Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups

We present a Galois theory of parameterized linear differential equations where the Galois groups are linear differential algebraic groups, that is, groups of matrices whose entries are functions of the parameters and satisfy a set of differential equations with respect to these parameters. We present the basic constructions and results, give examples, discuss how isomonodromic families fit into this theory and show how results from the theory of linear differential algebraic groups may be used to classify systems of second order linear differential equations

Capture, Learning, and Synthesis of 3D Speaking Styles

Audio-driven 3D facial animation has been widely explored, but achieving realistic, human-like performance is still unsolved. This is due to the lack of available 3D datasets, models, and standard evaluation metrics. To address this, we introduce a unique 4D face dataset with about 29 minutes of 4D scans captured at 60 fps and synchronized audio from 12 speakers. We then train a neural network on our dataset that factors identity from facial motion. The learned model, VOCA (Voice Operated Character Animation) takes any speech signal as input - even speech in languages other than English - and realistically animates a wide range of adult faces. Conditioning on subject labels during training allows the model to learn a variety of realistic speaking styles. VOCA also provides animator controls to alter speaking style, identity-dependent facial shape, and pose (i.e. head, jaw, and eyeball rotations) during animation. To our knowledge, VOCA is the only realistic 3D facial animation model that is readily applicable to unseen subjects without retargeting. This makes VOCA suitable for tasks like in-game video, virtual reality avatars, or any scenario in which the speaker, speech, or language is not known in advance. We make the dataset and model available for research purposes at http://voca.is.tue.mpg.de.Comment: To appear in CVPR 201

Some traffic features at freeway bottlenecks

Observations from two freeway bottlenecks in and near Toronto, Canada indicate that the average rate vehicles discharge from a queue can be 10% lower than the flow measured prior to the queue\u27s formation. Absent any influences from downstream, the queue discharge flows exhibited nearly stationary patterns that alternated between higher and lower rates. These alternating flow patterns were especially evident at one of the two sites, although the feature occurred at both sites during periods that immediately followed the onset of upstream queuing; i.e. a queue\u27s formation was always accompanied by a relatively low discharge rate followed later by a temporary surge in the discharge flow. When plotted cumulatively over time, however, the counts of discharging vehicles generally did not deviate by more than about 50 vehicles from a trend line of constant slope. Thus, the discharge flows are described as being `nearly\u27 constant; i.e. they varied (slightly) about a fixed rate. At each site, this average discharge rate exhibited little deviation from day to day. The present findings came by visually comparing transformed curves of cumulative vehicle arrival number vs time and cumulative occupancy vs time measured at neighboring loop detectors. This treatment of the data provided clear presentations of some important traffic features and this facilitated a detailed study of bottleneck flows

Some observed queue discharge features at a freeway bottleneck downstream of a merge

Details of traffic evolution were studied upstream and downstream of a freeway bottleneck located near a busy on-ramp. It is shown that on certain days the bottleneck became active upon dissipation of a queue emanating from somewhere further downstream. On such occasions, the bottleneck occurred at a fixed location, approximately one kilometer downstream of the merge. Notably, even after the dissipation of a downstream queue, the discharge flows in the active bottleneck were nearly constant, since the cumulative counts never deviated much from a linear trend. The average bottleneck discharge flows were also reproducible from day to day. The diagnostic tools used in this study were curves of cumulative vehicle arrival number versus time and cumulative occupancy versus time constructed from data measured at neighboring freeway loop detectors. Once suitably transformed, these cumulative curves provided the measurement resolution necessary to observe the transitions between freely flowing and queued conditions and to identify some important traffic features

Mapping An Internal-External (I-E) Matrix Using Traditional And Extended Matrix Concepts

Internal Factor Evaluation (IFE) and External Factor Evaluation (EFE) matrices allow an organization to visualize their strengths, weaknesses, opportunities and threats while a Competitive Profile Matrix (CPM) utilizes critical success factors to allow an organization to compare itself to competitors.  Capps and Glissmeyer (2012) proposed an extension of the EFE and IFE concepts to an External Competitive Profile Matrix (ECPM) and an Internal Competitive Profile Matrix (ICPM) which provides greater insight in understanding the external and internal categories to which an organization must attend.  The authors of this paper extend the observations of Capps and Glissmeyer (2012) by suggesting that visual mapping of the ECPM and ICPM, in a manner similar on the Internal-External (I-E) matrix, would enable greater comparative understanding of the relative strengths, weaknesses, opportunities, and threats of the respective companies

Effects of unregulated international fishing on recovery potential of the sandbar shark within the southeast United States

Coastal sharks are challenging to manage in the United States due to their slow life history, limited data availability, history of overexploitation, and competing stakeholder interests. Furthermore, species like the sandbar shark are subjected to international exploitation unmanaged by the U.S. We conducted a management strategy evaluation using Stock Synthesis on the sandbar shark to test the performance of various configurations of a threshold harvest control rule. In addition to uncertainties addressed in the operating model, we built multiple implementation models to address uncertainties related to future levels of a partially unmanaged source of removals, the combined Mexican and U.S. recreational (MexRec) fleet. We found that the presence of unregulated removals had the potential to significantly influence the success of the various management procedures tested. Notably, if MexRec catches continue to increase with total stock abundance following historical trends, the rate of MexRec removals will be too large to allow the sandbar shark to recover across operating models. We present trade-offs between performance metrics across a range of 24 management procedures and three implementation models