Solving generic nonarchimedean semidefinite programs using stochastic game algorithms

A general issue in computational optimization is to develop combinatorial algorithms for semidefinite programming. We address this issue when the base field is nonarchimedean. We provide a solution for a class of semidefinite feasibility problems given by generic matrices. Our approach is based on tropical geometry. It relies on tropical spectrahedra, which are defined as the images by the valuation of nonarchimedean spectrahedra. We establish a correspondence between generic tropical spectrahedra and zero-sum stochastic games with perfect information. The latter have been well studied in algorithmic game theory. This allows us to solve nonarchimedean semidefinite feasibility problems using algorithms for stochastic games. These algorithms are of a combinatorial nature and work for large instances.Comment: v1: 25 pages, 4 figures; v2: 27 pages, 4 figures, minor revisions + benchmarks added; v3: 30 pages, 6 figures, generalization to non-Metzler sign patterns + some results have been replaced by references to the companion work arXiv:1610.0674

A quotient of the Lubin-Tate tower II

In this article we construct the quotient M_1/P(K) of the infinite-level Lubin-Tate space M_1 by the parabolic subgroup P(K) of GL(n,K) of block form (n-1,1) as a perfectoid space, generalizing results of one of the authors (JL) to arbitrary n and K/Q_p finite. For this we prove some perfectoidness results for certain Harris-Taylor Shimura varieties at infinite level. As an application of the quotient construction we show a vanishing theorem for Scholze's candidate for the mod p Jacquet-Langlands and the mod p local Langlands correspondence. An appendix by David Hansen gives a local proof of perfectoidness of M_1/P(K) when n = 2, and shows that M_1/Q(K) is not perfectoid for maximal parabolics Q not conjugate to P.Comment: with an appendix by David Hanse

Microscopic origin of the mobility enhancement at a spinel/perovskite oxide heterointerface revealed by photoemission spectroscopy

The spinel/perovskite heterointerface $\gamma$-Al$_2$O$_3$/SrTiO$_3$ hosts a two-dimensional electron system (2DES) with electron mobilities exceeding those in its all-perovskite counterpart LaAlO$_3$/SrTiO$_3$ by more than an order of magnitude despite the abundance of oxygen vacancies which act as electron donors as well as scattering sites. By means of resonant soft x-ray photoemission spectroscopy and \textit{ab initio} calculations we reveal the presence of a sharply localized type of oxygen vacancies at the very interface due to the local breaking of the perovskite symmetry. We explain the extraordinarily high mobilities by reduced scattering resulting from the preferential formation of interfacial oxygen vacancies and spatial separation of the resulting 2DES in deeper SrTiO$_3$ layers. Our findings comply with transport studies and pave the way towards defect engineering at interfaces of oxides with different crystal structures.Comment: Accepted as Rapid Communications in Physical Review

Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions

This paper is aimed to show the essential role played by the theory of quasi-analytic functions in the study of the determinacy of the moment problem on finite and infinite-dimensional spaces. In particular, the quasi-analytic criterion of self-adjointness of operators and their commutativity are crucial to establish whether or not a measure is uniquely determined by its moments. Our main goal is to point out that this is a common feature of the determinacy question in both the finite and the infinite-dimensional moment problem, by reviewing some of the most known determinacy results from this perspective. We also collect some properties of independent interest concerning the characterization of quasi-analytic classes associated to log-convex sequences.Comment: 28 pages, Stochastic and Infinite Dimensional Analysis, Chapter 9, Trends in Mathematics, Birkh\"auser Basel, 201

Noradrenergic Control of Gene Expression and Long-Term Neuronal Adaptation Evoked by Learned Vocalizations in Songbirds

Norepinephrine (NE) is thought to play important roles in the consolidation and retrieval of long-term memories, but its role in the processing and memorization of complex acoustic signals used for vocal communication has yet to be determined. We have used a combination of gene expression analysis, electrophysiological recordings and pharmacological manipulations in zebra finches to examine the role of noradrenergic transmission in the brain’s response to birdsong, a learned vocal behavior that shares important features with human speech. We show that noradrenergic transmission is required for both the expression of activity-dependent genes and the long-term maintenance of stimulus-specific electrophysiological adaptation that are induced in central auditory neurons by stimulation with birdsong. Specifically, we show that the caudomedial nidopallium (NCM), an area directly involved in the auditory processing and memorization of birdsong, receives strong noradrenergic innervation. Song-responsive neurons in this area express α-adrenergic receptors and are in close proximity to noradrenergic terminals. We further show that local α-adrenergic antagonism interferes with song-induced gene expression, without affecting spontaneous or evoked electrophysiological activity, thus dissociating the molecular and electrophysiological responses to song. Moreover, α-adrenergic antagonism disrupts the maintenance but not the acquisition of the adapted physiological state. We suggest that the noradrenergic system regulates long-term changes in song-responsive neurons by modulating the gene expression response that is associated with the electrophysiological activation triggered by song. We also suggest that this mechanism may be an important contributor to long-term auditory memories of learned vocalizations