48,882 research outputs found
Delta-Nabla Optimal Control Problems
We present a unified treatment to control problems on an arbitrary time scale
by introducing the study of forward-backward optimal control problems.
Necessary optimality conditions for delta-nabla isoperimetric problems are
proved, and previous results in the literature obtained as particular cases. As
an application of the results of the paper we give necessary and sufficient
Pareto optimality conditions for delta-nabla bi-objective optimal control
problems.Comment: Preprint version of an article submitted 28-Nov-2009; revised
02-Jul-2010; accepted 20-Jul-2010; for publication in Journal of Vibration
and Contro
Optogenetic perturbations reveal the dynamics of an oculomotor integrator
Many neural systems can store short-term information in persistently firing neurons. Such persistent activity is believed to be maintained by recurrent feedback among neurons. This hypothesis has been fleshed out in detail for the oculomotor integrator (OI) for which the so-called “line attractor” network model can explain a large set of observations. Here we show that there is a plethora of such models, distinguished by the relative strength of recurrent excitation and inhibition. In each model, the firing rates of the neurons relax toward the persistent activity states. The dynamics of relaxation can be quite different, however, and depend on the levels of recurrent excitation and inhibition. To identify the correct model, we directly measure these relaxation dynamics by performing optogenetic perturbations in the OI of zebrafish expressing halorhodopsin or channelrhodopsin. We show that instantaneous, inhibitory stimulations of the OI lead to persistent, centripetal eye position changes ipsilateral to the stimulation. Excitatory stimulations similarly cause centripetal eye position changes, yet only contralateral to the stimulation. These results show that the dynamics of the OI are organized around a central attractor state—the null position of the eyes—which stabilizes the system against random perturbations. Our results pose new constraints on the circuit connectivity of the system and provide new insights into the mechanisms underlying persistent activity
Derived equivalence classification of the cluster-tilted algebras of Dynkin type E
We obtain a complete derived equivalence classification of the cluster-tilted
algebras of Dynkin type E. There are 67, 416, 1574 algebras in types E6, E7 and
E8 which turn out to fall into 6, 14, 15 derived equivalence classes,
respectively. This classification can be achieved computationally and we
outline an algorithm which has been implemented to carry out this task. We also
make the classification explicit by giving standard forms for each derived
equivalence class as well as complete lists of the algebras contained in each
class; as these lists are quite long they are provided as supplementary
material to this paper. From a structural point of view the remarkable outcome
of our classification is that two cluster-tilted algebras of Dynkin type E are
derived equivalent if and only if their Cartan matrices represent equivalent
bilinear forms over the integers which in turn happens if and only if the two
algebras are connected by a sequence of "good" mutations. This is reminiscent
of the derived equivalence classification of cluster-tilted algebras of Dynkin
type A, but quite different from the situation in Dynkin type D where a
far-reaching classification has been obtained using similar methods as in the
present paper but some very subtle questions are still open.Comment: 19 pages. v4: completely rewritten version, to appear in Algebr.
Represent. Theory. v3: Main theorem strengthened by including "good"
mutations (cf. also arXiv:1001.4765). Minor editorial changes. v2: Third
author added. Major revision. All questions left open in the earlier version
by the first two authors are now settled in v2 and the derived equivalence
classification is completed. arXiv admin note: some text overlap with
arXiv:1012.466
From non-semisimple Hopf algebras to correlation functions for logarithmic CFT
We use factorizable finite tensor categories, and specifically the
representation categories of factorizable ribbon Hopf algebras H, as a
laboratory for exploring bulk correlation functions in local logarithmic
conformal field theories. For any ribbon Hopf algebra automorphism omega of H
we present a candidate for the space of bulk fields and endow it with a natural
structure of a commutative symmetric Frobenius algebra. We derive an expression
for the corresponding bulk partition functions as bilinear combinations of
irreducible characters; as a crucial ingredient this involves the Cartan matrix
of the category. We also show how for any candidate bulk state space of the
type we consider, correlation functions of bulk fields for closed oriented
world sheets of any genus can be constructed that are invariant under the
natural action of the relevant mapping class group.Comment: 41 pages, several figures. version 2: typos corrected, bibliography
updated, introduction extended, a few minor clarifications adde
Obstructing mucocele of the cystic duct after transplantation of the liver
A tension mucocele was created in three hepatic homografts by ligating a low-lying cystic duct during transplant cholecystectomy and by incorporating its outflow end into the anastomosis of the common hepatic duct to the recipient common duct or Roux limb of jejunum. The consequent complication of obstruction of the biliary tract that necessitated reoperation and excision of the mucocele in all three patients can be avoided by the simple expedient of completely removing the cystic duct when feasible or providing egress to the secretion of the cystic duct as described
Exactly solvable Wadati potentials in the PT-symmetric Gross-Pitaevskii equation
This note examines Gross-Pitaevskii equations with PT-symmetric potentials of
the Wadati type: . We formulate a recipe for the construction of
Wadati potentials supporting exact localised solutions. The general procedure
is exemplified by equations with attractive and repulsive cubic nonlinearity
bearing a variety of bright and dark solitons.Comment: To appear in Proceedings of the 15 Conference on Pseudo-Hermitian
Hamiltonians in Quantum Physics, May 18-23 2015, Palermo, Italy (Springer
Proceedings in Physics, 2016
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