On the fast convergence of random perturbations of the gradient flow

We consider in this work small random perturbations (of multiplicative noise type) of the gradient flow. We prove that under mild conditions, when the potential function is a Morse function with additional strong saddle condition, the perturbed gradient flow converges to the neighborhood of local minimizers in $O(\ln (\varepsilon^{-1}))$ time on the average, where $\varepsilon$ is the scale of the random perturbation. Under a change of time scale, this indicates that for the diffusion process that approximates the stochastic gradient method, it takes (up to logarithmic factor) only a linear time of inverse stepsize to evade from all saddle points. This can be regarded as a manifestation of fast convergence of the discrete-time stochastic gradient method, the latter being used heavily in modern statistical machine learning.Comment: Revise and Resubmit at Asymptotic Analysi

Opportunities and challenges in using AI Chatbots in Higher Education

Artificial intelligence (AI) conversational chatbots have gained popularity over time, and have been widely used in the fields of e-commerce, online banking, and digital healthcare and well-being, among others. The technology has the potential to provide personalised service to a range of consumers. However, the use of chatbots within educational settings is still limited. In this paper, we present three chatbot prototypes, the Warwick Manufacturing Group, University of Warwick, are currently developing, and discuss the potential opportunities and technical challenges we face when considering AI chatbots to support our daily activities within the department. Three AI virtual agents are under development: 1) to support the delivery of a taught Master's course simulation game; 2) to support the training and use of a newly introduced educational application; 3) to improve the processing of helpdesk requests within a university department. We hope this paper is informative to those interested in using chatbots in the educational domain. We also aim to improve awareness among those within the chatbot development industry, in particular the chatbot engine providers, about the educational and operational needs within educational institutes, which may differ from those in other domains

Forum Session at the First International Conference on Service Oriented Computing (ICSOC03)

The First International Conference on Service Oriented Computing (ICSOC) was held in Trento, December 15-18, 2003. The focus of the conference ---Service Oriented Computing (SOC)--- is the new emerging paradigm for distributed computing and e-business processing that has evolved from object-oriented and component computing to enable building agile networks of collaborating business applications distributed within and across organizational boundaries. Of the 181 papers submitted to the ICSOC conference, 10 were selected for the forum session which took place on December the 16th, 2003. The papers were chosen based on their technical quality, originality, relevance to SOC and for their nature of being best suited for a poster presentation or a demonstration. This technical report contains the 10 papers presented during the forum session at the ICSOC conference. In particular, the last two papers in the report ere submitted as industrial papers

An Empirical Analysis of Liquidity and Order Flow in the Brokered Interdealer Market for Government of Canada Bonds

The authors empirically measure Canadian bond market liquidity using a number of indicators proposed in the literature and detail, for the first time, price and trade dynamics in the Government of Canada secondary bond market. They find, consistent with Inoue (1999), that the Canadian brokered interdealer fixed-income market is relatively liquid for its size. Liquidity measures are analyzed relative to each other and across securities, and intraday patterns are identified. The authors' results show that trading activity is positively correlated with price volatility, and that signed order flow is significant in explaining contemporaneous high-frequency price movements. They find evidence that trading activity is positively related to liquidity measures in some markets, which suggests that indicators such as trade frequency and trading volume, despite certain drawbacks, can be seen as useful proxies for liquidity. The authors also document Canadian participants' prevalent use of an order expansion protocol, whereby order size can be negotiated upward once a trade has been initiated; although Boni and Leach (2002) identify this practice as consistent with a market where there is relatively strong concern regarding information asymmetry, the authors observe no consistent link between the frequency of its use and observations of trading activity, market liquidity, or price volatility.Financial markets; Market structure and pricing

Effective thermal conductivity of polycrystalline materials with randomly oriented superlattice grains

A model has been established for the effective thermal conductivity of a bulk polycrystal made of randomly oriented superlattice grains with anisotropic thermal conductivity. The in-plane and cross-plane thermal conductivities of each superlattice grain are combined using an analytical averaging rule that is verified using finite element methods. The superlattice conductivities are calculated using frequency dependent solutions of the Boltzmann transport equation, which capture greater thermal conductivity reductions as compared to the simpler gray medium approximation. The model is applied to a PbTe/Sb_2Te_3 nanobulk material to investigate the effects of period, specularity, and temperature. The calculations show that the effective thermal conductivity of the polycrystal is most sensitive to the in-plane conductivity of each superlattice grain, which is generally four to five times larger than the cross-plane conductivity of a grain. The model is compared to experimental measurements of the same system for periods ranging from 287 to 1590 nm and temperatures from 300 to 500 K. The comparison suggests that the effective specularity increases with increasing annealing temperature and shows that these samples are in a mixed regime where both Umklapp and boundary scattering are important

On the Strategic Use of Debt and Capacity in Imperfectly Competitive Product Markets

In capital intensive industries, firms face complicated multi-stage financing, investment, and production decisions under the watchful eye of existing and potential industry rivals. We consider a two-stage simplification of this environment. In the first stage, an incumbent firm benefits from two first-mover advantages by precommiting to a debt financing policy and a capacity investment policy. In the second stage, the incumbent and a single-stage rival simultaneously choose production levels and realize stochastic profits. We characterize the incumbent's first-stage debt and capacity choices as factors in the production of an intermediate good we call "output deterrence." In our two-factor deterrence model, we show that the incumbent chooses a unique capacity policy and a threshold debt policy to achieve the optimal level of deterrence coinciding with full Stackelberg leadership. When we remove the incumbent's first-mover advantage in capacity, the full Stackelberg level of deterrence is still achievable, albeit with a higher level of debt than the threshold. In contrast, when we remove the incumbent's first-mover advantage in debt, the Stackelberg level of deterrence may no longer be achievable and the incumbent may suffer a dead-weight loss. Evidence on the telecommunications industry shows that firms have increased their leverage in a manner consistent with deterring potential rivals following the 1996 deregulation.Industrial organization; Deregulation; Deterrence; Capital structure; Capacity; Telecommunications