Derivative Formula and Applications for Degenerate Diffusion Semigroups

By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack inequalities are derived.Comment: 18 page

Sense, Model and Identify the Load Signatures of HVAC Systems in Metro Stations

The HVAC systems in subway stations are energy consuming giants, each of which may consume over 10, 000 Kilowatts per day for cooling and ventilation. To save energy for the HVAC systems, it is critically important to firstly know the "load signatures" of the HVAC system, i.e., the quantity of heat imported from the outdoor environments and by the passengers respectively in different periods of a day, which will significantly benefit the design of control policies. In this paper, we present a novel sensing and learning approach to identify the load signature of the HVAC system in the subway stations. In particular, sensors and smart meters were deployed to monitor the indoor, outdoor temperatures, and the energy consumptions of the HVAC system in real-time. The number of passengers was counted by the ticket checking system. At the same time, the cooling supply provided by the HVAC system was inferred via the energy consumption logs of the HVAC system. Since the indoor temperature variations are driven by the difference of the loads and the cooling supply, linear regression model was proposed for the load signature, whose coefficients are derived via a proposed algorithm . We collected real sensing data and energy log data from HaiDianHuangZhuang Subway station, which is in line 4 of Beijing from the duration of July 2012 to Sept. 2012. The data was used to evaluate the coefficients of the regression model. The experiment results show typical variation signatures of the loads from the passengers and from the outdoor environments respectively, which provide important contexts for smart control policies.Comment: 5 pages, 5 figure

Algorithms to test open set condition for self-similar set related to P.V. numbers

Fix a P.V. number $\lambda ^{-1}>1.$ Given $\mathbf{p}=(p_{1},\cdots,p_{m})\in \mathbb{N}^{m}$, \mathbf{b}=(b_{1},\cdots,b_{m})\in \mathbb{Q^{m}, for the self-similar set $E_{\mathbf{p},\mathbf{b}}=\cup_{i=1}^{m}(\lambda ^{p_{i}}E_{\mathbf{p},\mathbf{b}}+b_{i})$ we find an efficient algorithm to test whether $E_{\mathbf{p},\mathbf{b}}$ satisfies the open set condition (strong separation condition) or not

Primordial Black Holes from Sound Speed Resonance during Inflation

We report on a novel phenomenon of the resonance effect of primordial density perturbations arisen from a sound speed parameter with an oscillatory behavior, which can generically lead to the formation of primordial black holes in the early Universe. For a general inflaton field, it can seed primordial density fluctuations and their propagation is governed by a parameter of sound speed square. Once if this parameter achieves an oscillatory feature for a while during inflation, a significant non-perturbative resonance effect on the inflaton field fluctuations takes place around a critical length scale, which results in significant peaks in the primordial power spectrum. By virtue of this robust mechanism, primordial black holes with specific mass function can be produced with a sufficient abundance for dark matter in sizable parameter ranges.Comment: 6 pages, 4 figures; v2: figures replotted with corrections, analysis extended, version accepted by Phys.Rev.Let