352 research outputs found
Bistable reaction equations with doubly nonlinear diffusion
Reaction-diffusion equations appear in biology and chemistry, and combine
linear diffusion with different kind of reaction terms. Some of them are
remarkable from the mathematical point of view, since they admit families of
travelling waves that describe the asymptotic behaviour of a larger class of
solutions of the problem posed in the real line. We
investigate here the existence of waves with constant propagation speed, when
the linear diffusion is replaced by the "slow" doubly nonlinear diffusion. In
the present setting we consider bistable reaction terms, which present
interesting differences w.r.t. the Fisher-KPP framework recently studied in
\cite{AA-JLV:art}. We find different families of travelling waves that are
employed to describe the wave propagation of more general solutions and to
study the stability/instability of the steady states, even when we extend the
study to several space dimensions. A similar study is performed in the critical
case that we call "pseudo-linear", i.e., when the operator is still nonlinear
but has homogeneity one. With respect to the classical model and the
"pseudo-linear" case, the travelling waves of the "slow" diffusion setting
exhibit free boundaries. \\ Finally, as a complement of \cite{AA-JLV:art}, we
study the asymptotic behaviour of more general solutions in the presence of a
"heterozygote superior" reaction function and doubly nonlinear diffusion
("slow" and "pseudo-linear").Comment: 42 pages, 11 figures. Accepted version on Discrete Contin. Dyn. Sys
Generic Large Cardinals and Systems of Filters
We introduce the notion of -system of filters, generalizing the
standard definitions of both extenders and towers of normal ideals. This
provides a framework to develop the theory of extenders and towers in a more
general and concise way. In this framework we investigate the topic of
definability of generic large cardinals properties.Comment: 36 page
Resilient Blocks for Summarising Distributed Data
Summarising distributed data is a central routine for parallel programming,
lying at the core of widely used frameworks such as the map/reduce paradigm. In
the IoT context it is even more crucial, being a privileged mean to allow
long-range interactions: in fact, summarising is needed to avoid data explosion
in each computational unit.
We introduce a new algorithm for dynamic summarising of distributed data,
weighted multi-path, improving over the state-of-the-art multi-path algorithm.
We validate the new algorithm in an archetypal scenario, taking into account
sources of volatility of many sorts and comparing it to other existing
implementations. We thus show that weighted multi-path retains adequate
accuracy even in high-variability scenarios where the other algorithms are
diverging significantly from the correct values.Comment: In Proceedings ALP4IoT 2017, arXiv:1802.0097
The Fisher-KPP problem with doubly nonlinear "fast" diffusion
The famous Fisher-KPP reaction diffusion model combines linear diffusion with
the typical Fisher-KPP reaction term, and appears in a number of relevant
applications. It is remarkable as a mathematical model since, in the case of
linear diffusion, it possesses a family of travelling waves that describe the
asymptotic behaviour of a wide class solutions of the
problem posed in the real line. The existence of propagation wave with finite
speed has been confirmed in the cases of "slow" and "pseudo-linear" doubly
nonlinear diffusion too, see arXiv:1601.05718. We investigate here the
corresponding theory with "fast" doubly nonlinear diffusion and we find that
general solutions show a non-TW asymptotic behaviour, and exponential
propagation in space for large times. Finally, we prove precise bounds for the
level sets of general solutions, even when we work in with spacial dimension . In particular, we show that location of the level sets is
approximately linear for large times, when we take spatial logarithmic scale,
finding a strong departure from the linear case, in which appears the famous
Bramson logarithmic correction.Comment: 42 pages, 6 figure
Absoluteness via Resurrection
The resurrection axioms are forcing axioms introduced recently by Hamkins and
Johnstone, developing on ideas of Chalons and Velickovi\'c. We introduce a
stronger form of resurrection axioms (the \emph{iterated} resurrection axioms
for a class of forcings and a given
ordinal ), and show that implies generic
absoluteness for the first-order theory of with respect to
forcings in preserving the axiom, where is a
cardinal which depends on ( if is any
among the classes of countably closed, proper, semiproper, stationary set
preserving forcings).
We also prove that the consistency strength of these axioms is below that of
a Mahlo cardinal for most forcing classes, and below that of a stationary limit
of supercompact cardinals for the class of stationary set preserving posets.
Moreover we outline that simultaneous generic absoluteness for
with respect to and for with respect to
with is in principle
possible, and we present several natural models of the Morse Kelley set theory
where this phenomenon occurs (even for all simultaneously). Finally,
we compare the iterated resurrection axioms (and the generic absoluteness
results we can draw from them) with a variety of other forcing axioms, and also
with the generic absoluteness results by Woodin and the second author.Comment: 34 page
The Extracellular NADome Modulates Immune Responses
The term NADome refers to the intricate network of intracellular and extracellular enzymes that regulate the synthesis or degradation of nicotinamide adenine dinucleotide (NAD) and to the receptors that engage it. Traditionally, NAD was linked to intracellular energy production through shuffling electrons between oxidized and reduced forms. However, recent data indicate that NAD, along with its biosynthetic and degrading enzymes, has a life outside of cells, possibly linked to immuno-modulating non-enzymatic activities. Extracellular NAD can engage puriginergic receptors triggering an inflammatory response, similar - to a certain extent – to what described for adenosine triphosphate (ATP). Likewise, NAD biosynthetic and degrading enzymes have been amply reported in the extracellular space, where they possess both enzymatic and non-enzymatic functions. Modulation of these enzymes has been described in several acute and chronic conditions, including obesity, cancer, inflammatory bowel diseases and sepsis. In this review, the role of the extracellular NADome will be discussed, focusing on its proposed role in immunomodulation, together with the different strategies for its targeting and their potential therapeutic impact
Preface for the special issue on tool papers of the 23rd International Conference on Coordination Models and Languages, COORDINATION 2021
The dual face of NAMPT: Intracellular/extracellular protein and diagnostic/therapeutic target in cancer
- …