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The modes of Pacific decadal-scale variability (PDV), traditionally defined as statistical patterns of variance, reflect to first order the ocean's integration (i.e., reddening) of atmospheric forcing that arises from both a shift and a change in strength of the climatological (time-mean) atmospheric circulation. While these patterns concisely describe PDV, they do not distinguish among the key dynamical processes driving the evolution of PDV anomalies, including atmospheric and ocean teleconnections and coupled feedbacks with similar spatial structures that operate on different timescales. In this review, we synthesize past analysis using an empirical dynamical model constructed from monthly ocean surface anomalies drawn from several reanalysis products, showing that the PDV modes of variance result from two fundamental low-frequency dynamical eigenmodes: the North Pacific–central Pacific (NP-CP) and Kuroshio–Oyashio Extension (KOE) modes. Both eigenmodes highlight how two-way tropical–extratropical teleconnection dynamics are the primary mechanisms energizing and synchronizing the basin-scale footprint of PDV. While the NP-CP mode captures interannual- to decadal-scale variability, the KOE mode is linked to the basin-scale expression of PDV on decadal to multidecadal timescales, including contributions from the South Pacific.

In multi-objective search, edges are annotated with cost vectors consisting of multiple cost components. A path dominates another path with the same start and goal vertices iff the component-wise sum of the cost vectors of the edges of the former path is 'less than' the component-wise sum of the cost vectors of the edges of the latter path. The Pareto-optimal solution set is the set of all undominated paths from a given start vertex to a given goal vertex. Its size can be exponential in the size of the graph being searched, which makes multi-objective search time-consuming. In this paper, we therefore study how to find an approximate Pareto-optimal solution set for a user-provided vector of approximation factors. The size of such a solution set can be significantly smaller than the size of the Pareto-optimal solution set, which enables the design of approximate multi-objective search algorithms that are efficient and produce small solution sets. We present such an algorithm in this paper, called A*pex. A*pex builds on PPA*, a state-of-the-art approximate bi-objective search algorithm (where there are only two cost components) but (1) makes PPA* more efficient for bi-objective search and (2) generalizes it to multi-objective search for any numbermore »of cost components. We first analyze the correctness of A*pex and then experimentally demonstrate its efficiency advantage over existing approximate algorithms for bi- and tri-objective search.« less

The Pareto-optimal frontier for a bi-objective search problem instance consists of all solutions that are not worse than any other solution in both objectives. The size of the Pareto-optimal frontier can be exponential in the size of the input graph, and hence finding it can be hard. Some existing works leverage a user-specified approximation factor ε to compute an approximate Pareto-optimal frontier that can be significantly smaller than the Pareto-optimal frontier. In this paper, we propose an anytime approximate bi-objective search algorithm, called Anytime Bi-Objective A*-ε (A-BOA*ε). A-BOA*ε is useful when deliberation time is limited. It first finds an approximate Pareto-optimal frontier quickly, iteratively improves it while time allows, and eventually finds the Pareto-optimal frontier. It efficiently reuses the search effort from previous iterations and makes use of a novel pruning technique. Our experimental results show that A-BOA*ε substantially outperforms baseline algorithms that do not reuse previous search effort, both in terms of runtime and number of node expansions. In fact, the most advanced variant of A-BOA*ε even slightly outperforms BOA*, a state-of-the-art bi-objective search algorithm, for finding the Pareto-optimal frontier. Moreover, given only a limited amount of deliberation time, A-BOA*ε finds solutions that collectively approximate the Pareto-optimal frontier muchmore »better than the solutions found by BOA*.« less