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In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the nodes, which takes into account a long-range interaction between them, does not exhibit concentration phenomena typical of spectral rankings which take into account just local interactions. We show that the predictive value of the rankings obtained using our proposals is considerably improved on different real world problems.

The main focus of this paper is the characterization and exploitation of the asymptotic spectrum of the saddle--point matrix sequences arising from the discretization of optimization problems constrained by elliptic partial differential equations. They uncover the existence of an hidden structure in these matrix sequences, namely, they show that these are indeed an example of Generalized Locally Toeplitz (GLT) sequences.

Extended versions of the Bourgain-Brezis-Mironescu theorems on the limit as s->1^- of the Gagliardo-Slobodeckij fractional seminorm are established in the Orlicz space setting. Our results hold for fractional Orlicz-Sobolev spaces built upon general Young functions, and complement those of [13], where Young functions satisfying the $\Delta_2$ and the $\nabla_2$ conditions are dealt with. The case of Young functions with an asymptotic linear growth is also considered in connection with the space of functions of bounded variation.

Tumor resistance to chemotherapy represents an important challenge in modern oncology. Although platinum (Pt)-based drugs have demonstrated excellent therapeutic potential, their effectiveness in a wide range of tumors is limited by the development of resistance mechanisms. One of these mechanisms includes increased cisplatin sequestration/efflux by the copper-transporting ATPase, ATP7B. However, targeting ATP7B to reduce Pt tolerance in tumors could represent a serious risk because suppression of ATP7B might compromise copper homeostasis, as happens in Wilson disease.

Recent numerical analyses to optimize the design of microfluidic devices for more effective entrapment or segregation of surrogate circulating tumor cells (CTCs) from healthy cells have been reported in the literature without concurrently accommodating the non-Newtonian nature of the body fluid and the non-uniform geometric shapes of the CTCs.

In this work we developed a mathematical model describing the crystallization process of salt dissolved in water flowing within a porous medium (in this case the common brick). Starting from this model a numerical tool was developed that allows to describe the effects of salt penetrating inside porous media and to forecast the effects of the application of crystallization inibitors.

Using the new methodology introduced in a recent paper [D. Bini, T. Damour, and A. Geralico, Phys. Rev. Lett. 123, 231104 (2019)], we present the details of the computation of the conservative dynamics of gravitationally interacting binary systems at the fifth post-Newtonian (5PN) level, together with its extension at the fifth-and-a-half post-Newtonian level. We present also the sixth post-Newtonian (6PN) contribution to the third-post-Minkowskian (3PM) dynamics.