Sparsely Aggregated Convolutional Networks

We explore a key architectural aspect of deep convolutional neural networks: the pattern of internal skip connections used to aggregate outputs of earlier layers for consumption by deeper layers. Such aggregation is critical to facilitate training of very deep networks in an end-to-end manner. This is a primary reason for the widespread adoption of residual networks, which aggregate outputs via cumulative summation. While subsequent works investigate alternative aggregation operations (e.g. concatenation), we focus on an orthogonal question: which outputs to aggregate at a particular point in the network. We propose a new internal connection structure which aggregates only a sparse set of previous outputs at any given depth. Our experiments demonstrate this simple design change offers superior performance with fewer parameters and lower computational requirements. Moreover, we show that sparse aggregation allows networks to scale more robustly to 1000+ layers, thereby opening future avenues for training long-running visual processes.Comment: Accepted to ECCV 201

Robust pricing--hedging duality for American options in discrete time financial markets

We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we consider an abstract setting, which includes the classical case with a fixed reference probability measure as well as the robust framework with a non-dominated family of probability measures. Our first insight is that by considering a (universal) enlargement of the space, we can see American options as European options and recover the pricing-hedging duality, which may fail in the original formulation. This may be seen as a weak formulation of the original problem. Our second insight is that lack of duality is caused by the lack of dynamic consistency and hence a different enlargement with dynamic consistency is sufficient to recover duality: it is enough to consider (fictitious) extensions of the market in which all the assets are traded dynamically. In the second part of the paper we study two important examples of robust framework: the setup of Bouchard and Nutz (2015) and the martingale optimal transport setup of Beiglb\"ock et al. (2013), and show that our general results apply in both cases and allow us to obtain pricing-hedging duality for American options.Comment: 29 page

Robustness of Random Graphs Based on Natural Connectivity

Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the weighted number of closed walks of all lengths and can be regarded as the average eigenvalue obtained from the graph spectrum. In this article, we explore the natural connectivity of random graphs both analytically and numerically and show that it increases linearly with the average degree. By comparing with regular ring lattices and random regular graphs, we show that random graphs are more robust than random regular graphs; however, the relationship between random graphs and regular ring lattices depends on the average degree and graph size. We derive the critical graph size as a function of the average degree, which can be predicted by our analytical results. When the graph size is less than the critical value, random graphs are more robust than regular ring lattices, whereas regular ring lattices are more robust than random graphs when the graph size is greater than the critical value.Comment: 12 pages, 4 figure

Merits and Qualms of Work Fluctuations in Classical Fluctuation Theorems

Work is one of the most basic notion in statistical mechanics, with work fluctuation theorems being one central topic in nanoscale thermodynamics. With Hamiltonian chaos commonly thought to provide a foundation for classical statistical mechanics, here we present general salient results regarding how (classical) Hamiltonian chaos generically impacts on nonequilibrium work fluctuations. For isolated chaotic systems prepared with a microcanonical distribution, work fluctuations are minimized and vanish altogether in adiabatic work protocols. For isolated chaotic systems prepared at an initial canonical distribution at inverse temperature $\beta$, work fluctuations depicted by the variance of $e^{-\beta W}$ are also minimized by adiabatic work protocols. This general result indicates that if the variance of $e^{-\beta W}$ diverges for an adiabatic work protocol, then it diverges for all nonadiabatic work protocols sharing the same initial and final Hamiltonians. How such divergence explicitly impacts on the efficiency of using the Jarzynski's equality to simulate free energy differences is studied in a Sinai model. Our general insights shall boost studies in nanoscale thermodynamics and are of fundamental importance in designing useful work protocols.Comment: 11 pages, 5 figures, close to published versio

Assessment of natural ventilation potential for residential buildings across different climate zones in Australia

In this study, the natural ventilation potential of residential buildings was numerically investigated based on a typical single-story house in the three most populous climate zones in Australia. Simulations using the commercial simulation software TRNSYS (Transient System Simulation Tool) were performed for all seasons in three representative cities, i.e., Darwin for the hot humid summer and warm winter zone, Sydney for the mild temperate zone, and Melbourne for the cool temperate zone. A natural ventilation control strategy was generated by the rule-based decision-tree method based on the local climates. Natural ventilation hour (NVH) and satisfied natural ventilation hour (SNVH) were employed to evaluate the potential of natural ventilation in each city considering local climate and local indoor thermal comfort requirements, respectively. The numerical results revealed that natural ventilation potential was related to the local climate. The greatest natural ventilation potential for the case study building was observed in Darwin with an annual 4141 SNVH out of 4728 NVH, while the least natural ventilation potential was found in the Melbourne case. Moreover, summer and transition seasons (spring and autumn) were found to be the optimal periods to sustain indoor thermal comfort by utilising natural ventilation in Sydney and Melbourne. By contrast, natural ventilation was found applicable over the whole year in Darwin. In addition, the indoor operative temperature results demonstrated that indoor thermal comfort can be maintained only by utilising natural ventilation for all cases during the whole year, except for the non-natural ventilation periods in summer in Darwin and winter in Melbourne. These findings could improve the understanding of natural ventilation potential in different climates, and are beneficial for the climate-conscious design of residential buildings in Australia