Our Universal Growth Equation describes how user population of products and services, membership subscriptions, even your publications and citations, grow as time goes

We derive from first principle a growth equation that fits all data of growing user population, such as Facebook signups, electronic products, services, app downloads, and virtually everything that grows as time goes, like the number of papers you publish and the number of times your papers get cited. If x(t) is the quantity of the item you are interested in, it will grow according to

where *c*_{1} and *c*_{2} are growth parameters corresponding to peer influence and personal decision, respectively, and *N* is the total potential user population. The basis of our theory is a network of people who make decision on whether to sign up for a service or use a product according to the individuals’ independent judgement as well as peer influence. Statistical analysis is used to derive the above growth equation.

**Key References:**

C. Zhan and C.K. Tse, "A universal model for growth of user population of products and services," Network Science, vol. 4, no. 4, pp. 491-507, December 2016. [Link to Online Journal Viewing]

C. Zhan and C.K. Tse, "A network model for growth of publications and citations,” Journal of Complex Networks, Advance Access, doi: 10.1093/comnet/cnw019, August 2016 [Link to Online Journal Viewing]

Network Research in Finance

Network of World’s Stock Markets: Nodes are stock indices of different countries. A link indicates that the two connected markets are correlated in the sense that the time series of the pair of indices over 2005-2007 have a Pearson correlation of over 85%.

**Key References:**

C. K. Tse, J. Liu, and F. C. M. Lau, “A network perspective of stock markets,” Journal of Empirical Finance, vol. 17, no. 4, pp. 659-667, September 2010. [Download]

J. Liu, C. K. Tse, and K. He, “Fierce stock market fluctuation disrupts scalefree distribution,” Quantitative Finance, vol. 11, no. 6, pp. 817-823, June 2011. [Download]

Nonlinear Phenomena in Renewable Energy Systems and Grid-Connected Power Converter Systems: Interactions, Stability and Design [Awarded Best Paper (Second Place) by IEEE Transactions on Power Electronics 2015]

Our latest initiative in power electronics research has been motivated by the recent development of energy systems which emphasizes the integration of the various renewable sources with the power grid and other distribution infra-structures. The new development has spawned new interests and serious concerns about stability and the impacts of interactions of a large number of systems through the distribution network. Moreover, renewable sources are also subject to fluctuation of availability, e.g., solar, wind, tidal, etc. The systems are therefore expected to be multi-structural and operating with multi-operating modes. Our research focus is on the complex behavior of such systems interacting via a common distribution network.

**Key References:**

C. Wan, M. Huang, C. K. Tse, and X. Ruan, "Effects of interaction of power converters coupled via power grid: a design-oriented study," IEEE Transactions on Power Electronics, vol. 30, no. 7, pp. 3589-3600, July 2015. [Prize Paper (Second Place) Award 2015]

LED Drivers (Gold Medals at International Exhibition of Inventions, Geneva 2013 and 2009)

A novel two-level current driving method has been developed for LED lamps. The driver takes advantage of the intrinsic characteristic of LEDs to improve the luminous level by around 15%. The idea is to adjust the two ends of the PWM current such that throughout the linear control range, the luminous level of the LEDs is always higher than the usual PWM driven LEDs.

**Key References:**

X. Qu, S. C. Wong and C. K. Tse, "A current balancing scheme with high luminous efficacy for high power LED lighting," IEEE Transactions on Power Electronics, vol. 29, no. 6, pp. 2649-2654, June 2014.

S. K. Ng, K. H. Loo, S. K. Ip, Y. M. Lai, K.T. Mok and C. K. Tse, "Sequential variable bi-level driving approach suitable for use in high color precision LED display panels," IEEE Transactions on Industrial Electronics, vol. 59, no. 12, pp. 4637-4645, December 2012.

Inductive Power Transfer Applications

Power supplies using remote inductive power transfer have become realistic options for charging moving vehicles and in biomedical uses. The reactive element compensation problem is critical for achieving good efficiency. Our recent work has focused on the basic theory of reactive compensation and efficiency optimization, and application focuses are a charging platform for moving vehicles and LED lighting systems.

**Key References:**

X. Qu, Y. Jing, H. Han, S. C. Wong and C. K. Tse, "Higher order compensation for inductive-power-transfer converters with constant-voltage or constant-current output combating transformer parameter constraints," IEEE Transactions on Power Electronics, vol. 32, no. 1, pp. 394-405, January 2017.

J. Hou, Q. Chen. X. Ren, X. Ruan, S. C. Wong and C. K. Tse, "Precise characteristics analysis of series/series-parallel compensated contactless resonant converter," IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 3, no. 1, 101-110, March 2015.