48,260 research outputs found
An Improved Tight Closure Algorithm for Integer Octagonal Constraints
Integer octagonal constraints (a.k.a. ``Unit Two Variables Per Inequality''
or ``UTVPI integer constraints'') constitute an interesting class of
constraints for the representation and solution of integer problems in the
fields of constraint programming and formal analysis and verification of
software and hardware systems, since they couple algorithms having polynomial
complexity with a relatively good expressive power. The main algorithms
required for the manipulation of such constraints are the satisfiability check
and the computation of the inferential closure of a set of constraints. The
latter is called `tight' closure to mark the difference with the (incomplete)
closure algorithm that does not exploit the integrality of the variables. In
this paper we present and fully justify an O(n^3) algorithm to compute the
tight closure of a set of UTVPI integer constraints.Comment: 15 pages, 2 figure
Magnification Control in Self-Organizing Maps and Neural Gas
We consider different ways to control the magnification in self-organizing
maps (SOM) and neural gas (NG). Starting from early approaches of magnification
control in vector quantization, we then concentrate on different approaches for
SOM and NG. We show that three structurally similar approaches can be applied
to both algorithms: localized learning, concave-convex learning, and winner
relaxing learning. Thereby, the approach of concave-convex learning in SOM is
extended to a more general description, whereas the concave-convex learning for
NG is new. In general, the control mechanisms generate only slightly different
behavior comparing both neural algorithms. However, we emphasize that the NG
results are valid for any data dimension, whereas in the SOM case the results
hold only for the one-dimensional case.Comment: 24 pages, 4 figure
The relation between degrees of belief and binary beliefs: A general impossibility theorem
Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that this problem generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. “Locality” means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the “functionality” restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a “holistic” one. We explore several concrete forms this “holistic” relation could take
An exact solution method for binary equilibrium problems with compensation and the power market uplift problem
We propose a novel method to find Nash equilibria in games with binary
decision variables by including compensation payments and
incentive-compatibility constraints from non-cooperative game theory directly
into an optimization framework in lieu of using first order conditions of a
linearization, or relaxation of integrality conditions. The reformulation
offers a new approach to obtain and interpret dual variables to binary
constraints using the benefit or loss from deviation rather than marginal
relaxations. The method endogenizes the trade-off between overall (societal)
efficiency and compensation payments necessary to align incentives of
individual players. We provide existence results and conditions under which
this problem can be solved as a mixed-binary linear program.
We apply the solution approach to a stylized nodal power-market equilibrium
problem with binary on-off decisions. This illustrative example shows that our
approach yields an exact solution to the binary Nash game with compensation. We
compare different implementations of actual market rules within our model, in
particular constraints ensuring non-negative profits (no-loss rule) and
restrictions on the compensation payments to non-dispatched generators. We
discuss the resulting equilibria in terms of overall welfare, efficiency, and
allocational equity
Combining and Relating Control Effects and their Semantics
Combining local exceptions and first class continuations leads to programs
with complex control flow, as well as the possibility of expressing powerful
constructs such as resumable exceptions. We describe and compare games models
for a programming language which includes these features, as well as
higher-order references. They are obtained by contrasting methodologies: by
annotating sequences of moves with "control pointers" indicating where
exceptions are thrown and caught, and by composing the exceptions and
continuations monads.
The former approach allows an explicit representation of control flow in
games for exceptions, and hence a straightforward proof of definability (full
abstraction) by factorization, as well as offering the possibility of a
semantic approach to control flow analysis of exception-handling. However,
establishing soundness of such a concrete and complex model is a non-trivial
problem. It may be resolved by establishing a correspondence with the monad
semantics, based on erasing explicit exception moves and replacing them with
control pointers.Comment: In Proceedings COS 2013, arXiv:1309.092
The computability path ordering
This paper aims at carrying out termination proofs for simply typed
higher-order calculi automatically by using ordering comparisons. To this end,
we introduce the computability path ordering (CPO), a recursive relation on
terms obtained by lifting a precedence on function symbols. A first version,
core CPO, is essentially obtained from the higher-order recursive path ordering
(HORPO) by eliminating type checks from some recursive calls and by
incorporating the treatment of bound variables as in the com-putability
closure. The well-foundedness proof shows that core CPO captures the essence of
computability arguments \'a la Tait and Girard, therefore explaining its name.
We further show that no further type check can be eliminated from its recursive
calls without loosing well-foundedness, but for one for which we found no
counterexample yet. Two extensions of core CPO are then introduced which allow
one to consider: the first, higher-order inductive types; the second, a
precedence in which some function symbols are smaller than application and
abstraction
Enacting children's citizenship: developing understandings of how children enact themselves as citizens through actions and acts of citizenship
Children have an unsettled relationship with the status of citizenship, being given some rights, responsibilities and opportunities for participation, and being denied others. Yet if citizenship is conceived of as a practice, children can be firmly seen as citizens in the sense that they are social actors, negotiating and contributing to relationships of social interdependence.
This article develops understandings of children’s agency in citizenship and some of the different ways in which children’s actions enact them as interdependent citizens. It presents one aspect of the understanding of citizenship generated from research by six groups of marginalised children, aged 5-13, in Wales and France. Synthesising the research groups’ descriptions of activities they associated with the component parts of citizenship with citizenship theory, these children can be seen to engage in actions of citizenship that include making rules of social existence, furthering social good and exercising freedoms to achieve their own rights. Their activities also transgress the boundaries of existing balances of rights, responsibilities and statuses, through their (mis)behaviour, in ways that can be interpreted as Acts of citizenship. In children’s everyday activities, however, the distinction between actions and Acts of citizenship can at times be blurred. This is because recognizing aspects of children’s practices as citizenship is a challenge to dominant definitions of citizenship, and claims a new status for children. Exploring children’s citizenship in these ways has potential for widening understandings of participation and appreciating broader aspects of children’s agency in citizenship
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