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1. Signed permutohedra, delta‐matroids, and beyond

   https://doi.org/10.1112/plms.12592  

   Eur, Christopher; Fink, Alex; Larson, Matt; Spink, Hunter (March 2024, Proceedings of the London Mathematical Society)

   Abstract We establish a connection between the algebraic geometry of the type permutohedral toric variety and the combinatorics of delta‐matroids. Using this connection, we compute the volume and lattice point counts of type generalized permutohedra. Applying tropical Hodge theory to a new framework of “tautological classes of delta‐matroids,” modeled after certain vector bundles associated to realizable delta‐matroids, we establish the log‐concavity of a Tutte‐like invariant for a broad family of delta‐matroids that includes all realizable delta‐matroids. Our results include new log‐concavity statements for all (ordinary) matroids as special cases. 

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2. Vandermondes, superspace, and Delta conjecture modules

   Rhoades, B.; Wilson, A. T. (January 2020, Formal power series and algebraic combinatorics)

   null (Ed.)
3. Delta Embedding Learning

   https://doi.org/10.18653/v1/P19-1322  

   Zhang, Xiao; Wu, Ji; Dou, Dejing (January 2019, Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics)

   Unsupervised word embeddings have become a popular approach of word representation in NLP tasks. However there are limitations to the semantics represented by unsupervised embeddings, and inadequate fine-tuning of embeddings can lead to suboptimal performance. We propose a novel learning technique called Delta Embedding Learning, which can be applied to general NLP tasks to improve performance by optimized tuning of the word embeddings. A structured regularization is applied to the embeddings to ensure they are tuned in an incremental way. As a result, the tuned word embeddings become better word representations by absorbing semantic information from supervision without “forgetting.” We apply the method to various NLP tasks and see a consistent improvement in performance. Evaluation also confirms the tuned word embeddings have better semantic properties. 

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4. Delta Compression Techniques

   https://doi.org/10.1007/978-3-319-63962-8_63-1  

   Suel, Torsten (January 2019, Encyclopedia of Big Data Technologies)
5. A global delta dataset and the environmental variables that predict delta formation on marine coastlines

   https://doi.org/10.5194/esurf-7-773-2019  

   Caldwell, Rebecca L.; Edmonds, Douglas A.; Baumgardner, Sarah; Paola, Chris; Roy, Samapriya; Nienhuis, Jaap H. (January 2019, Earth Surface Dynamics)

   Abstract. River deltas are sites of sediment accumulation along thecoastline that form critical biological habitats, host megacities, andcontain significant quantities of hydrocarbons. Despite their importance, wedo not know which factors most significantly promote sediment accumulationand dominate delta formation. To investigate this issue, we present a globaldataset of 5399 coastal rivers and data on eight environmental variables.Of these rivers, 40 % (n=2174) have geomorphic deltas defined eitherby a protrusion from the regional shoreline, a distributary channel network,or both. Globally, coastlines average one delta forevery ∼300 km of shoreline, but there are hotspots of delta formation, for examplein Southeast Asia where there is one delta per 100 km of shoreline. Ouranalysis shows that the likelihood of a river to form a delta increases withincreasing water discharge, sediment discharge, and drainage basin area. Onthe other hand, delta likelihood decreases with increasing wave height andtidal range. Delta likelihood has a non-monotonic relationship withreceiving-basin slope: it decreases with steeper slopes, but for slopes >0.006 delta likelihood increases. This reflects differentcontrols on delta formation on active versus passive margins. Sedimentconcentration and recent sea level change do not affect delta likelihood. Alogistic regression shows that water discharge, sediment discharge, waveheight, and tidal range are most important for delta formation. The logisticregression correctly predicts delta formation 74 % of the time. Our globalanalysis illustrates that delta formation and morphology represent a balancebetween constructive and destructive forces, and this framework may helppredict tipping points at which deltas rapidly shift morphologies. 

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