Skyrmions and domain walls in (2+1) dimensions

We study classical solutions of the vector O(3) sigma model in (2+1) dimensions, spontaneously broken to O(2)xZ2. The model possesses Skyrmion-type solutions as well as stable domain walls which connect different vacua. We show that different types of waves can propagate on the wall, including waves carrying a topological charge. The domain wall can also absorb Skyrmions and, under appropriate initial conditions, it is possible to emit a Skyrmion from the wall.Comment: plain tex : 15 pages, 21 Postscript figures, uses epsf.te

Dynamics of the topological structures in inhomogeneous media

We present a general review of the dynamics of topological solitons in 1 and 2 dimensions and then discuss some recent work on the scattering of various solitonic objects (such as kinks and breathers etc) on potential obstructions.Comment: based on the talk given by W.J. Zakrzewski at QTS5. To appear in the Proceedings in a special issue of Journal of Physics

Dynamics of the topological structures in inhomogeneous media

We present a general review of the dynamics of topological solitons in 1 and 2 dimensions and then discuss some recent work on the scattering of various solitonic objects (such as kinks and breathers etc) on potential obstructions.Comment: based on the talk given by W.J. Zakrzewski at QTS5. To appear in the Proceedings in a special issue of Journal of Physics

Mesons, Baryons and Waves in the Baby Skyrmion Model

We study various classical solutions of the baby-Skyrmion model in $(2+1)$ dimensions. We point out the existence of higher energy states interpret them as resonances of Skyrmions and anti-Skyrmions and study their decays. Most of the discussion involves a highly exited Skyrmion-like state with winding number one which decays into an ordinary Skyrmion and a Skyrmion-anti-Skyrmion pair. We also study wave-like solutions of the model and show that some of such solutions can be constructed from the solutions of the sine-Gordon equation. We also show that the baby-Skyrmion has non-topological stationary solutions. We study their interactions with Skyrmions.Comment: plain tex : 17 pages, 14 Postscript figures, uses epsf.te

Dynamics of the topological structures in inhomogeneous media

We present a general review of the dynamics of topological solitons in 1 and 2 dimensions and then discuss some recent work on the scattering of various solitonic objects (such as kinks and breathers etc) on potential obstructions.Comment: based on the talk given by W.J. Zakrzewski at QTS5. To appear in the Proceedings in a special issue of Journal of Physics

Building thermal load prediction through shallow machine learning and deep learning

Building thermal load prediction informs the optimization of cooling plant and thermal energy storage. Physics-based prediction models of building thermal load are constrained by the model and input complexity. In this study, we developed 12 data-driven models (7 shallow learning, 2 deep learning, and 3 heuristic methods) to predict building thermal load and compared shallow machine learning and deep learning. The 12 prediction models were compared with the measured cooling demand. It was found XGBoost (Extreme Gradient Boost) and LSTM (Long Short Term Memory) provided the most accurate load prediction in the shallow and deep learning category, and both outperformed the best baseline model, which uses the previous day's data for prediction. Then, we discussed how the prediction horizon and input uncertainty would influence the load prediction accuracy. Major conclusions are twofold: first, LSTM performs well in short-term prediction (1 h ahead) but not in long term prediction (24 h ahead), because the sequential information becomes less relevant and accordingly not so useful when the prediction horizon is long. Second, the presence of weather forecast uncertainty deteriorates XGBoost's accuracy and favors LSTM, because the sequential information makes the model more robust to input uncertainty. Training the model with the uncertain rather than accurate weather data could enhance the model's robustness. Our findings have two implications for practice. First, LSTM is recommended for short-term load prediction given that weather forecast uncertainty is unavoidable. Second, XGBoost is recommended for long term prediction, and the model should be trained with the presence of input uncertainty

Direct investment and Belgium’s attractiveness

Belgium, which has long had direct investment links with other countries, is participating fully in the increasingly global economy. At the end of 2005, almost half of the equity capital invested in Belgian companies as a whole was owned directly or indirectly by foreign shareholders. The purpose of the article is to analyse Belgium’s foreign direct investment (FDI) and the incoming investment from abroad, and to view it in perspective, both over time and in relation to other developed countries, especially neighbouring countries. In addition, it aims to identify the main factors determining recent developments and Belgium’s relative position in 2005, the latest year for which data on FDI stocks are available. Although influenced by the same factors as those which determine the development of FDI on a global scale, direct investment links in Belgium differ from those in other developed economies in their magnitude. In fact, the ratio between FDI flows or stocks and GDP is significantly higher in Belgium than in the majority of other developed countries, for both incoming and outgoing FDI. The scale of Belgium’s direct investment links with foreign countries reflects both its function as a financial centre, particularly via the activities of the coordination centres, and its status as a small, open economy in a European Union where integration began earlier – and has progressed farther – than in other free trade areas. In the past ten years, Belgium’s FDI has expanded constantly and at a faster pace than domestic economic activity. While outgoing FDI has, like that of other developed countries, focused more on developing countries, driven by the search for new markets and lower costs, particularly for labourintensive activities, it is nevertheless still concentrated mainly on the developed countries, including the new EU members. The main protagonists in these capital transfers, effected partly via mergers and acquisitions, are Belgian firms active in the service sector. Over the same period, incoming FDI seems to have grown a little more slowly. In terms of stock, it actually stagnated in the early years of this century. However, the recent dynamism of FDI in Belgium has been at least as favourable as in the other European countries taken as a whole, and especially the neighbouring countries. Looking at greenfield investments, which actually lead to the creation or expansion of activities, the number of projects launched in Belgium has been rising, and at a similar rate to those developed in the EU as a whole. Belgium’s main strengths in terms of activity are chemicals – including life sciences – and transport and communications, particularly logistics and distribution. In general, the main motive for FDI projects in Belgium appears to be to serve the European market, or at least its most highly developed core, which includes Belgium. When a location is being selected for a project, Belgium is therefore competing with other EU countries and, more particularly, with neighbouring countries whose economic characteristics are comparable, notably in regard to their standard of living. Compared to other EU countries, especially the new members whose economies are less advanced, Belgium has a handicap in terms of hourly labour costs but, at the same time, it offers high productivity and various advantages as regards environmental and operational criteria, especially the quality of its infrastructures.foreign direct investment, attractiveness

Baby Skyrmions stabilized by canonical quantization

We analyse the effect of the canonical quantization of the rotational mode of the O(3) $\sigma$-model which includes the Skyrme term. Numerical evidence is presented that the quantum correction to the mass of the rotationally-invariant charge $n=1,2$ configurations may stabilize the solution even in the limit of vanishing potential. The corresponding range of values of the parameters is discussed.Comment: 10 pages, 4 figure