Benign Overfitting without Linearity: Neural Network Classifiers Trained by Gradient Descent for Noisy Linear Data

Benign overfitting, the phenomenon where interpolating models generalize well in the presence of noisy data, was first observed in neural network models trained with gradient descent. To better understand this empirical observation, we consider the generalization error of two-layer neural networks trained to interpolation by gradient descent on the logistic loss following random initialization. We assume the data comes from well-separated class-conditional log-concave distributions and allow for a constant fraction of the training labels to be corrupted by an adversary. We show that in this setting, neural networks exhibit benign overfitting: they can be driven to zero training error, perfectly fitting any noisy training labels, and simultaneously achieve minimax optimal test error. In contrast to previous work on benign overfitting that require linear or kernel-based predictors, our analysis holds in a setting where both the model and learning dynamics are fundamentally nonlinear.Comment: 39 pages; updated proof of loss ratio boun

Using productivity and susceptibility indices to assess the vulnerability of United States fish stocks to overfishing

Assessing the vulnerability of stocks to fishing practices in U.S. federal waters was recently highlighted by the National Marine Fisheries Service (NMFS), National Oceanic and Atmospheric Administration, as an important factor to consider when 1) identifying stocks that should be managed and protected under a fishery management plan; 2) grouping data-poor stocks into relevant management complexes; and 3) developing precautionary harvest control rules. To assist the regional fishery management councils in determining vulnerability, NMFS elected to use a modified version of a productivity and susceptibility analysis (PSA) because it can be based on qualitative data, has a history of use in other fisheries, and is recommended by several organizations as a reasonable approach for evaluating risk. A number of productivity and susceptibility attributes for a stock are used in a PSA and from these attributes, index scores and measures of uncertainty are computed and graphically displayed. To demonstrate the utility of the resulting vulnerability evaluation, we evaluated six U.S. fisheries targeting 162 stocks that exhibited varying degrees of productivity and susceptibility, and for which data quality varied. Overall, the PSA was capable of differentiating the vulnerability of stocks along the gradient of susceptibility and productivity indices, although fixed thresholds separating low-, moderate-, and highly vulnerable species were not observed. The PSA can be used as a flexible tool that can incorporate regional-specific information on fishery and management activity

Synthesis of hybrid anticancer agents based on kinase and histone deacetylase inhibitors

Fragments based on the VEGFR2i Semaxanib (SU5416, (vascular endothelial growth factor receptor-2 inhibitor) and the HDACi (histone deacetylase inhibitor) SAHA (suberanilohydroxamic acid) have been merged to form a range of low molecular weight dual action hybrids. Vindication of this approach is provided by SAR, docking studies, in vitro cancer cell line and biochemical enzyme inhibition data as well as in vivo Xenopus data for the lead molecule (Z)-N1-(3-((1H-pyrrol-2-yl)methylene)-2-oxoindolin-5-yl)- N8-hydroxyoctanediamide 6

Historical setting and neuropathology of lathyrism: insights from the neglected 1944 report by Oliveras de la Riva

Lathyrism is a central motor system disorder recognized since antiquity resulting from prolonged dietary dependence on the grasspea (Lathyrus sativus). The neuropathology underlying the characteristic spastic paraparesis of lathyrism is sketchy. Described here is a landmark but little-known Spanish-language neuropathological study of two patients with lathyrism of recent onset. Due to erroneous interpretations of Filimonov's influential work in 1926, it was assumed that spastic paraparesis of lathyrism was explained by destruction of Betz's pyramidal cells in the motor cortex. Contrary to present understanding, Betz cells and anterior horn cells were preserved, and pathological findings dominated by myelin loss were largely limited to pyramidal tracts in the lumbar cord. Thickening of the adventitia of capillaries and arterioles, together with proliferation of perivascular astrocytes, was found along the length of the spinal cord. Oliveras de la Riva proposed that the segmental spinal pathology arose because distal regions of elongate pyramidal tract axons are distant from their trophic center in the motor cortex, a view not far from the current distal axonopathy concept of lathyrism. In addition, we review the historical circumstances of Filimonov's work in Russia, a summary of the epidemic of lathyrism in Spain following its Civil War (1936-1939), and some historical aspects of the Cajal Institute in Madrid, where Oliveras de la Riva's work was carried out under the supervision of Fernando de Castro, one of Cajal's favorite students

Cold Blockade of Axonal Transport Activates Premitotic Activity of Schwann Cells and Wallerian Degeneration

Between 3 and 4 days after transection of cat sciatic nerve, Schwann cell-associated premitotic activity spreads anterogradely along degenerating distal nerve stumps at a rate of approximately 200 mm/day. We inves- tigated whether fast anterograde axonal transport contrib- utes to the initiation of this component of Wallenan de- generation. Axonal transport was blocked in intact and transected cat sciatic nerves by focally chilling a proximal segment to temperatures below 11“C for 24 hr. Incorpora- tion of t3H]thymidine(a marker of premitotic DNA syn- thesis) was then measured 3 and 4 days posttransection in cold blocked- and control-degenerating nerves. Effects of cold block prior to and concomitant with nerve transectionwere studied. Results failed to support the hypothesis that Schwann-cell premitotic activity after axotomy is asso- ciatedwithentryintotheaxonofmitogenicsubstancesand their anterograde fast transport along the distal stump. In- stead, data suggested that progressive anterograde failure of fast anterograde transport distal to transection serves to effect the Schwann-cell premitotic response to axotomy. Key Words: Peripheral nerve-Axonal transport- Schwann cell-Wallerian degeneration-Cold block. Oak- lander A. L. and Spencer P. S. Cold blockade of axonal transport activates premitotic activity of Schwann cells and Wallerian degeneratio

A model for the break-up of a tuft of fibers

A simple model for the forces acting on a single fiber as it is withdrawn from a tangled fiber assembly is proposed. Particular emphasis is placed on understanding the dynamics of the reptating fiber with respect to the entanglement of fibers within the tuft. The resulting two-parameter model captures the qualitative features of experimental simulation. The model is extended to describe the break-up of a tuft. The results show good agreement with experiment and indicate where a fiber is most likely to fracture based on the density of fiber end-points