TY - JOUR
AB - Traditional scientific conferences and seminar events have been hugely disrupted by the COVID-19 pandemic, paving the way for virtual forms of scientific communication to take hold and be put to the test.
AU - Bozelos, Panagiotis
AU - Vogels, Tim P
ID - 8757
IS - 1
JF - Nature Reviews Neuroscience
SN - 1471003X
TI - Talking science, online
VL - 22
ER -
TY - JOUR
AB - Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell.
AU - Brown, Adam
AU - Romanov, Anna
ID - 8773
IS - 1
JF - Proceedings of the American Mathematical Society
KW - Applied Mathematics
KW - General Mathematics
SN - 0002-9939
TI - Contravariant forms on Whittaker modules
VL - 149
ER -
TY - JOUR
AB - We study optimal election sequences for repeatedly selecting a (very) small group of leaders among a set of participants (players) with publicly known unique ids. In every time slot, every player has to select exactly one player that it considers to be the current leader, oblivious to the selection of the other players, but with the overarching goal of maximizing a given parameterized global (“social”) payoff function in the limit. We consider a quite generic model, where the local payoff achieved by a given player depends, weighted by some arbitrary but fixed real parameter, on the number of different leaders chosen in a round, the number of players that choose the given player as the leader, and whether the chosen leader has changed w.r.t. the previous round or not. The social payoff can be the maximum, average or minimum local payoff of the players. Possible applications include quite diverse examples such as rotating coordinator-based distributed algorithms and long-haul formation flying of social birds. Depending on the weights and the particular social payoff, optimal sequences can be very different, from simple round-robin where all players chose the same leader alternatingly every time slot to very exotic patterns, where a small group of leaders (at most 2) is elected in every time slot. Moreover, we study the question if and when a single player would not benefit w.r.t. its local payoff when deviating from the given optimal sequence, i.e., when our optimal sequences are Nash equilibria in the restricted strategy space of oblivious strategies. As this is the case for many parameterizations of our model, our results reveal that no punishment is needed to make it rational for the players to optimize the social payoff.
AU - Zeiner, Martin
AU - Schmid, Ulrich
AU - Chatterjee, Krishnendu
ID - 8793
IS - 1
JF - Discrete Applied Mathematics
SN - 0166218X
TI - Optimal strategies for selecting coordinators
VL - 289
ER -
TY - JOUR
AB - Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.
AU - Runkel, Ingo
AU - Szegedy, Lorant
ID - 8816
IS - 1
JF - Communications in Mathematical Physics
SN - 00103616
TI - Area-dependent quantum field theory
VL - 381
ER -
TY - JOUR
AB - The hippocampus has a major role in encoding and consolidating long-term memories, and undergoes plastic changes during sleep1. These changes require precise homeostatic control by subcortical neuromodulatory structures2. The underlying mechanisms of this phenomenon, however, remain unknown. Here, using multi-structure recordings in macaque monkeys, we show that the brainstem transiently modulates hippocampal network events through phasic pontine waves known as pontogeniculooccipital waves (PGO waves). Two physiologically distinct types of PGO wave appear to occur sequentially, selectively influencing high-frequency ripples and low-frequency theta events, respectively. The two types of PGO wave are associated with opposite hippocampal spike-field coupling, prompting periods of high neural synchrony of neural populations during periods of ripple and theta instances. The coupling between PGO waves and ripples, classically associated with distinct sleep stages, supports the notion that a global coordination mechanism of hippocampal sleep dynamics by cholinergic pontine transients may promote systems and synaptic memory consolidation as well as synaptic homeostasis.
AU - Ramirez Villegas, Juan F
AU - Besserve, Michel
AU - Murayama, Yusuke
AU - Evrard, Henry C.
AU - Oeltermann, Axel
AU - Logothetis, Nikos K.
ID - 8818
IS - 7840
JF - Nature
SN - 00280836
TI - Coupling of hippocampal theta and ripples with pontogeniculooccipital waves
VL - 589
ER -