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revisions + benchmarks added; v3: 30 pages, 6 figures, generalization to non-Metzler sign patterns + some results have been replaced by references to the companion work arXiv:1610.0674

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

Comparison of Different Fixation Techniques of the Long Head of the Biceps Tendon in Superior Capsule Reconstruction for Irreparable Posterosuperior Rotator Cuff Tears: A Dynamic Biomechanical Evaluation

Background: In the past decade, superior capsular reconstruction has emerged as a potential surgical approach in young patients with irreparable posterosuperior rotator cuff tears (RCT) and absence of severe degenerative changes. Recently, the use of locally available and biological viable autografts, such as the long head of the biceps tendon (LHBT) for SCR has emerged, with promising early results. Purpose/Hypothesis: The purpose of this study was to investigate the effect of using the LHBT for reconstruction of the superior capsule on shoulder kinematics, along with different fixation constructs in a dynamic biomechanical model. The authors hypothesized that each of the 3 proposed fixation techniques would restore native joint kinematics, including glenohumeral superior translation (ghST), maximum abduction angle (MAA), maximum cumulative deltoid force (cDF), and subacromial peak contact pressure (sCP). Study Design: Controlled laboratory study. Methods: Eight fresh-frozen cadaveric shoulders (mean age, 53.4 ± 14.2 years) were tested using a dynamic shoulder simulator. Each specimen underwent the following 5 conditions: (1) intact, (2) irreparable posterosuperior rotator cuff tear (psRCT), (3) V-shaped LHBT reconstruction, (4) box-shaped LHBT reconstruction, and (5) single-stranded LHBT reconstruction. MAA, ghST, cDF and sCP were assessed in each tested condition. Results: Each of the 3 LHBT techniques for reconstruction of the superior capsule significantly increased MAA while significantly decreasing ghST and cDF compared with the psRCT (P <.001 and P <.001, respectively). Additionally, the V-shaped and box-shaped techniques significantly decreased sCP (P =.009 and P =.016, respectively) compared with the psRCT. The V-shaped technique further showed a significantly increased MAA (P <.001, respectively) and decreased cDF (P =.042 and P =.039, respectively) when compared with the box-shaped and single-stranded techniques, as well as a significantly decreased ghST (P =.027) when compared with the box-shaped technique. Conclusion: In a dynamic biomechanical cadaveric model, using the LHBT for reconstruction of the superior capsule improved shoulder function by preventing superior humeral migration, decreasing deltoid forces and sCP. As such, the development of rotator cuff tear arthropathy in patients with irreparable psRCTs could potentially be delayed. Clinical Relevance: Using a biologically viable and locally available LHBT autograft is a cost-effective, potentially time-saving, and technically feasible alternative for reconstruction of the superior capsule, which may result in favorable outcomes in irreparable psRCTs. Moreover, each of the 3 techniques restored native shoulder biomechanics, which may help improve shoulder function by preventing superior humeral head migration and the development of rotator cuff tear arthropathy in young patients with irreparable rotator cuff tears