2,618 research outputs found
Derivations and Dirichlet forms on fractals
We study derivations and Fredholm modules on metric spaces with a local
regular conservative Dirichlet form. In particular, on finitely ramified
fractals, we show that there is a non-trivial Fredholm module if and only if
the fractal is not a tree (i.e. not simply connected). This result relates
Fredholm modules and topology, and refines and improves known results on p.c.f.
fractals. We also discuss weakly summable Fredholm modules and the Dixmier
trace in the cases of some finitely and infinitely ramified fractals (including
non-self-similar fractals) if the so-called spectral dimension is less than 2.
In the finitely ramified self-similar case we relate the p-summability question
with estimates of the Lyapunov exponents for harmonic functions and the
behavior of the pressure function.Comment: to appear in the Journal of Functional Analysis 201
Transductive Learning with String Kernels for Cross-Domain Text Classification
For many text classification tasks, there is a major problem posed by the
lack of labeled data in a target domain. Although classifiers for a target
domain can be trained on labeled text data from a related source domain, the
accuracy of such classifiers is usually lower in the cross-domain setting.
Recently, string kernels have obtained state-of-the-art results in various text
classification tasks such as native language identification or automatic essay
scoring. Moreover, classifiers based on string kernels have been found to be
robust to the distribution gap between different domains. In this paper, we
formally describe an algorithm composed of two simple yet effective
transductive learning approaches to further improve the results of string
kernels in cross-domain settings. By adapting string kernels to the test set
without using the ground-truth test labels, we report significantly better
accuracy rates in cross-domain English polarity classification.Comment: Accepted at ICONIP 2018. arXiv admin note: substantial text overlap
with arXiv:1808.0840
Weighted Low-Regularity Solutions of the KP-I Initial Value Problem
In this paper we establish local well-posedness of the KP-I problem, with
initial data small in the intersection of the natural energy space with the
space of functions which are square integrable when multiplied by the weight y.
The result is proved by the contraction mapping principle. A similar (but
slightly weaker) result was the main Theorem in the paper " Low regularity
solutions for the Kadomstev-Petviashvili I equation " by Colliander, Kenig and
Staffilani (GAFA 13 (2003),737-794 and math.AP/0204244). Ionescu found a
counterexample (included in the present paper) to the main estimate used in the
GAFA paper, which renders incorrect the proof there. The present paper thus
provides a correct proof of a strengthened version of the main result in the
GAFA paper
Reliability of Strategic Environmental Assessment for Territorial Management: General Criticisms and a Proposed Approach in the Presence of Relevant Accident Risk Facilities
The Strategic Environmental Assessment (SEA) is a procedure with a wide application, that has a very important role in sustainable territorial development. The aim of this work is to make some evaluations after the initial period of application also based on data of a particular complex territory, Lombardy Region (Northern Italy), which is characterized by a very high concentration of population, industrial activities and economic interests. The evaluations reveal some critical aspects that negatively influence the correct application of the SEA in Italy, with consequences on the territorial governance and the determination of expected effects corresponding to specific aims. One of these critical aspects is the need to define specific standards and parameters for carrying out a SEA on the different environmental themes. One of these is the assessment of the anthropic risk, which may initially be approximately identified as the industrial risk during territorial planning and programming. On this matter, we suggest adopting a methodological approach that is found in specific guidelines for anyone that produces the Environmental Report to support the SEA, and for councils that have to produce a Technical Examination Paper of the Relevant Accident Risk, to assess the industrial risk, also when there are companies with a relevant accident risk
- …