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The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventies of the twentieth century by B. Zelinka and the first author (see e.g. [6] and the monograph [1] and the references therein). Since tolerances need not be transitive, their blocks may overlap and hence in general the set of all blocks of a tolerance cannot be converted into a quotient algebra in the same way as in the case of congruences. However, G. Czédli ([7]) showed that lattices can be factorized by means of tolerances in a natural way, and J. Grygiel and S. Radeleczki ([8]) proved some variant of an Isomorphism Theorem for tolerances on lattices. The aim of the present paper is to extend the concept of a tolerance on a lattice to posets in such a way that results similar to those obtained for tolerances on lattices can be derived. [ABSTRACT FROM AUTHOR]

Information is often described as a reduction of uncertainty associated with a restriction of possible choices. Despite appearing in Hartley's foundational work on information theory, there is a surprising lack of a formal treatment of this interpretation in terms of exclusions. This paper addresses the gap by providing an explicit characterisation of information in terms of probability mass exclusions. It then demonstrates that different exclusions can yield the same amount of information and discusses the insight this provides about how information is shared amongst random variables—lack of progress in this area is a key barrier preventing us from understanding how information is distributed in complex systems. The paper closes by deriving a decomposition of the mutual information which can distinguish between differing exclusions; this provides surprising insight into the nature of directed information. [ABSTRACT FROM AUTHOR]

Information is often described as a reduction of uncertainty associated with a restriction of possible choices. Despite appearing in Hartley’s foundational work on information theory, there is a surprising lack of a formal treatment of this interpretation in terms of exclusions. This paper addresses the gap by providing an explicit characterisation of information in terms of probability mass exclusions. It then demonstrates that different exclusions can yield the same amount of information and discusses the insight this provides about how information is shared amongst random variables—lack of progress in this area is a key barrier preventing us from understanding how information is distributed in complex systems. The paper closes by deriving a decomposition of the mutual information which can distinguish between differing exclusions; this provides surprising insight into the nature of directed information.

This brief addresses the cooperative formation of self-propelled vehicles via the phase-based steering control. When the steering control law is designed for a directed Kuramoto-oscillator model with a pacemaker, all agents almost globally converge to either the synchronized formation or a two-cluster formation, if the following two conditions hold: 1) the augmented digraph contains a directed spanning tree and satisfies the decoupling assumption and 2) one of the strengths that influenced by the pacemaker is larger than the critical value. Cooperative formation in the case of pacemaker-free steering control may also hold under its conditions. Numerical examples illustrate the effectiveness of the derived analytical results. [ABSTRACT FROM AUTHOR]

A simple, high-yield procedure has been developed for the ortho-lithiation and subsequent ortho-substitution of phenols by a manifold of electrophiles. N,C-Dilithiation of O-aryl N-monoalkylcarbamates proved to be impossible due to a cleavage reaction of the monolithiated intermediates. However, in situ N-silylation of O-aryl N-isopropylcarbamates proceeds smoothly with trialkylsilyl triflates – N,N,N',N'-tetramethylethylenediamine (TMEDA). Separation of the formed O-aryl N-isopropyl-N-trialkylsilylcarbamates from the byproduct TMEDA·HOTf, which is insoluble in diethyl ether or toluene, is not required. ortho-Lithiation with n-butyllithium–TMEDA at –78°C leads to the corresponding aryllithium, which does not undergo anionic ortho-Fries rearrangement under the reaction conditions, but is efficiently substituted by electrophilic reagents. During the aqueous work-up, the N-silyl group is removed and the corresponding ortho-substituted O-aryl N-isopropylcarbamate is isolated. Among the introduced electrophiles are: Me[sub 3] Si, Bu[sub 3] Sn, PhS, I, Br, Cl, alkyl, α-hydroxyalkyl. Liberation of the free phenols is performed under mild alkaline conditions.Key words: directed ortho-metalation, ortho-lithiated O-aryl carbamates, ortho-substituted phenols, in situ protection of N-monoalkylcarbamates.On a mis au point une méthode simple qui permet d'effectuer avec des rendements élevés l'ortho-lithiation et l'ortho-substitution subséquente de phénols par un grand nombre d'électrophiles. Les N,C-dilithiations d'O-aryl N-monoalkylcarbamates s'avèrent impossibles en raison de la réaction de clivage des intermédiaires monolithiés. Toutefois, la N-silylation in situ des O-aryl N-isopropylcarbamates peut être réalisée facilement avec les couples triflates de trialkylsilyle – N,N,N',N'-tétraméthyléthylènediamine (TMEDA). Il n'est pas nécessaire de séparer les O-aryl N-isopropyl-N-trialkylsilylcarbamates des sous-produits, TMEDA·HOTf qui sont insolubles dans l'éther éthylique ou le toluène. L'ortho-lithiation avec du n-butyllithium–TMEDA, à –78°C, conduit à la formation de l'aryllithien correspondant, qui ne donne pas lieu à un réarrangement d'ortho-Fries anionique dans les conditions de la réaction mais qui donne lieu à des réactions de substitution sous l'influence de réactifs électrophiles. Lors de la procédure d'extraction, le groupe N-silyle est éliminé et on peut isoler le O-aryl N-isopropylcarbamate ortho-substitué. Les électrophiles qui ont été introduits sont: Me[sub 3] Si, Bu[sub 3] Sn, PhS, I, Br, Cl, alkyle, α-hydroxyalkyle. La libération des phénols se fait dans des conditions alcalines douces.Mots clés : ortho-métallation orientée, O-aryl carbamates ortho-lithiés, phénols ortho-substitués, protection in situ de N-monoalkylcarbamates.[Traduit par la Rédaction] [ABSTRACT FROM AUTHOR]