Improved Second-Order Bounds for Prediction with Expert Advice

This work studies external regret in sequential prediction games with both positive and negative payoffs. External regret measures the difference between the payoff obtained by the forecasting strategy and the payoff of the best action. In this setting, we derive new and sharper regret bounds for the well-known exponentially weighted average forecaster and for a new forecaster with a different multiplicative update rule. Our analysis has two main advantages: first, no preliminary knowledge about the payoff sequence is needed, not even its range; second, our bounds are expressed in terms of sums of squared payoffs, replacing larger first-order quantities appearing in previous bounds. In addition, our most refined bounds have the natural and desirable property of being stable under rescalings and general translations of the payoff sequence

Reynolds stress models of homogeneous turbulence

Existing and new models for the rapid and the return terms in the Reynolds stress equations were tested in two ways. One, by direct comparison of the model with simulation data. The other, by simulating the flows using the models and comparing the predicted Reynolds stresses with the data. It was found that existing linear models can be improved and that nonlinear models are in better agreement with the simulation data for a wide variety of flows

A tale of two arteries: dual posterior cerebral arteries with vascular bridges. A possible protective pattern?

Stroke is a common morbidity and a frequent cause of disability and even death. The impact of cerebrovascular events is dictated by the brain region involved and can be complicated by anatomical variations. One of the most common variations impacting the cerebral vasculature is the presence of a foetal posterior cerebral artery. This vessel arises from the internal carotid artery instead of the basilar artery and is often associated with more extensive injury in cerebrovascular events. Herein, we report the case of a 60-year-old male who had numerous arterial abnormalities, including a kink and a coil of the left internal carotid, two posterior communicating arteries on the right and two posterior cerebral arteries (PCA) on the left, one arising from the internal carotid (foetal PCA) and one from the basilar. The foetal PCA supplied the thalamus, splenium of the corpus callosum and primary visual cortex. The basilar PCA supplied the midbrain and parts of the occipital lobe. These PCA were connected to each other by a vascular bridge and the foetal PCA was connected to the middle cerebral artery by an additional vascular bridge. This vascular pattern would appear to provide collateral support around blockages in the internal carotid and main stem middle and PCA

Z3-graded Grassmann Variables, Parafermions and their Coherent States

A relation between the $Z_3$-graded Grassmann variables and parafermions is established. Coherent states are constructed as a direct consequence of such a relationship. We also give the analog of the Bargmann-Fock representation in terms of these Grassmann variables.Comment: 8 page

Adaptation Algorithm and Theory Based on Generalized Discrepancy

We present a new algorithm for domain adaptation improving upon a discrepancy minimization algorithm previously shown to outperform a number of algorithms for this task. Unlike many previous algorithms for domain adaptation, our algorithm does not consist of a fixed reweighting of the losses over the training sample. We show that our algorithm benefits from a solid theoretical foundation and more favorable learning bounds than discrepancy minimization. We present a detailed description of our algorithm and give several efficient solutions for solving its optimization problem. We also report the results of several experiments showing that it outperforms discrepancy minimization