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Graph Model Simulation of Human Brain’s Functional Activity at Resting State by Means of the FD Model

Dulio P., Finotelli P., Frosini A., Pergola E., Presenti A.

Fundamenta Informaticae

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2018

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Vol. 163, nr 1

93--109

EN

It is commonly accepted that the various parts of the human brain interact as a network at macroscopic, mesoscopic and microscopic level. Recently, different network models have been proposed to mime the brain behavior both at resting state and during tasks: Our study concerns one of those model that consider both the physical and functional connectivity as well as topological metrics of the brain networks. We provide evidence of the soundness of the model by means of a synthetic dataset based on the existing literature concerning the active cerebral areas at the resting state. Furthermore, we consider Ruzicka similarity measure in order to stress the predictive capability of the model and provide a thresholding criterium. Some network statistics are finally provided.

2

Regions of Uniqueness Quickly Reconstructed by Three Directions in Discrete Tomography

Dulio P., Pagani S. M. C., Frosini A.

Fundamenta Informaticae

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2017

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Vol. 155, nr 4

407--423

EN

In discrete tomographic image reconstruction, projections are taken along a finite set S of valid directions for a working grid A. In general, uniqueness cannot be achieved in the whole grid A. Usually, some information on the object to be reconstructed is introduced, that, sometimes, allows possible ambiguities to be removed. From a different perspective, one aims in finding subregions of A where uniqueness can be guaranteed, and obtained in linear time, only from the knowledge of S. When S consists of two lattice directions, the shape of any such region of uniqueness, say ROU, have been completely characterized in previous works by means of a double Euclidean division algorithm called DEDA. Results have been later extended to special triples of directions, under a suitable assumption on their entries. In this paper we remove the previous assumption, so providing a complete characterization of the shape of the ROU for such kind of triples. We also show that the employed strategy can be even applied to more general sets of three directions, where the corresponding ROU can be characterized as well. Independently of the combinatorial interest of the problem, the result can be exploited to define in advance, namely before using any kind of radiation, suitable sets of directions that allow regions of interest to be included in the corresponding ROU. Results have been proved in all details, and several experiments are considered, in order to support the theoretical steps and to clarify possible applications.

3

The Identity Transform of a Permutation and its Applications

Frosini A., Battaglino D., Rinaldi S., Socci S.

Fundamenta Informaticae

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2015

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Vol. 141, nr 2/3

191--205

EN

Starting from a Theorem by Hall, we define the identity transform of a permutation π as C(π) = (0 + π(0), 1 + π(1), ..., (n - 1) + π(n - 1)), and we define the set Cn = {(C(π) : π ∈ Sn}, where Sn is the set of permutations of the elements of the cyclic group Zn. In the first part of this paper we study the set Cn: we show some closure properties of this set, and then provide some of its combinatorial and algebraic characterizations and connections with other combinatorial structures. In the second part of the paper, we use some of the combinatorial properties we have determined to provide a different algorithm for the proof of Hall's Theorem.