Beyond Convexity: Stochastic Quasi-Convex Optimization

Stochastic convex optimization is a basic and well studied primitive in machine learning. It is well known that convex and Lipschitz functions can be minimized efficiently using Stochastic Gradient Descent (SGD). The Normalized Gradient Descent (NGD) algorithm, is an adaptation of Gradient Descent, which updates according to the direction of the gradients, rather than the gradients themselves. In this paper we analyze a stochastic version of NGD and prove its convergence to a global minimum for a wider class of functions: we require the functions to be quasi-convex and locally-Lipschitz. Quasi-convexity broadens the con- cept of unimodality to multidimensions and allows for certain types of saddle points, which are a known hurdle for first-order optimization methods such as gradient descent. Locally-Lipschitz functions are only required to be Lipschitz in a small region around the optimum. This assumption circumvents gradient explosion, which is another known hurdle for gradient descent variants. Interestingly, unlike the vanilla SGD algorithm, the stochastic normalized gradient descent algorithm provably requires a minimal minibatch size

On Graduated Optimization for Stochastic Non-Convex Problems

The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms of theoretical convergence analysis. In this paper we describe a new first-order algorithm based on graduated optimiza- tion and analyze its performance. We characterize a parameterized family of non- convex functions for which this algorithm provably converges to a global optimum. In particular, we prove that the algorithm converges to an {\epsilon}-approximate solution within O(1/\epsilon^2) gradient-based steps. We extend our algorithm and analysis to the setting of stochastic non-convex optimization with noisy gradient feedback, attaining the same convergence rate. Additionally, we discuss the setting of zero-order optimization, and devise a a variant of our algorithm which converges at rate of O(d^2/\epsilon^4).Comment: 17 page

Gender-based violence and the need for evidence-based primary prevention in South Africa

Gender-based violence is a significant problem globally and in South Africa. The public and political discourse has been dominated by calls for increased penalties and convictions for perpetrators of various types of gender-based violence. However, these responses are unlikely to prevent such violence from occurring in the first place. Primary prevention strategies should address the underlying causes and drivers of gender-based violence in order to prevent violence and promote safer, respectful, happy relations between men and women. Through rigorous research, these factors have been identified and specific strategies based on these findings include: (a) building gender equality and challenging hegemonic masculinities; (b) challenging the widespread acceptance of violence; (c) improving conflict resolution and communication skills; (d) developing relationship-building skills; (e) reducing substance abuse; and (f) improved gun control. Each of these strategies and the evidence-base for the recommendations is discussed. Interventions that combine these strategies and are informed by research evidence during development are most likely to be effective in preventing gender-based violence on a large scale.Keywords: gender equality, masculinities, primary prevention, gender-based violence, South Afric

Reversible surface aggregation in pore formation by pardaxin

The mechanism of leakage induced by surface active peptides is not yet fully understood. To gain insight into the molecular events underlying this process, the leakage induced by the peptide pardaxin from phosphatidylcholine/ phosphatidylserine/cholesterol large unilamellar vesicles was studied by monitoring the rate and extent of dye release and by theoretical modeling. The leakage occurred by an all-or-none mechanism: vesicles either leaked or retained all of their contents. We further developed a mathematical model that includes the assumption that certain peptides become incorporated into the vesicle bilayer and aggregate to form a pore. The current experimental results can be explained by the model only if the surface aggregation of the peptide is reversible. Considering this reversibility, the model can explain the final extents of calcein leakage for lipid/peptide ratios of > 2000:1 to 25:1 by assuming that only a fraction of the bound peptide forms pores consisting of M = 6 +/- 3 peptides. Interestingly, less leakage occurred at 43 degrees C, than at 30 degrees C, although peptide partitioning into the bilayer was enhanced upon elevation of the temperature. We deduced that the increased leakage at 30 degrees C was due to an increase in the extent of reversible surface aggregation at the lower temperature. Experiments employing fluorescein-labeled pardaxin demonstrated reversible aggregation of the peptide in suspension and within the membrane, and exchange of the peptide between liposomes. In summary, our experimental and theoretical results support reversible surface aggregation as the mechanism of pore formation by pardaxin

A Spinal Opsin Controls Early Neural Activity and Drives a Behavioral Light Response

SummaryNonvisual detection of light by the vertebrate hypothalamus, pineal, and retina is known to govern seasonal and circadian behaviors [1]. However, the expression of opsins in multiple other brain structures [2–4] suggests a more expansive repertoire for light regulation of physiology, behavior, and development. Translucent zebrafish embryos express extraretinal opsins early on [5, 6], at a time when spontaneous activity in the developing CNS plays a role in neuronal maturation and circuit formation [7]. Though the presence of extraretinal opsins is well documented, the function of direct photoreception by the CNS remains largely unknown. Here, we show that early activity in the zebrafish spinal central pattern generator (CPG) and the earliest locomotory behavior are dramatically inhibited by physiological levels of environmental light. We find that the photosensitivity of this circuit is conferred by vertebrate ancient long opsin A (VALopA), which we show to be a Gαi-coupled receptor that is expressed in the neurons of the spinal network. Sustained photoactivation of VALopA not only suppresses spontaneous activity but also alters the maturation of time-locked correlated network patterns. These results uncover a novel role for nonvisual opsins and a mechanism for environmental regulation of spontaneous motor behavior and neural activity in a circuit previously thought to be governed only by intrinsic developmental programs

Primary monocytes regulate endothelial cell survival through secretion of Angiopoietin-1 and activation of endothelial Tie2

Objective—Monocyte recruitment and interaction with the endothelium is imperative to vascular recovery. Tie2 plays a key role in endothelial health and vascular remodeling. We studied monocyte-mediated Tie2/angiopoietin signaling following interaction of primary monocytes with endothelial cells and its role in endothelial cell survival. Methods and Results—The direct interaction of primary monocytes with subconfluent endothelial cells resulted in transient secretion of angiopoietin-1 from monocytes and the activation of endothelial Tie2. This effect was abolished by preactivation of monocytes with tumor necrosis factor-α. Although primary monocytes contained high levels of both angiopoietin 1 and 2, endothelial cells contained primarily angiopoietin 2. Seeding of monocytes on serum-starved endothelial cells reduced caspase-3 activity by 46±5.1%, and 52±5.8% after tumor necrosis factor-α treatment and decreased detected single-stranded DNA levels by 41±4.2% and 40±3.5%, respectively. This protective effect of monocytes on endothelial cells was reversed by Tie2 silencing with specific short interfering RNA. The antiapoptotic effect of monocytes was further supported by the activation of cell survival signaling pathways involving phosphatidylinositol 3-kinase, STAT3, and AKT. Conclusion—Monocytes and endothelial cells form a unique Tie2/angiopoietin-1 signaling system that affects endothelial cell survival and may play critical a role in vascular remodeling and homeostasis

Photoactivatable genetically encoded calcium indicators for targeted neuronal imaging.

Circuit mapping requires knowledge of both structural and functional connectivity between cells. Although optical tools have been made to assess either the morphology and projections of neurons or their activity and functional connections, few probes integrate this information. We have generated a family of photoactivatable genetically encoded Ca(2+) indicators that combines attributes of high-contrast photolabeling with high-sensitivity Ca(2+) detection in a single-color protein sensor. We demonstrated in cultured neurons and in fruit fly and zebrafish larvae how single cells could be selected out of dense populations for visualization of morphology and high signal-to-noise measurements of activity, synaptic transmission and connectivity. Our design strategy is transferrable to other sensors based on circularly permutated GFP (cpGFP)