Probabilistic ODE Solvers with Runge-Kutta Means

Runge-Kutta methods are the classic family of solvers for ordinary differential equations (ODEs), and the basis for the state of the art. Like most numerical methods, they return point estimates. We construct a family of probabilistic numerical methods that instead return a Gauss-Markov process defining a probability distribution over the ODE solution. In contrast to prior work, we construct this family such that posterior means match the outputs of the Runge-Kutta family exactly, thus inheriting their proven good properties. Remaining degrees of freedom not identified by the match to Runge-Kutta are chosen such that the posterior probability measure fits the observed structure of the ODE. Our results shed light on the structure of Runge-Kutta solvers from a new direction, provide a richer, probabilistic output, have low computational cost, and raise new research questions.Comment: 18 pages (9 page conference paper, plus supplements); appears in Advances in Neural Information Processing Systems (NIPS), 201

Probabilistic Numerics and Uncertainty in Computations

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data has led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimisers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.Comment: Author Generated Postprint. 17 pages, 4 Figures, 1 Tabl

Can the Balanced Scorecard Help in Designing Conference Calls? The Effect of Balanced Information Composition on the Cost of Capital

Most recent studies on conference calls focus on the costs for firms that can arise from the calls' open nature. We study the benefits of conference calls and hypothesize that firms could use the balanced scorecard concept as a framework for presenting the information (i.e. balanced information composition) in conference calls to lower the cost of capital. Our results show a negative association between a more balanced information composition in conference calls and a firm's cost of capital. Additional tests substantiate that the effect of such a balanced information composition on the cost of capital is driven by a reduction in information asymmetry. Overall, the findings suggest that firms can benefit from the balanced scorecard concept by using it as a framework for preparing their conference calls

Immunotherapy of Peritoneal Carcinomatosis with the Antibody Catumaxomab in Colon, Gastric, or Pancreatic Cancer: An Open-Label, Multicenter, Phase I/II Trial

Background: Peritoneal carcinomatosis (PC) is common in gastrointestinal (GI) cancer and there is no effective standard treatment. We investigated the tolerability and maximum tolerated dose (MTD) of the trifunctional antibody catumaxomab in patients with PC. Methods: In this open-label, phase I/II clinical trial, patients with epithelial cell adhesion molecule (EpCAM)-positive PC from GI cancer received 4 sequential intraperitoneal catumaxomab infusions: day 0: 10 mu g; day 3: 10 or 20 mu g; day 7: 30, 50, or 100 mu g; and day 10: 50, 100, or 200 mu g. Dose escalation was guided by dose-limiting toxicities. Results: The MTD was 10, 20, 50, and 200 mu g on days 0, 3, 7, and 10, respectively. Catumaxomab had an acceptable safety profile: Most common treatment-related adverse events (at the MTD) were fever, vomiting, and abdominal pain. At final examination, 11/17 evaluable patients (65%) were progression free: 1 patient had a complete and 3 a partial response. Median overall survival from the time of diagnosis of PC was 502 days. Conclusions: Intraperitoneal catumaxomab is a promising option for the treatment of PC from GI cancer