4,176 research outputs found

### Implicit equations involving the $p$-Laplace operator

In this work we study the existence of solutions $u \in W^{1,p}_0(\Omega)$ to
the implicit elliptic problem $f(x, u, \nabla u, \Delta_p u)= 0$ in $\Omega$, where $\Omega$ is a bounded domain in $\mathbb R^N$, $N \ge 2$, with
smooth boundary $\partial \Omega$, $1< p< +\infty$, and $f\colon \Omega
\times \mathbb R \times \mathbb R^N \times \R \to \R$. We choose the
particular case when the function $f$ can be expressed in the form $f(x, z,
w, y)= \varphi(x, z, w)- \psi(y)$, where the function $\psi$ depends only on
the $p$-Laplacian $\Delta_p u$. We also present some applications of our
results.Comment: 15 pages; comments are welcom

### Theoretical thermodynamic analysis of a closed-cycle process for the conversion of heat into electrical energy by means of a distiller and an electrochemical cell

We analyse a device aimed at the conversion of heat into electrical energy,
based on a closed cycle in which a distiller generates two solutions at
different concentrations, and an electrochemical cell consumes the
concentration difference, converting it into electrical current. We first study
an ideal model of such a process. We show that, if the device works at a single
fixed pressure (i.e. with a ``single effect''), then the efficiency of the
conversion of heat into electrical power can approach the efficiency of a
reversible Carnot engine operating between the boiling temperature of the
concentrated solution and that of the pure solvent. When two heat reservoirs
with a higher temperature difference are available, the overall efficiency can
be incremented by employing an arrangement of multiple cells working at
different pressures (``multiple effects''). We find that a given efficiency can
be achieved with a reduced number of effects by using solutions with a high
boiling point elevation.Comment: The following article has been submitted to Journal of Renewable and
Sustainable Energy. After it is published, it will be found at
http://scitation.aip.org/content/aip/journal/jrs

### Entity-Linking via Graph-Distance Minimization

Entity-linking is a natural-language-processing task that consists in
identifying the entities mentioned in a piece of text, linking each to an
appropriate item in some knowledge base; when the knowledge base is Wikipedia,
the problem comes to be known as wikification (in this case, items are
wikipedia articles). One instance of entity-linking can be formalized as an
optimization problem on the underlying concept graph, where the quantity to be
optimized is the average distance between chosen items. Inspired by this
application, we define a new graph problem which is a natural variant of the
Maximum Capacity Representative Set. We prove that our problem is NP-hard for
general graphs; nonetheless, under some restrictive assumptions, it turns out
to be solvable in linear time. For the general case, we propose two heuristics:
one tries to enforce the above assumptions and another one is based on the
notion of hitting distance; we show experimentally how these approaches perform
with respect to some baselines on a real-world dataset.Comment: In Proceedings GRAPHITE 2014, arXiv:1407.7671. The second and third
authors were supported by the EU-FET grant NADINE (GA 288956

### Synchronous Context-Free Grammars and Optimal Linear Parsing Strategies

Synchronous Context-Free Grammars (SCFGs), also known as syntax-directed
translation schemata, are unlike context-free grammars in that they do not have
a binary normal form. In general, parsing with SCFGs takes space and time
polynomial in the length of the input strings, but with the degree of the
polynomial depending on the permutations of the SCFG rules. We consider linear
parsing strategies, which add one nonterminal at a time. We show that for a
given input permutation, the problems of finding the linear parsing strategy
with the minimum space and time complexity are both NP-hard

### A deep learning integrated Lee-Carter model

In the field of mortality, the LeeâCarter based approach can be considered the milestone
to forecast mortality rates among stochastic models. We could define a âLeeâCarter model familyâ
that embraces all developments of this model, including its first formulation (1992) that remains the
benchmark for comparing the performance of future models. In the LeeâCarter model, the kt parameter,
describing the mortality trend over time, plays an important role about the future mortality behavior.
The traditional ARIMA process usually used to model kt shows evident limitations to describe the future
mortality shape. Concerning forecasting phase, academics should approach a more plausible way in
order to think a nonlinear shape of the projected mortality rates. Therefore, we propose an alternative
approach the ARIMA processes based on a deep learning technique. More precisely, in order to catch
the pattern of kt series over time more accurately, we apply a Recurrent Neural Network with a Long
Short-Term Memory architecture and integrate the LeeâCarter model to improve its predictive capacity.
The proposed approach provides significant performance in terms of predictive accuracy and also allow
for avoiding the time-chunksâ a priori selection. Indeed, it is a common practice among academics to
delete the time in which the noise is overflowing or the data quality is insufficient. The strength of
the Long Short-Term Memory network lies in its ability to treat this noise and adequately reproduce it
into the forecasted trend, due to its own architecture enabling to take into account significant long-term
patterns

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