665 research outputs found
Regulation of neuronal excitability through pumilio-dependent control of a sodium channel gene
Dynamic changes in synaptic connectivity and strength, which occur during both embryonic development and learning, have the tendency to destabilize neural circuits. To overcome this, neurons have developed a diversity of homeostatic mechanisms to maintain firing within physiologically defined limits. In this study, we show that activity-dependent control of mRNA for a specific voltage-gated Na+ channel [encoded by paralytic (para)] contributes to the regulation of membrane excitability in Drosophila motoneurons. Quantification of para mRNA, by real-time reverse-transcription PCR, shows that levels are significantly decreased in CNSs in which synaptic excitation is elevated, whereas, conversely, they are significantly increased when synaptic vesicle release is blocked. Quantification of mRNA encoding the translational repressor pumilio (pum) reveals a reciprocal regulation to that seen for para. Pumilio is sufficient to influence para mRNA. Thus, para mRNA is significantly elevated in a loss-of-function allele of pum (pumbemused), whereas expression of a full-length pum transgene is sufficient to reduce para mRNA. In the absence of pum, increased synaptic excitation fails to reduce para mRNA, showing that Pum is also necessary for activity-dependent regulation of para mRNA. Analysis of voltage-gated Na+ current (INa) mediated by para in two identified motoneurons (termed aCC and RP2) reveals that removal of pum is sufficient to increase one of two separable INa components (persistent INa), whereas overexpression of a pum transgene is sufficient to suppress both components (transient and persistent). We show, through use of anemone toxin (ATX II), that alteration in persistent INa is sufficient to regulate membrane excitability in these two motoneurons
On character amenability of Banach algebras
AbstractWe continue our work [E. Kaniuth, A.T. Lau, J. Pym, On φ-amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc. 144 (2008) 85–96] in the study of amenability of a Banach algebra A defined with respect to a character φ of A. Various necessary and sufficient conditions of a global and a pointwise nature are found for a Banach algebra to possess a φ-mean of norm 1. We also completely determine the size of the set of φ-means for a separable weakly sequentially complete Banach algebra A with no φ-mean in A itself. A number of illustrative examples are discussed
Definite Formulae, Negation-as-Failure, and the Base-extension Semantics of Intuitionistic Propositional Logic
Proof-theoretic semantics (P-tS) is the paradigm of semantics in which
meaning in logic is based on proof (as opposed to truth). A particular instance
of P-tS for intuitionistic propositional logic (IPL) is its base-extension
semantics (B-eS). This semantics is given by a relation called support,
explaining the meaning of the logical constants, which is parameterized by
systems of rules called bases that provide the semantics of atomic
propositions. In this paper, we interpret bases as collections of definite
formulae and use the operational view of the latter as provided by uniform
proof-search -- the proof-theoretic foundation of logic programming (LP) -- to
establish the completeness of IPL for the B-eS. This perspective allows
negation, a subtle issue in P-tS, to be understood in terms of the
negation-as-failure protocol in LP. Specifically, while the denial of a
proposition is traditionally understood as the assertion of its negation, in
B-eS we may understand the denial of a proposition as the failure to find a
proof of it. In this way, assertion and denial are both prime concepts in P-tS.Comment: submitte
Proof-theoretic Semantics and Tactical Proof
The use of logical systems for problem-solving may be as diverse as in
proving theorems in mathematics or in figuring out how to meet up with a
friend. In either case, the problem solving activity is captured by the search
for an \emph{argument}, broadly conceived as a certificate for a solution to
the problem. Crucially, for such a certificate to be a solution, it has be
\emph{valid}, and what makes it valid is that they are well-constructed
according to a notion of inference for the underlying logical system. We
provide a general framework uniformly describing the use of logic as a
mathematics of reasoning in the above sense. We use proof-theoretic validity in
the Dummett-Prawitz tradition to define validity of arguments, and use the
theory of tactical proof to relate arguments, inference, and search.Comment: submitte
Defining Logical Systems via Algebraic Constraints on Proofs
We comprehensively present a program of decomposition of proof systems for
non-classical logics into proof systems for other logics, especially classical
logic, using an algebra of constraints. That is, one recovers a proof system
for a target logic by enriching a proof system for another, typically simpler,
logic with an algebra of constraints that act as correctness conditions on the
latter to capture the former; for example, one may use Boolean algebra to give
constraints in a sequent calculus for classical propositional logic to produce
a sequent calculus for intuitionistic propositional logic. The idea behind such
forms of reduction is to obtain a tool for uniform and modular treatment of
proof theory and provide a bridge between semantics logics and their proof
theory. The article discusses the theoretical background of the project and
provides several illustrations of its work in the field of intuitionistic and
modal logics. The results include the following: a uniform treatment of modular
and cut-free proof systems for a large class of propositional logics; a general
criterion for a novel approach to soundness and completeness of a logic with
respect to a model-theoretic semantics; and a case study deriving a
model-theoretic semantics from a proof-theoretic specification of a logic.Comment: submitte
From Proof-theoretic Validity to Base-extension Semantics for Intuitionistic Propositional Logic
Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on
\emph{proof} (as opposed to truth). There are two major approaches to P-tS:
proof-theoretic validity (P-tV) and base-extension semantics (B-eS). The former
is a semantics of arguments, and the latter is a semantics of logical constants
in a logic. This paper demonstrates that the B-eS for intuitionistic
propositional logic (IPL) encapsulates the declarative content of a basic
version of P-tV. Such relationships have been considered before yielding
incompleteness results. This paper diverges from these approaches by accounting
for the constructive, hypothetical setup of P-tV. It explicates how the B-eS
for IPL works
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic
This work is the first exploration of proof-theoretic semantics for a
substructural logic. It focuses on the base-extension semantics (B-eS) for
intuitionistic multiplicative linear logic (IMLL). The starting point is a
review of Sandqvist's B-eS for intuitionistic propositional logic (IPL), for
which we propose an alternative treatment of conjunction that takes the form of
the generalized elimination rule for the connective. The resulting semantics is
shown to be sound and complete. This motivates our main contribution, a B-eS
for IMLL, in which the definitions of the logical constants all take the form
of their elimination rule and for which soundness and completeness are
established.Comment: 27 page
Trust economics feasibility study
We believe that enterprises and other organisations currently lack sophisticated methods and tools to determine if and how IT changes should be introduced in an organisation, such that objective, measurable goals are met. This is especially true when dealing with security-related IT decisions. We report on a feasibility study, Trust Economics, conducted to demonstrate that such methodology can be developed. Assuming a deep understanding of the IT involved, the main components of our trust economics approach are: (i) assess the economic or financial impact of IT security solutions; (ii) determine how humans interact with or respond to IT security solutions; (iii) based on above, use probabilistic and stochastic modelling tools to analyse the consequences of IT security decisions. In the feasibility study we apply the trust economics methodology to address how enterprises should protect themselves against accidental or malicious misuse of USB memory sticks, an acute problem in many industries
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