In this paper we introduce the TorontoCity benchmark, which covers the full greater Toronto area (GTA) with 712.5km 2 of land, 8439km of road and around 400, 000 buildings. Our benchmark provides different perspectives of the world captured from airplanes, drones and cars driving around the city. Manually labeling such a large scale dataset is infeasible. Instead, we propose to utilize different sources of high-precision maps to create our ground truth. Towards this goal, we develop algorithms that allow us to align all data sources with the maps while requiring minimal human supervision. We have designed a wide variety of tasks including building height estimation (reconstruction), road centerline and curb extraction, building instance segmentation, building contour extraction (reorganization), semantic labeling and scene type classification (recognition). Our pilot study shows that most of these tasks are still difficult for modern convolutional neural networks.

In this paper, a new heat-map-based algorithm is proposed for group activity recognition. The proposed algorithm first models human trajectories as series of heat sources and then applies a thermal diffusion process to create a heat map (HM) for representing the group activities. Based on this HM, a new keypoint-based (KPB) method is used for handling the alignments among HMs with different scales and rotations. A surface-fitting (SF) method is also proposed for recognizing group activities. Our proposed HM feature can efficiently embed the temporal motion information of the group activities while the proposed KPB and SF methods can effectively utilize the characteristics of the HM for activity recognition. Section IV demonstrates the effectiveness of our proposed algorithms.

We present a comprehensive review of the most fundamental and practical aspects of thermo-field dynamics (TFD), including some of the most recent developments in the field. To make TFD fully consistent, some suitable changes in the structure of the thermal doublets and the Bogoliubov transformation matrices have been made. A close comparison between TFD and the Schwinger-Keldysh closed time path formalism (SKF) is presented. We find that TFD and SKF are in many ways the same in form; in particular, the two approaches are identical in stationary situations. However, TFD and SKF are quite different in time-dependent nonequilibrium situations. The main source of this difference is that the time evolution of the density matrix itself is ignored in SKF while in TFD it is replaced by a time-dependent Bogoliubov transformation. In this sense TFD is a better candidate for time-dependent quantum field theory. Even in equilibrium situations, TFD has some remarkable advantages over the Matsubara approach and SKF, the most notable being the Feynman diagram recipes, which we will present. We will show that the calculations of two-point functions are simplified, instead of being complicated, by the matrix nature of the formalism. We will present some explicit calculations using TFD, including space-time inhomogeneous situations and the vacuum polarization in equilibrium relativistic QED.

The concept of thermoalgebra, a kind of representation for the Lie-symmetries developed in connection with thermal quantum field theory, is extended to study unitary representations of the Galilei group for thermal classical systems. One of the representations results in the first-quantized Scho nberg formalism for the classical statistical mechanics. Furthermore, the close analogy between thermal classical mechanics and thermal quantum field theory is analysed, and such an analogy is almost exact for harmonic oscillator systems. The other unitary representation studied results in a field-operator version of the Scho nberg approach. As a consequence, in this case the counterpart of the thermofield dynamics (TFD) in classical theory is identified as both the first and second-quantized form of the Liouville equation. Non-unitary representations are also studied, being, in this case, the Lie product of the thermoalgebra identified as the Poisson brackets. A representation of the thermal SU(1, 1) is analysed, such that the tilde variables (introduced in TFD) are functions in a double phase space. As a result the equations of motion for dissipative classical oscillators are derived.

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