A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desirable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to first order in the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.Comment: 18 Pages, 4 Figures. This updated version has a slightly more detailed introduction. In the current form, the paper will appear in SIAM Journal on Numerical Analysi

HammerDrive: A task-aware driving visual attention model

We introduce HammerDrive, a novel architecture for task-aware visual attention prediction in driving. The proposed architecture is learnable from data and can reliably infer the current focus of attention of the driver in real-time, while only requiring limited and easy-to-access telemetry data from the vehicle. We build the proposed architecture on two core concepts: 1) driving can be modeled as a collection of sub-tasks (maneuvers), and 2) each sub-task affects the way a driver allocates visual attention resources, i.e., their eye gaze fixation. HammerDrive comprises two networks: a hierarchical monitoring network of forward-inverse model pairs for sub-task recognition and an ensemble network of task-dependent convolutional neural network modules for visual attention modeling. We assess the ability of HammerDrive to infer driver visual attention on data we collected from 20 experienced drivers in a virtual reality-based driving simulator experiment. We evaluate the accuracy of our monitoring network for sub-task recognition and show that it is an effective and light-weight network for reliable real-time tracking of driving maneuvers with above 90% accuracy. Our results show that HammerDrive outperforms a comparable state-of-the-art deep learning model for visual attention prediction on numerous metrics with ~13% improvement for both Kullback-Leibler divergence and similarity, and demonstrate that task-awareness is beneficial for driver visual attention prediction

Some Results on the Boundary Control of Systems of Conservation Laws

This note is concerned with the study of the initial boundary value problem for systems of conservation laws from the point of view of control theory, where the initial data is fixed and the boundary data are regarded as control functions. We first consider the problem of controllability at a fixed time for genuinely nonlinear Temple class systems, and present a description of the set of attainable configurations of the corresponding solutions in terms of suitable Oleinik-type estimates. We next present a result concerning the asymptotic stabilization near a constant state for general $n\times n$ systems. Finally we show with an example that in general one cannot achieve exact controllability to a constant state in finite time.Comment: 10 pages, 4 figures, conferenc

Real-time workload classification during driving using hyperNetworks

Classifying human cognitive states from behavioral and physiological signals is a challenging problem with important applications in robotics. The problem is challenging due to the data variability among individual users, and sensor artifacts. In this work, we propose an end-to-end framework for real-time cognitive workload classification with mixture Hyper Long Short Term Memory Networks (m-HyperLSTM), a novel variant of HyperNetworks. Evaluating the proposed approach on an eye-gaze pattern dataset collected from simulated driving scenarios of different cognitive demands, we show that the proposed framework outperforms previous baseline methods and achieves 83.9% precision and 87.8% recall during test. We also demonstrate the merit of our proposed architecture by showing improved performance over other LSTM-based method

Random Expert Distillation: Imitation Learning via Expert Policy Support Estimation

We consider the problem of imitation learning from a finite set of expert trajectories, without access to reinforcement signals. The classical approach of extracting the expert's reward function via inverse reinforcement learning, followed by reinforcement learning is indirect and may be computationally expensive. Recent generative adversarial methods based on matching the policy distribution between the expert and the agent could be unstable during training. We propose a new framework for imitation learning by estimating the support of the expert policy to compute a fixed reward function, which allows us to re-frame imitation learning within the standard reinforcement learning setting. We demonstrate the efficacy of our reward function on both discrete and continuous domains, achieving comparable or better performance than the state of the art under different reinforcement learning algorithms

Holomorphic transforms with application to affine processes

In a rather general setting of It\^o-L\'evy processes we study a class of transforms (Fourier for example) of the state variable of a process which are holomorphic in some disc around time zero in the complex plane. We show that such transforms are related to a system of analytic vectors for the generator of the process, and we state conditions which allow for holomorphic extension of these transforms into a strip which contains the positive real axis. Based on these extensions we develop a functional series expansion of these transforms in terms of the constituents of the generator. As application, we show that for multidimensional affine It\^o-L\'evy processes with state dependent jump part the Fourier transform is holomorphic in a time strip under some stationarity conditions, and give log-affine series representations for the transform.Comment: 30 page

Occlusal traits in children with neurofibromatosis type 1

Literature is poor of data about the occlusion in children affected by neurofibromatosis type 1 (NF1). This case-control study investigated the occlusal traits in a group of children with NF1

New Insight on Medieval Painting in Sicily: The Virgin Hodegetria Panel in Monreale Cathedral (Palermo, Italy)

: The Virgin Hodegetria, located in the Cathedral of Santa Maria Nuova in Monreale, near Palermo (Italy), probably dating the first half of the 13th century, is one of the earliest examples of medieval panel painting in Sicily. A diagnostic campaign was carried out on the panel aiming to identify the constituting materials and the executive technique, as well as to assess the state of conservation for supporting the methodological choice of the restoration intervention. Both non invasive (X-ray radiography, digital microscope, multispectral imaging, ED-X-ray fluorescence) and micro-invasive (polarised light microscopy, ESEM-EDX, ATR-FTIR spectroscopy and micro-Raman spectroscopy) analyses were performed. According to the results, the executive technique followed the 13th–14th-century Italian painting tradition. A complex structure was applied on the wooden support, consisting of a double layer of canvas and several ground layers of gypsum and glue based binder. The underdrawing was made by a brush using carbonaceous black pigment. The original palette includes red ochre, red lead, azurite, carbon black and bone black. During the several restorations, mercury-based red, indigo, smalt blue, orpiment and synthetic mars were used. The original silver leaf of the frame was covered with red tin-based lake and subsequently regilded with gold leaf. Proteinaceous and oil binders were also detecte