700 research outputs found
Positive Geometries and Differential Forms with Non-Logarithmic Singularities I
Positive geometries encode the physics of scattering amplitudes in flat
space-time and the wavefunction of the universe in cosmology for a large class
of models. Their unique canonical forms, providing such quantum mechanical
observables, are characterised by having only logarithmic singularities along
all the boundaries of the positive geometry. However, physical observables have
logarithmic singularities just for a subset of theories. Thus, it becomes
crucial to understand whether a similar paradigm can underlie their structure
in more general cases. In this paper we start a systematic investigation of a
geometric-combinatorial characterisation of differential forms with
non-logarithmic singularities, focusing on projective polytopes and related
meromorphic forms with multiple poles. We introduce the notions of covariant
forms and covariant pairings. Covariant forms have poles only along the
boundaries of the given polytope; moreover, their leading Laurent coefficients
along any of the boundaries are still covariant forms on the specific boundary.
Whereas meromorphic forms in covariant pairing with a polytope are associated
to a specific (signed) triangulation, in which poles on spurious boundaries do
not cancel completely, but their order is lowered. These meromorphic forms can
be fully characterised if the polytope they are associated to is viewed as the
restriction of a higher dimensional one onto a hyperplane. The canonical form
of the latter can be mapped into a covariant form or a form in covariant
pairing via a covariant restriction. We show how the geometry of the higher
dimensional polytope determines the structure of these differential forms.
Finally, we discuss how these notions are related to Jeffrey-Kirwan residues
and cosmological polytopes.Comment: 47 pages, figures in Tik
Type Annotation for Adaptive Systems
We introduce type annotations as a flexible typing mechanism for graph
systems and discuss their advantages with respect to classical typing based on
graph morphisms. In this approach the type system is incorporated with the
graph and elements can adapt to changes in context by changing their type
annotations. We discuss some case studies in which this mechanism is relevant.Comment: In Proceedings GaM 2016, arXiv:1612.0105
Conditions, constraints and contracts: on the use of annotations for policy modeling.
Organisational policies express constraints on generation and processing of resources. However, application domains rely on transformation processes, which are in principle orthogonal to policy specifications and domain rules and policies may evolve in a non-synchronised way. In previous papers, we have proposed annotations as a flexible way to model aspects of some policy, and showed how they could be used to impose constraints on domain configurations, how to derive application conditions on transformations, and how to annotate complex patterns. We extend the approach by: allowing domain model elements to be annotated with collections of elements, which can be collectively applied to individual resources or collections thereof; proposing an original construction to solve the problem of annotations remaining orphan , when annotated resources are consumed; introducing a notion of contract, by which a policy imposes additional pre-conditions and post-conditions on rules for deriving new resources. We discuss a concrete case study of linguistic resources, annotated with information on the licenses under which they can be used. The annotation framework allows forms of reasoning such as identifying conflicts among licenses, enforcing the presence of licenses, or ruling out some modifications of a licence configuration
Ictal epileptic headache. an old story with courses and appeals
The term "ictal epileptic headache" has been recently proposed to classify the clinical picture in which headache is the isolated ictal symptom of a seizure. There is emerging evidence from both basic and clinical neurosciences that cortical spreading depression and an epileptic focus may facilitate each other, although with a different degree of efficiency. This review address the long history which lead to the 'migralepsy' concept to the new emerging pathophysiological aspects, and clinical and electroencephalography evidences of ictal epileptic headache. Here, we review and discuss the common physiopathology mechanisms and the historical aspects underlying the link between headache and epilepsy. Either experimental or clinical measures are required to better understand this latter relationship: the development of animal models, molecular studies defining more precise genotype/phenotype correlations as well as multicenter clinical studies with revision of clinical criteria for headache-/epilepsy-related disorders represent the start of future research. Therefore, the definition of ictal epileptic headache should be used to classify the rare events in which headache is the only manifestation of a seizure. Finally, using our recently published criteria, we will be able to clarify if ictal epileptic headache represents an underestimated phenomenon or not
Cross correlations of the American baby names
The quantitative description of cultural evolution is a challenging task. The
most difficult part of the problem is probably to find the appropriate
measurable quantities that can make more quantitative such evasive concepts as,
for example, dynamics of cultural movements, behavior patterns and traditions
of the people. A strategy to tackle this issue is to observe particular
features of human activities, i.e. cultural traits, such as names given to
newborns. We study the names of babies born in the United States of America
from 1910 to 2012. Our analysis shows that groups of different correlated
states naturally emerge in different epochs, and we are able to follow and
decrypt their evolution. While these groups of states are stable across many
decades, a sudden reorganization occurs in the last part of the twentieth
century. We think that this kind of quantitative analysis can be possibly
extended to other cultural traits: although databases covering more than one
century (as the one we used) are rare, the cultural evolution on shorter time
scales can be studied thanks to the fact that many human activities are usually
recorded in the present digital era.Comment: submitted for consideration to PNA
Profit Shifting by Debt Financing in Europe
This article aims at analyzing the link between subsidiaries’ capital structure and taxation in Europe. First we introduce a trade-off model, which studies a MNCs’ financial strategy and shows how debt policy allows multinational groups to shift profits from low-tax to high-tax jurisdictions. By letting the MNC choose both leverage and the percentage of profit shifting, we depart from the relevant literature which has mainly focused on the latter. Using the AMADEUS dataset we show that: i) subsidiaries’ leverage increases with the statutory tax rate, levied in the country where it operates; ii) this positive effect is lower, the higher the parent company tax rate is. Furthermore, an increase in the parent company’s tax rate is estimated to raise its subsidiaries’ leverage.capital structure, default, multinationals, profit shifting, taxation
Scaling and asymptotic scaling in two-dimensional models
Two-dimensional models are investigated by Monte Carlo methods on
the lattice, for values of ranging from 2 to 21. Scaling and rotation
invariance are studied by comparing different definitions of correlation length
. Several lattice formulations are compared and shown to enjoy scaling for
as small as . Asymptotic scaling is investigated using as bare
coupling constant both the usual and (related to the internal
energy); the latter is shown to improve asymptotic scaling properties. Studies
of finite size effects show their -dependence to be highly non-trivial, due
to the increasing radius of the bound states at large .Comment: 5 pages + 12 figures (PostScript), report no. IFUP-TH 46/9
Mosaic multi-state scenario vs. one-state description of supercooled liquids
According to the mosaic scenario, relaxation in supercooled liquids is ruled
by two competing mechanisms: surface tension, opposing the creation of local
excitations, and entropy, providing the drive to the configurational
rearrangement of a given region. We test this scenario through numerical
simulations well below the Mode Coupling temperature. For an equilibrated
configuration, we freeze all the particles outside a sphere and study the
thermodynamics of this sphere. The frozen environment acts as a pinning field.
Measuring the overlap between the unpinned and pinned equilibrium
configurations of the sphere, we can see whether it has switched to a different
state. We do not find any clear evidence of the mosaic scenario. Rather, our
results seem compatible with the existence of a single (liquid) state. However,
we find evidence of a growing static correlation length, apparently unrelated
to the mosaic one.Comment: 4 pages, 3 figures, final version accepted in PR
A Termination Criterion for Graph Transformations with Negative Application Conditions
Termination of graph transformations is in general undecidable, but it is possible to prove it for specific systems by checking for sufficient conditions. In the presence of rules with negative application conditions, the difficulties increase.
In this paper we propose a different approach to the identification of a (sufficient) criterion for termination, based on the construction of a labelled transition system whose states represent overlaps between the negative application condition and the right hand side that can give rise to cycles
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