10,754 research outputs found
Information and The Brukner-Zeilinger Interpretation of Quantum Mechanics: A Critical Investigation
In Brukner and Zeilinger's interpretation of quantum mechanics, information
is introduced as the most fundamental notion and the finiteness of information
is considered as an essential feature of quantum systems. They also define a
new measure of information which is inherently different from the Shannon
information and try to show that the latter is not useful in defining the
information content in a quantum object.
Here, we show that there are serious problems in their approach which make
their efforts unsatisfactory. The finiteness of information does not explain
how objective results appear in experiments and what an instantaneous change in
the so-called information vector (or catalog of knowledge) really means during
the measurement. On the other hand, Brukner and Zeilinger's definition of a new
measure of information may lose its significance, when the spin measurement of
an elementary system is treated realistically. Hence, the sum of the individual
measures of information may not be a conserved value in real experiments.Comment: 20 pages, two figures, last version. Section 4 is replaced by a new
argument. Other sections are improved. An appendix and new references are
adde
A Field-theoretical Interpretation of the Holographic Renormalization Group
A quantum-field theoretical interpretation is given to the holographic RG
equation by relating it to a field-theoretical local RG equation which
determines how Weyl invariance is broken in a quantized field theory. Using
this approach we determine the relation between the holographic C theorem and
the C theorem in two-dimensional quantum field theory which relies on the
Zamolodchikov metric. Similarly we discuss how in four dimensions the
holographic C function is related to a conjectured field-theoretical C
function. The scheme dependence of the holographic RG due to the possible
presence of finite local counterterms is discussed in detail, as well as its
implications for the holographic C function. We also discuss issues special to
the situation when mass deformations are present. Furthermore we suggest that
the holographic RG equation may also be obtained from a bulk diffeomorphism
which reduces to a Weyl transformation on the boundary.Comment: 24 pages, LaTeX, no figures; references added, typos corrected,
paragraph added to section
Finiteness and children with specific language impairment: an exploratory study
Children with specific language impairment (SLI) are well known for their difficulties in mastering the inflectional paradigms; in the case of learning German they also have problems with the appropriate verb position, in particular with the verb in second position. This paper explores the possibilities of applying a broader concept of finiteness to data from children with SLI in order to put their deficits, or rather their skills, into a wider perspective. The concept, as developed by Klein (1998, 2000), suggests that finiteness is tied to the assertion that a certain state of affairs is valid with regard to some topic time; that is, finiteness relates the propositional content to the topic component. Its realization involves the interaction of various grammatical devices and, possibly, lexical means like temporal adverbs. Furthermore, in the acquisition of finiteness it has been found that scope particles play a major role in both first- and second-language learning. The purpose of this paper is to analyze to what extent three German-learning children with SLI have mastered these grammatical and lexical means and to pinpoint the phase in the development of finiteness they have reached. The data to be examined are mostly narrative and taken from conversations and experiments. It will be shown that each child chooses a different developmental path to come to grips with the interaction of these devices
Beyond cash-additive risk measures: when changing the num\'{e}raire fails
We discuss risk measures representing the minimum amount of capital a
financial institution needs to raise and invest in a pre-specified eligible
asset to ensure it is adequately capitalized. Most of the literature has
focused on cash-additive risk measures, for which the eligible asset is a
risk-free bond, on the grounds that the general case can be reduced to the
cash-additive case by a change of numeraire. However, discounting does not work
in all financially relevant situations, typically when the eligible asset is a
defaultable bond. In this paper we fill this gap allowing for general eligible
assets. We provide a variety of finiteness and continuity results for the
corresponding risk measures and apply them to risk measures based on
Value-at-Risk and Tail Value-at-Risk on spaces, as well as to shortfall
risk measures on Orlicz spaces. We pay special attention to the property of
cash subadditivity, which has been recently proposed as an alternative to cash
additivity to deal with defaultable bonds. For important examples, we provide
characterizations of cash subadditivity and show that, when the eligible asset
is a defaultable bond, cash subadditivity is the exception rather than the
rule. Finally, we consider the situation where the eligible asset is not
liquidly traded and the pricing rule is no longer linear. We establish when the
resulting risk measures are quasiconvex and show that cash subadditivity is
only compatible with continuous pricing rules
Proof of ultra-violet finiteness for a planar non-supersymmetric Yang-Mills theory
This paper focuses on a three-parameter deformation of N=4 Yang-Mills that
breaks all the supersymmetry in the theory. We show that the resulting
non-supersymmetric gauge theory is scale invariant, in the planar
approximation, by proving that its Green functions are ultra-violet finite to
all orders in light-cone perturbation theory.Comment: 13 pages, 1 figure; v2: minor correction
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Modelling syntactic development in a cross-linguistic context
Mainstream linguistic theory has traditionally assumed that children come into the world with rich innate knowledge about language and grammar. More recently, computational work using distributional algorithms has shown that the information contained in the input is much richer than proposed by the nativist approach. However, neither of these approaches has been developed to the point of providing detailed and quantitative predictions about the developmental data. In this paper, we champion a third approach, in which computational models learn from naturalistic input and produce utterances that can be directly compared with the utterances of language-learning children. We demonstrate the feasibility of this approach by showing how MOSAIC, a simple distributional analyser, simulates the optional-infinitive phenomenon in English, Dutch, and Spanish. The model accounts for young children's tendency to use both correct finites and incorrect (optional) infinitives in finite contexts, for the generality of this phenomenon across languages, and for the sparseness of other types of errors (e.g., word order errors). It thus shows how these phenomena, which have traditionally been taken as evidence for innate knowledge of Universal Grammar, can be explained in terms of a simple distributional analysis of the language to which children are exposed
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