Erasure-Resilient Sublinear-Time Graph Algorithms

We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial erasures in adjacency entries. We focus on two computational tasks: testing if a graph is connected or ε-far from connected and estimating the average degree. For testing connectedness, we discover a threshold phenomenon: when the fraction of erasures is less than ε, this property can be tested efficiently (in time independent of the size of the graph); when the fraction of erasures is at least ε, then a number of queries linear in the size of the graph representation is required. Our erasure-resilient algorithm (for the special case with no erasures) is an improvement over the previously known algorithm for connectedness in the standard property testing model and has optimal dependence on the proximity parameter ε. For estimating the average degree, our results provide an “interpolation” between the query complexity for this computational task in the model with no erasures in two different settings: with only degree queries, investigated by Feige (SIAM J. Comput. ‘06), and with degree queries and neighbor queries, investigated by Goldreich and Ron (Random Struct. Algorithms ‘08) and Eden et al. (ICALP ‘17). We conclude with a discussion of our model and open questions raised by our work.

Models, Conceptual and Predictive: A Response to Johnson’s Models-as-Fables

James Johnson argues that formal models are best conceived as fables which provide lessons about empirical phenomena and the “standard rationale” of testing model predictions fails. Without justifying the “standard rationale” as such, we argue that models produce scientific predictions. These predictions come at different levels or granularity of description and in different forms each bearing some degree of uncertainty, but still give conditions for the existence of political phenomena. Models and their predictions require projection onto the world, and that projection involves interpretation. Tests utilize inference to the best explanation, and it is the conceptual or theoretical aspect of models that make them explanatory. We discuss the extent to which our characterisation of models and their explanatory form versus that of Johnson constitutes a verbal or substantive dispute.

Experimental Study on the Influence of Bulbous Bow Form on the Velocity Field around the Bow of a Trimaran Using Towed Underwater 2D-3C SPIV

In this study, particle image velocimetry was applied to measure the flow field around the bow region of a trimaran with different appendages. The dimensionless axial velocity u/U in test planes 1 and 2 of the testing model was measured by using a towed underwater stereoscopic particle image velocimetry (SPIV) system. Based on the measured flow field data, the local sinkage values in test planes 1 and 2 of the testing model with different appendages at speeds of 1.766 and 2.943 m/s were presented. In addition, the effects of speed, bulbous bow type, T foils, and bow wave on the axial velocity u/U were studied in detail. The acquired experimental data help in understanding the distribution of the flow field around the ship bow, and the data can also act as a reference to verify computational fluid dynamics (CFD) results.

Stochastic Probing with Increasing Precision

We consider a selection problem with stochastic probing. There is a set of items whose values are drawn from independent distributions. The distributions are known in advance. Each item can be \emph{tested} repeatedly. Each test reduces the uncertainty about the realization of its value. We study a testing model, where the first test reveals if the realized value is smaller or larger than the median of the underlying distribution. Subsequent tests allow to further narrow down the interval in which the realization is located. There is a limited number of possible tests, and our goal is to design near-optimal testing strategies that allow to maximize the expected value of the chosen item. We study both identical and non-identical distributions and develop polynomial-time algorithms with constant approximation factors in both scenarios.