Nulla $e^{i\pi}+1=0$.

2018-01-25T17:38:25+01:00

Bruno Iannazzo

Tables, bounds and graphics of short linear codes with covering radius 3
and codimension 4 and 5

2017-12-19T17:48:04Z

Daniele Bartoli, Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco,

cs.IT

22 pages, 7 figures, 2 tables, 24 references

The length function $\ell_q(r,R)$ is the smallest length of a $ q $-ary
linear code of covering radius $R$ and codimension $r$. In this work, by
computer search in wide regions of $q$, we obtained short $[n,n-4,5]_q3$
quasiperfect MDS codes and $[n,n-5,5]_q3$ quasiperfect Almost MDS codes with
covering radius $R=3$. The new codes imply the following upper bounds:
\begin{align*} &\ell_q(4,3)<2.8\sqrt[3]{q\ln q}\text{ for }8\le q\le3323\text{
and }q=3511,3761,4001;\\ &\ell_q(5,3)<3\sqrt[3]{q^2\ln q}\text{ for }5\le
q\le563. \end{align*} For $r\neq 3t$ and $q\neq (q^{\prime})^3$, the new bounds
have the form \begin{align*} \ell_q(r,3)< c\sqrt[3]{\ln q}\cdot
q^{(r-3)/3},~~c\text{ is a universal constant},~~r=4,5. \end{align*} As far as
it is known to the authors, such bounds have not been previously described in
the literature. In computer search, we use the leximatrix algorithm to obtain
parity check matrices of codes. The algorithm is a version of the recursive
g-parity check algorithm for greedy codes.

No journal ref

ID: 1712.07078v1

Linear codes from Denniston maximal arcs

2017-11-28T09:29:42Z

Daniele Bartoli, Massimo Giulietti, Maria Montanucci,

math.CO

No journal ref

In this paper we construct functional codes from Denniston maximal arcs. For
$q=2^{4n+2}$ we obtain linear codes with parameters $[(\sqrt{q}-1)(q+1),5,d]_q$
where $\lim_{q \to +\infty} d=(\sqrt{q}-1)q-3\sqrt{q}$. We also find for
$q=16,32$ a number of linear codes which appear to have larger minimum distance
with respect to the known codes with same length and dimension.

No journal ref

ID: 1711.10478v1

A general approximation approach for the simultaneous treatment of
integral and discrete operators

2017-11-25T12:06:36Z

Gianluca Vinti, Luca Zampogni,

math.FA

24 pages, 12 figures

In this paper we give a unitary approach for the simultaneous study of the
convergence of discrete and integral operators described by means of a family
of linear continuous functionals acting on functions defined on locally compact
Hausdorff topological groups. The general family of operators introduced and
studied includes very well-known operators in the literature. We give results
of uniform convergence, and modular convergence in the general setting of
Orlicz spaces.The latter result allow us to cover many other settings as the
$L^p$-spaces, the interpolation spaces, the exponential spaces and many others.

No journal ref

ID: 1711.09230v1

A characterization of the convergence in variation for the generalized
sampling series

2017-10-12T17:14:46Z

Laura Angeloni, Danilo Costarelli, Gianluca Vinti,

math.FA

18 pages, 6 figures

In this paper, we study the convergence in variation for the generalized
sampling operators based upon averaged-type kernels and we obtain a
characterization of absolutely continuous functions. This result is proved
exploiting a relation between the first derivative of the above operator acting
on $f$ and the sampling Kantorovich series of f'. By such approach, also a
variation detracting-type property is established. Finally, examples of
averaged kernels are provided, such as the central B-splines of order $n$
(duration limited functions) or other families of kernels generated by the
Fejer and the Bochner-Riesz kernels (bandlimited functions).

No journal ref

ID: 1710.04621v1

Accelerating Energy Games Solvers on Modern Architectures

2017-10-10T15:15:32Z

Andrea Formisano, Raffaella Gentilini, Flavio Vella,

cs.DC

No journal ref

Quantitative games, where quantitative objectives are defined on weighted
game arenas, provide natural tools for designing faithful models of embedded
controllers. Instances of these games that recently gained interest are the so
called Energy Games. The fast-known algorithm solves Energy Games in O(EVW)
where W is the maximum weight. Starting from a sequential baseline
implementation, we investigate the use of massively data computation
capabilities supported by modern Graphics Processing Units to solve the
`initial credit problem' for Energy Games. We present four different parallel
implementations on multi-core CPU and GPU systems. Our solution outperforms the
baseline implementation by up to 36x speedup and obtains a faster convergence
time on real-world graphs.

No journal ref

ID: 1710.03647v1

Nonsingular systems of generalized Sylvester equations: an algorithmic
approach

2017-09-12T11:15:21Z

Fernando De TerĂ¡n, Bruno Iannazzo, Federico Poloni, Leonardo Robol,

math.NA

No journal ref

We consider the uniqueness of solution (nonsingularity) of systems of $r$
generalized Sylvester and $\star$-Sylvester equations with $n\times n$
coefficient matrices. After several reductions, we show that it is sufficient
to analyze periodic systems having, at most, one generalized $\star$-Sylvester
equation. We provide characterizations for the nonsingularity in terms of
spectral properties of either matrix pencils or formal matrix products, both
constructed from the coefficients of the system. The proposed approach uses the
periodic Schur decomposition, and leads to an $O(n^3r)$ algorithm for computing
the (unique) solution. We prove that the proposed algorithm is backward stable.
The asymptotic cost and the stability are then verified by some numerical
experiments.

No journal ref

ID: 1709.03783v1

Colored Point-set Embeddings of Acyclic Graphs

2017-08-30T08:39:49Z

Emilio Di Giacomo, Leszek Gasieniec, Giuseppe Liotta, Alfredo Navarra,

cs.CG

Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017)

We show that any planar drawing of a forest of three stars whose vertices are
constrained to be at fixed vertex locations may require $\Omega(n^\frac{2}{3})$
edges each having $\Omega(n^\frac{1}{3})$ bends in the worst case. The lower
bound holds even when the function that maps vertices to points is not a
bijection but it is defined by a 3-coloring. In contrast, a constant number of
bends per edge can be obtained for 3-colored paths and for 3-colored
caterpillars whose leaves all have the same color. Such results answer to a
long standing open problem.

No journal ref

ID: 1708.09167v1

Permutation polynomials, fractional polynomials, and algebraic curves

2017-08-16T10:42:48Z

Daniele Bartoli, Massimo Giulietti,

math.CO

No journal ref

In this note we prove a conjecture by Li, Qu, Li, and Fu on permutation
trinomials over $\mathbb{F}_3^{2k}$. In addition, new examples and
generalizations of some families of permutation polynomials of
$\mathbb{F}_{3^k}$ and $\mathbb{F}_{5^k}$ are given. We also study permutation
quadrinomials of type $Ax^{q(q-1)+1} + Bx^{2(q-1)+1} + Cx^{q} + x$. Our method
is based on the investigation of an algebraic curve associated with a
{fractional polynomial} over a finite field.

No journal ref

ID: 1708.04841v1

Detection of thermal bridges from thermographic images for the analysis
of buildings energy performance

2017-08-04T11:56:50Z

Francesco Asdrubali, Giorgio Baldinelli, Francesco Bianchi, Danilo Costarelli, Antonella Rotili, Marco Seracini, Gianluca Vinti,

math.NA

22 pages, 10 figures

In this paper, we develop a procedure for the detection of the contours of
thermal bridges from thermographic images, in order to study the energetic
performance of buildings. Two main steps of the above method are: the
enhancement of the thermographic images by an optimized version of the
mathematical algorithm for digital image processing based on the theory of
sampling Kantorovich operators, and the application of a suitable thresholding
based on the analysis of the histogram of the enhanced thermographic images.
Finally, an accuracy improvement of the parameter that defines the thermal
bridge is obtained.

No journal ref

ID: 1708.01463v1