Joint Modeling of Multiple Network Views

Latent space models (LSM) for network data rely on the basic assumption that each node of the network has an unknown position in a D-dimensional Euclidean latent space: generally the smaller the distance between two nodes in the latent space, the greater their probability of being connected. In this article, we propose a variational inference approach to estimate the intractable posterior of the LSM. In many cases, different network views on the same set of nodes are available. It can therefore be useful to build a model able to jointly summarize the information given by all the network views. For this purpose, we introduce the latent space joint model (LSJM) that merges the information given by multiple network views assuming that the probability of a node being connected with other nodes in each network view is explained by a unique latent variable. This model is demonstrated on the analysis of two datasets: an excerpt of 50 girls from “Teenage Friends and Lifestyle Study” data at three time points and the Saccharomyces cerevisiae genetic and physical protein–protein interactions. Supplementary materials for this article are available online.     

Low-energy positron scattering from gas-phase uracil

Quantum scattering calculations are presented for the interaction of low energy positrons with the uracil molecule, an important component of biological systems. The rotational elastic and inelastic cross sections and vibrational inelastic cross sections are reported and compared with existing experiments, indicating a general trend of the cross sections different from the experimental findings and in line with what should be expected from the behavior of the total cross sections in similar polar targets. Some specific considerations can be drawn on the reliability of existing experiments, as to their size vis-à-vis to the computed integral cross sections over the same range of energies.     

Computing sharp bounds for hard clustering problems on trees

Clustering problems with relational constraints in which the underlying graph is a tree arise in a variety of applications: hierarchical data base paging, communication and distribution networks, districting, biological taxonomy, and others. They are formulated here as optimal tree partitioning problems. In a previous paper, it was shown that their computational complexity strongly depends on the nature of the objective function and, in particular, that minimizing the total within-cluster dissimilarity or the diameter is computationally hard. We propose heuristics that find good partitions within a reasonable time, even for instances of relatively large size. Such heuristics are based on the solution of continuous relaxations of certain integer (or almost integer) linear programs. Experimental results on over 2000 randomly generated instances with up to 500 entities show that the values (total within-cluster dissimilarity or diameter) of the solutions provided by these heuristics are quite close to the minimum one.     

Synthesis and reactivity of N-heterocycle-B(C6F5)3 complexes. 4. Competition between pyridine- and pyrrole-type substrates toward B(C6F5)3: structure and dynamics of 7-B(C6F5)3-7-azaindole and [7-Azaindolium]+[HOB(C6F5)3]-

Reaction between 7-azaindole and B(C6F5)3 quantitatively yields 7-(C6F5)3B-7-azaindole (4), in which B(C6F5)3 coordinates to the pyridine nitrogen of 7-azaindole, leaving the pyrrole ring unreacted even in the presence of a second equivalent of B(C6F5)3. Reaction of 7-azaindole with H2O-B(C6F5)3 initially produces [7-azaindolium]+[HOB(C6F5)3]- (5) which slowly converts to 4 releasing a H2O molecule. Pyridine removes the borane from the known complexes (C6F5)3B-pyrrole (1) and (C6F5)3B-indole (2), with formation of free pyrrole or indole, giving the more stable adduct (C6F5)3B-pyridine (3). The competition between pyridine and 7-azaindole for the coordination with B(C6F5)3 again yields 3. The molecular structures of compounds 4 and 5 have been determined both in the solid state and in solution and compared to the structures of other (C6F5)3B-N-heterocycle complexes. Two dynamic processes have been found in compound 4. Their activation parameters (DeltaH = 66 (3) kJ/mol, DeltaS = -18 (10) J/mol K and DeltaH = 76 (5) kJ/mol, DeltaS = -5 (18) J/mol K) are comparable with those of other (C6F5)3B-based adducts. The nature of the intramolecular interactions that result in such energetic barriers is discussed.     

A maximal atmospheric mixing from a maximal CP violating phase

We point out an elegant mechanism to predict a maximal atmospheric angle, which is based on a maximal CP violating phase difference between second and third lepton families in the flavour symmetry basis. In this framework, a discussion of the general formulas for θ₁₂${\theta }_{12}$, |U_e3|$|U_{e3}|$, δ   and their possible correlations in some limiting cases is provided. We also present an explicit realisation in terms of an SO(3)$\mathit{SO}(3)$ flavour symmetry model.     

How Neighborly Can a Centrally Symmetric Polytope Be?

We show that there exist k-neighborly centrally symmetric d-dimensional polytopes with 2(n + d) vertices, where

Regularity for a fourth-order critical equation with gradient nonlinearity

Given Ω a smooth bounded domain of Rn, n?3, we consider functions that are weak solutions to the equation

     

Exact formulae and matrix-less eigensolvers for block banded symmetric Toeplitz matrices

Precise asymptotic expansions for the eigenvalues of a Toeplitz matrix \(T_n(f)\), as the matrix size n tends to infinity, have recently been obtained, under suitable assumptions on the associated generating function f. A restriction is that f has to be polynomial, monotone, and scalar-valued. In this paper we focus on the case where \(\mathbf {f}\) is an \(s\times s\) matrix-valued trigonometric polynomial with \(s\ge 1\), and \(T_n(\mathbf {f})\) is the block Toeplitz matrix generated by \(\mathbf {f}\), whose size is \(N(n,s)=sn\). The case \(s=1\) corresponds to that already treated in the literature. We numerically derive conditions which ensure the existence of an asymptotic expansion for the eigenvalues. Such conditions generalize those known for the scalar-valued setting. Furthermore, following a proposal in the scalar-valued case by the first author, Garoni, and the third author, we devise an extrapolation algorithm for computing the eigenvalues of banded symmetric block Toeplitz matrices with a high level of accuracy and a low computational cost. The resulting algorithm is an eigensolver that does not need to store the original matrix, does not need to perform matrix-vector products, and for this reason is called matrix-less. We use the asymptotic expansion for the efficient computation of the spectrum of special block Toeplitz structures and we provide exact formulae for the eigenvalues of the matrices coming from the \(\mathbb {Q}_p\) Lagrangian Finite Element approximation of a second order elliptic differential problem. Numerical results are presented and critically discussed.