Forecasting the impacts of climate change on species persistence in diverse natural communities requires a way to account for indirect effects mediated through interactions. In particular, we expect experience major changes competition as they track favorable climates. Here, combine experimental data with recently developed theoretical framework based coexistence theory measure impact climate-d...

Biodiversity is being severely affected by global change worldwide, but consequences differ across individual species and environments. Since rarity a condition associated with vulnerability extinction risk, it concerning factor itself that can also amplify the detrimental impact of drivers. Here, we assess differences in derived from environments South European mountain range, Pyrenees, comple...

the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generaliz...