An Extensive Assessment of Network Embedding in PPI Network Alignment

Network alignment is a fundamental task in network analysis. In the biological field, where the protein–protein interaction (PPI) is represented as a graph, network alignment allowed the discovery of underlying biological knowledge such as conserved evolutionary pathways and functionally conserved proteins throughout different species. A recent trend in network science concerns network embedding, i.e., the modelling of nodes in a network as a low-dimensional feature vector. In this survey, we present an overview of current PPI network embedding alignment methods, a comparison among them, and a comparison to classical PPI network alignment algorithms. The results of this comparison highlight that: (i) only five network embeddings for network alignment algorithms have been applied in the biological context, whereas the literature presents several classical network alignment algorithms; (ii) there is a need for developing an evaluation framework that may enable a unified comparison between different algorithms; (iii) the majority of the proposed algorithms perform network embedding through matrix factorization-based techniques; (iv) three out of five algorithms leverage external biological resources, while the remaining two are designed for domain agnostic network alignment and tested on PPI networks; (v) two algorithms out of three are stated to perform multi-network alignment, while the remaining perform pairwise network alignment.     

Decay Rates in Probability Metrics Towards Homogeneous Cooling States for the Inelastic Maxwell Model

We quantify the long-time behavior of solutions to the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell molecules by means of the contraction property of a suitable metric in the set of probability measures. Existence, uniqueness, and precise estimates of overpopulated high energy tails of the self-similar profile proved in ref. 9 are revisited and derived from this new Liapunov functional. For general initial conditions the solutions of the Boltzmann equation are then proved to converge with computable rate as t → ∞ to the self-similar solution in this distance, which metrizes the weak convergence of measures. Moreover, we can relate this Fourier distance to the Euclidean Wasserstein distance or Tanaka functional proving also its exponential convergence towards the homogeneous cooling states. The findings are relevant in the understanding of the conjecture formulated by Ernst and Brito in refs. 15, 16, and complement and improve recent studies on the same problem of Bobylev and Cercignani⁽⁹⁾ and Bobylev, Cercignani and one of the authors.⁽¹¹⁾     

The evaporation–condensation problem for a binary mixture of rarefied gases

Continuum Mechanics and Thermodynamics - Half space problems of evaporation and condensation for a binary mixture of inert gases are investigated when the dynamics is governed by a system of...     

Representing products of manifolds by edge-coloured graphs: the boundary case

In this paper we generalize the construction - introduced by Gagliardi and Grasselli in the closed case - of a coloured-graph representing the product of two manifolds, starting by two coloured graphs representing the manifolds themselves, to the boundary case. In particular we study the genus of the graph product of low dimensional manifold ( resp. n-spheres ) with m-disks. Received September 28, 1998; in final form January 5, 2000 / Published online October 11, 2000     

Microencapsulated Engineered <Emphasis Type="Italic">Lactococcus lactis Cells</Emphasis> for Heterologous Protein Delivery: Preparation and In Vitro Analysis

This article demonstrates the potential of encapsulated, engineered Lactococcus lactis as a vehicle for the oral delivery of therapeutic proteins. Using alginate-poly-l-lysine-alginate membrane-encapsulated L. lactis engineered to secrete the reporter protein Staphylococcal aureus nuclease, we show comparable viability and protein secretion between free and immobilized cells. After 12 h, microcapsules with a cell density of 4.8 × 10⁵ colony forming unit (CFU) ml⁻¹ grew to 2.2 × 10⁸ CFU ml⁻¹ and released 0.24 arbitrary unit (AU) ml⁻¹ of nuclease, producing similar results as free cells, which grew from 3.4 × 10⁵ to 1.9 × 10⁸ CFU ml⁻¹ and secreted 0.21 AU ml⁻¹ of nuclease. Moreover, encapsulated cells at a density of 4.4 × 10⁷ CFU ml⁻¹ grew to 2.2 × 10¹⁰ CFU ml⁻¹ in 12 h and secreted 15.3 AU ml⁻¹ of nuclease although 3.1 × 10⁷ CFU ml⁻¹ of free cells reached only 2.3 × 10⁹ CFU ml⁻¹ and released 5.6 AU ml⁻¹ of nuclease. We also show the sustained stability of the microcapsules during storage at 4°C over 8 weeks.