# SCIENTIFIC HIGHLIGHTS

# SCIENTIFIC HIGHLIGHTS

**Selected papers by our scientists**

In this new section of *Penta*, we would like to highlight the best scientific papers among those sent to us by the BGSMath community (authors in **bold **are BGSMath members). If you feel one of your published papers is especially relevant and would like to see it highlighted in the newsletter, please send it to highlights@bgsmath.cat, together with a brief assessment of its scientific relevance. Your proposal will be received by the Scientific Advisory Board, who will select 3/5 of them for any given *Penta* issue.

**M. Calvo-Schwarzwälder**, **M.G. Hennessy**, P. Torres, **T.G. Myers,** F.X.Alvarez

A slip-based model for the size-dependent effective thermal conductivity of nanowires

Int J Heat Mass Transf.** 91** (2018), 57-63

*Summary by the authors*

*In this article we present a model to predict the effective thermal conductivity in nanowires. One of the key features of the paper is a slip boundary condition with a temperature-dependent slip length that captures the transition between two very different heat transfer regimes: diffusive and hydrodynamic (or ballistic). We think that it is a very relevant study because it is able to perfectly fit experimental data in a wide range of temperatures and sizes without using any fitting parameter.*

**J. J. Joosten**, F. F. Lara Martín

Predicativity through Transfinite Reflection

J. Symb. Log.

**82**(3) (2017), 787-808

*Summary by the authors*

*In the paper we give a characterization of the formal second order number theoretical system ATR_0 (Arithmetical Transfinite Recursion) in terms of reflection principles (whatever is provable, is true) over a rather weak base theory. This new result extends results from the seventies by Kreisel and Levy and opens up the way to ordinal analysis of stronger second order arithmetical theories by means of transfinitely iterating adding consistency statements to a weak base theory.*

**J. J. Muñoz**, D. Amat, and V. Conte

Computation of forces from deformed visco-elastic biological tissues

Inverse Problems **34** (4) (2018).

*Summary of the authors*

*This article considers the modelling of embryo development and computation of mechanically optimal forces. *

**David Rossell** & Francisco J. Rubio

Tractable Bayesian variable selection: beyond normality

J Am Stat Assoc. (2017)

*Summary by the authors*

*The topic of the paper is on high-dimensional statistical inference, specifically on the problem of selecting a subset of variables amongst a potentially large set of predictors. The work considers some foundational aspects when dealing with this problem in a Bayesian framework. Specifically, prior to this work there was a fairly limited understanding on what happens when the assumed probability model is wrong. We characterized the consequences of such model misspecification on Bayesian variable selection, with the novel finding that asymptotically the effect on false positive inflation vanishes, however there is a drop in the sensitivity to detect truly active variables that does not vanish even when the sample size tends to infinite. Besides this foundational contribution, the paper then proposes several extensions of the linear model relying on models and techniques from robust statistics, the main contribution there is in proposing analytically and computationally tractable extensions of the linear model that remain practical in high-dimensional problems with potentially many variables. These contributions include asymptotic results, novel scalable optimization algorithms, and an R implementation in package mombf.*

**Victor Rotger**

Diagonal cycles and Euler systems II: The Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions

J. Amer. Math. Soc.

**30**(2017), 601-672

*Summary by the authors*

*It is the first important advancement in the Birch-Swinnerton-Dyer Conjecture for elliptic curves of rank 2. The most important contributions to this conjecture before this one we the theorems by Coates, Wiles, Gross, Zagier, Kolyvagin and Zhang, that were limited to rank 0 and 1. *