8,016 research outputs found
Calabi-Yau quotients with terminal singularities
In this paper we are interested in quotients of Calabi-Yau threefolds with
isolated singularities. In particular, we analyze the case when has
terminal singularities. We prove that, if is cyclic of prime order and
has terminal singularities, then has order or .Comment: 15 pages, no figures. Current version has some changes in the
structure of the article, some corrected typos and an up-to-date bibliograph
Covering of elliptic curves and the kernel of the Prym map
Motivated by a conjecture of Xiao, we study families of coverings of elliptic
curves and their corresponding Prym map . More precisely, we describe the
codifferential of the period map associated to in terms of the
residue of meromorphic -forms and then we use it to give a characterization
for the coverings for which the dimension of is the least possibile.
This is useful in order to exclude the existence of non isotrivial fibrations
with maximal relative irregularity and thus also in order to give
counterexamples to the Xiao's conjecture mentioned above. The first
counterexample to the original conjecture, due to Pirola, is then analysed in
our framework.Comment: 21 pages, no figures. The seminal ideas at the base of this article
were born in the framework of the PRAGMATIC project of year 201
Exceptional Point of Degeneracy in Backward-Wave Oscillator with Distributed Power Extraction
We show how an exceptional point of degeneracy (EPD) is formed in a system
composed of an electron beam interacting with an electromagnetic mode guided in
a slow wave structure (SWS) with distributed power extraction from the
interaction zone. Based on this kind of EPD, a new regime of operation is
devised for backward wave oscillators (BWOs) as a synchronous and degenerate
regime between a backward electromagnetic mode and the charge wave modulating
the electron beam. Degenerate synchronization under this EPD condition means
that two complex modes of the interactive system do not share just the
wavenumber, but they rather coalesce in both their wavenumbers and eigenvectors
(polarization states). In principle this new condition guarantees full
synchronization between the electromagnetic wave and the beam's charge wave for
any amount of output power extracted from the beam, setting the threshold of
this EPD-BWO to any arbitrary, desired, value. Indeed, we show that the
presence of distributed radiation in the SWS results in having high-threshold
electron-beam current to start oscillations which implies higher power
generation. These findings have the potential to lead to highly efficient BWOs
with very high output power and excellent spectral purity
New examples of Calabi-Yau threefolds and genus zero surfaces
We classify the subgroups of the automorphism group of the product of 4
projective lines admitting an invariant anticanonical smooth divisor on which
the action is free. As a first application, we describe new examples of
Calabi-Yau 3-folds with small Hodge numbers. In particular, the Picard number
is 1 and the number of moduli is 5. Furthermore, the fundamental group is
non-trivial. We also construct a new family of minimal surfaces of general type
with geometric genus zero, K^2=3 and fundamental group of order 16. We show
that this family dominates an irreducible component of dimension 4 of the
moduli space of the surfaces of general type.Comment: 18 pages; v2: simplified some arguments in the last section, final
version to appear on Communications in Contemporary Mathematic
A paradox in community detection
Recent research has shown that virtually all algorithms aimed at the
identification of communities in networks are affected by the same main
limitation: the impossibility to detect communities, even when these are
well-defined, if the average value of the difference between internal and
external node degrees does not exceed a strictly positive value, in literature
known as detectability threshold. Here, we counterintuitively show that the
value of this threshold is inversely proportional to the intrinsic quality of
communities: the detection of well-defined modules is thus more difficult than
the identification of ill-defined communities.Comment: 5 pages, 3 figure
Measuring Online Social Bubbles
Social media have quickly become a prevalent channel to access information,
spread ideas, and influence opinions. However, it has been suggested that
social and algorithmic filtering may cause exposure to less diverse points of
view, and even foster polarization and misinformation. Here we explore and
validate this hypothesis quantitatively for the first time, at the collective
and individual levels, by mining three massive datasets of web traffic, search
logs, and Twitter posts. Our analysis shows that collectively, people access
information from a significantly narrower spectrum of sources through social
media and email, compared to search. The significance of this finding for
individual exposure is revealed by investigating the relationship between the
diversity of information sources experienced by users at the collective and
individual level. There is a strong correlation between collective and
individual diversity, supporting the notion that when we use social media we
find ourselves inside "social bubbles". Our results could lead to a deeper
understanding of how technology biases our exposure to new information
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