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1. Width transfer: on the (in)variance of width optimization

   https://doi.org/10.1109/CVPRW53098.2021.00334  

   Chin, Ting-Wu; Marculescu, Diana; Morcos, Ari S. (June 2021, 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW))

   null (Ed.)
2. Any-Width Networks

   https://doi.org/10.1109/CVPRW50498.2020.00360  

   Vu, Thanh; Eder, Marc; Price, True; Frahm, Jan-Michael (June 2020, he IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops)

   null (Ed.)

   Despite remarkable improvements in speed and accuracy, convolutional neural networks (CNNs) still typically operate as monolithic entities at inference time. This poses a challenge for resource-constrained practical applications, where both computational budgets and performance needs can vary with the situation. To address these constraints, we propose the Any-Width Network (AWN), an adjustable-width CNN architecture and associated training routine that allow for fine-grained control over speed and accuracy during inference. Our key innovation is the use of lower-triangular weight matrices which explicitly address width-varying batch statistics while being naturally suited for multi-width operations. We also show that this design facilitates an efficient training routine based on random width sampling. We empirically demonstrate that our proposed AWNs compare favorably to existing methods while providing maximally granular control during inference. 

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3. What sets river width?

   https://doi.org/10.1126/sciadv.abc1505  

   Dunne, Kieran B.; Jerolmack, Douglas J. (October 2020, Science Advances)

   null (Ed.)

   One of the simplest questions in riverine science remains unanswered: “What determines the width of rivers?” While myriad environmental and geological factors have been proposed to control alluvial river size, no accepted theory exists to explain this fundamental characteristic of river systems. We combine analysis of a global dataset with a field study to support a simple hypothesis: River geometry adjusts to the threshold fluid entrainment stress of the most resistant material lining the channel. In addition, we demonstrate how changes in bank strength dictate planform morphology by exerting strong control on channel width. Our findings greatly extend the applicability of threshold channel theory, which was originally developed to explain straight gravel-bedded rivers with uniform grain size and stable banks. The parsimonious threshold-limiting channel model describes the average hydraulic state of natural rivers across a wide range of conditions and may find use in river management, stratigraphy, and planetary science. 

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4. Alluvial River Width Variability

   https://doi.org/10.4211/hs.56e0ac25249d4451845a843eb3154954  

   Phillips, Colin (November 2024, HydroShare)

   Data compilations of bankfull downstream hydraulic geometry for alluvial rivers, lidar derived high-resolution spatial series of bankfull width for 67 sites, and hydrograph metrics for sites with USGS hydrographs. This compilation is composed of three datasets: (1) a compilation of alluvial river geometry at bankfull for a variety of hydraulic attributes; (2) x, y, and z coordinates of channel bank lines for a selection of sites and their associated river widths derived from high-resolution lidar topography; and (3) statistics describing the hydrographs for a subset of the larger compilation. These data are divided into two primary sets, the larger compilation and a smaller set of sites where the bankfull width was derived from lidar topography. For the high-resolution dataset, the data are available as the coordinates of the bank lines, spatial series of distance downstream and bankfull width, and the spatial series filtered for quality. 

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5. Width Helps and Hinders Splitting Flows

   https://doi.org/10.1145/3641820  

   Cáceres, Manuel; Cairo, Massimo; Grigorjew, Andreas; Khan, Shahbaz; Mumey, Brendan; Rizzi, Romeo; Tomescu, Alexandru I.; Williams, Lucia (April 2024, ACM Transactions on Algorithms)

   Minimum flow decomposition (MFD) is the NP-hard problem of finding a smallest decomposition of a network flow/circulationXon a directed graphGinto weighted source-to-sink paths whose weighted sum equalsX. We show that, for acyclic graphs, considering thewidthof the graph (the minimum number of paths needed to cover all of its edges) yields advances in our understanding of its approximability. For the version of the problem that uses only non-negative weights, we identify and characterise a new class ofwidth-stablegraphs, for which a popular heuristic is aO(logVal(X))-approximation (Val(X) being the total flow ofX), and strengthen its worst-case approximation ratio from\(\Omega (\sqrt {m})\)to Ω (m/logm) for sparse graphs, wheremis the number of edges in the graph. We also study a new problem on graphs with cycles, Minimum Cost Circulation Decomposition (MCCD), and show that it generalises MFD through a simple reduction. For the version allowing also negative weights, we give a (⌈ log ‖ X ‖ ⌉ +1)-approximation (‖X‖ being the maximum absolute value ofXon any edge) using a power-of-two approach, combined with parity fixing arguments and a decomposition of unitary circulations (‖X‖ ≤ 1), using a generalised notion of width for this problem. Finally, we disprove a conjecture about the linear independence of minimum (non-negative) flow decompositions posed by Kloster et al. [2018], but show that its useful implication (polynomial-time assignments of weights to a given set of paths to decompose a flow) holds for the negative version. 

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