Small Bialgebras with a Projection: Applications

In this paper we continue the investigation started in [A.M.St.-Small], dealing with bialgebras $A$ with an $H$-bilinear coalgebra projection over an arbitrary subbialgebra $H$ with antipode. These bialgebras can be described as deformed bosonizations R#_{\xi} H of a pre-bialgebra $R$ by $H$ with a cocycle $\xi$. Here we describe the behavior of $\xi$ in the case when $R$ is f.d. and thin i.e. it is connected with one dimensional space of primitive elements. This is used to analyze the arithmetic properties of $A$. Meaningful results are obtained when $H$ is cosemisimple. By means of Ore extension construction, we provide some examples of atypical situations (e.g. the multiplication of $R$ is not $H$-colinear or $\xi$ is non-trivial)

Categories of comodules and chain complexes of modules

Let \lL(A) denote the coendomorphism left $R$-bialgebroid associated to a left finitely generated and projective extension of rings $R \to A$ with identities. We show that the category of left comodules over an epimorphic image of \lL(A) is equivalent to the category of chain complexes of left $R$-modules. This equivalence is monoidal whenever $R$ is commutative and $A$ is an $R$-algebra. This is a generalization, using entirely new tools, of results by B. Pareigis and D. Tambara for chain complexes of vector spaces over fields. Our approach relies heavily on the non commutative theory of Tannaka reconstruction, and the generalized faithfully flat descent for small additive categories, or rings with enough orthogonal idempotents.Comment: The title has been changed, the first part is removed and the construction of the coendomorphim bialgebroid is now freely used in the statement of the main Theorem

Noninteracting control with stability for Hamiltonian systems

Published versio

Braided Bialgebras of Type One

Braided bialgebras of type one in abelian braided monoidal categories are characterized as braided graded bialgebras which are strongly $\mathbb{N}$-graded both as an algebra and as a coalgebra

Anion and cation permeability of the mouse tmem16f calcium-activated channel

TMEM16F is involved in several physiological processes, such as blood coagulation, bone development and virus infections. This protein acts both as a Ca2+-dependent phospholipid scram-blase and a Ca2+-activated ion channel but several studies have reported conflicting results about the ion selectivity of the TMEM16F-mediated current. Here, we have performed a detailed side-by-side comparison of the ion selectivity of TMEM16F using the whole-cell and inside-out excised patch configurations to directly compare the results. In inside-out configuration, Ca2+-dependent activation was fast and the TMEM16F-mediated current was activated in a few milliseconds, while in whole-cell recordings full activation required several minutes. We determined the relative permeability between Na+ and Cl¯ (PNa /PCl ) using the dilution method in both configurations. The TMEM16F-mediated current was highly nonselective, but there were differences depending on the configuration of the recordings. In whole-cell recordings, PNa /PCl was approximately 0.5, indicating a slight preference for Cl¯ permeation. In contrast, in inside-out experiments the TMEM16F channel showed a higher permeability for Na+ with PNa /PCl reaching 3.7. Our results demonstrate that the time dependence of Ca2+ activation and the ion selectivity of TMEM16F depend on the recording configuration

Cotensor Coalgebras in Monoidal Categories

We introduce the concept of cotensor coalgebra for a given bicomodule over a coalgebra in an abelian monoidal category. Under some further conditions we show that such a cotensor coalgebra exists and satisfies a meaningful universal property. We prove that this coalgebra is formally smooth whenever the comodule is relative injective and the coalgebra itself is formally smooth

Modulation by internal protons of native cyclic nucleotide-gated channels from retinal rods

Ion channels directly activated by cyclic nucleotides are present in the plasma membrane of retinal rod outer segments. These channels can be modulated by several factors including internal pH (pH(i)). Native cyclic nucleotide-gated channels were studied in excised membrane patches from the outer segment of retinal rods of the salamander. Channels were activated by cGMP or cAMP and currents as a function of voltage and cyclic nucleotide concentrations were measured as pH(i) was varied between 7.6 and 5.0. Increasing internal proton concentrations reduced the current activated by cGMP without modifying the concentration (K(1/2)) of cGMP necessary for half-activation of the maximal current. This effect could be well described as a reduction of single-channel current by protonation of a single acidic residue with a pK(1) of 5.1. When channels were activated by cAMP a more complex phenomenon was observed. K(1/2) for cAMP decreased by increasing internal proton concentration whereas maximal currents activated by cAMP increased by lowering pH(i) from 7.6 to 5.7-5.5 and then decreased from pH(i) 5.5 to 5.0. This behavior was attributed both to a reduction in single-channel current as measured with cGMP and to an increase in channel open probability induced by the binding of three protons to sites with a pK(2) of 6

Design of controllers for hybrid linear systems with impulsive inputs and periodic jumps

In this study, the problem of designing a controller for a hybrid system with impulsive input and periodic jumps is addressed. In particular, it is shown that any hybrid system with impulsive inputs and periodic jumps can be recast into a discrete-time, linear, time-invariant system, which, in turn, can be used to design a controller by using classical methods. Furthermore, it is shown that, once such a controller has been designed, it can be readily used to control the hybrid system by mean of an interfacing system that is based just on the continuous-time dynamics of the plant to be controlled. Several examples, spanning from aerospace to biomedical applications, are reported in order to corroborate the theoretical results