introduced to improve the quality of the solutions and to include combinatorial choices, for example, to optimize over aircraft sequences in merging streams. Simulation results demonstrate the efficiency of the approach on various aircraft separation problems, including miles-in-trail and minutes-in-trail restrictions through airspace fixes and boundaries.

A multi-purpose microfluidic perfusion system with combinatorial choice of inputs, mixtures, gradient patterns, and flow rates

Microfluidic perfusion systems, characterized by deterministic flow, low reagent consumption, small dead volumes, large integration in small footprints, high-throughput operation, and low-cost fabrication, are being increasingly used for cell culture studies in applications such as basic cell biology, molecular biological assays, tissue engineering, and systems biology. We report a multipurpose, pressure-driven and computer-controlled microfluidic perfusion device containing sixteen inlets and a large cell culture chamber. The user can choose, with sub-second temporal resolution, (a) to feed the chamber with one of 16 inlets, all 16 inlets, or one of 64 combinations of 2, 4, or 8 inlets using a binary multiplexer; (b) to introduce into the chamber a heterogeneous laminar flow of the inlets, a smoothened gradient, or a fully homogenized mixture; (c) to bypass the chamber in order to purge the inlet lines so as to minimize the dead volume; (d) to generate asymmetrical and curvilinear flow patterns within the chamber by opening side outlets; and (e) to slow down the flow by combinatorially adding segments of high fluid resistance (sixteen different levels of flow rates are possible using only four valves). All functionalities are combined to create complex gradient patterns and sequential perfusions within the central chamber.

Adding ecosystem function to agent-based land use models

The objective of this paper is to examine issues in the inclusion of simulations of ecosystem functions in agent-based models of land use decision-making. The reasons for incorporating these simulations include local interests in land fertility and global interests in carbon sequestration. Biogeochemical models are needed in order to calculate such fluxes. The Century model is described with particular attention to the land use choices that it can encompass. When Century is applied to a land use problem the combinatorial choices lead to a potentially unmanageable number of simulation runs. Century is also parameter-intensive. Three ways of including Century output in agent-based models, ranging from separately calculated look-up tables to agents running Century within the simulation, are presented. The latter may be most efficient, but it moves the computing costs to where they are most problematic. Concern for computing costs should not be a roadblock.

Counting combinatorial choice rules

I count the number of combinatorial choice rules that satisfy certain properties: Kelso–Crawford substitutability, and independence of irrelevant alternatives. The results are important for two-sided matching theory, where agents are modeled by combinatorial choice rules with these properties. The rules are a small, and asymptotically vanishing, fraction of all choice rules. But they are still exponentially more than the preference relations over individual agents—which has positive implications for the Gale–Shapley algorithm of matching theory.