Research | Frank's Notebook

Quantum Engineering LinkedIn Group

May 14th, 2010

We have just created a group to discuss applications of quantum phenomena for engineering applications and how to address related challenges in modelling, simulating, designing and controlling quantum devices on linked in: Quantum Engineering. This is related to our overall aim of turning quantum physics into quantum technology. Join us, if you are interested.

While the rich physics of quantum phenomena continues to provide amble opportunity for physics research, quantum effects, once considered strange, have moved into the realm of engineering as novel means to find innovative solutions to current problems. However, there are many challenges that must be overcome to make such technologies a reality, including building tools to model, design, simulate and control such devices. A further challenge that remains is to find novel quantum device designs and integrate them with current technology, and to find novel approaches to utilise quantum effects. This requires an interdisciplinary effort and presents an opportunity for many engineering disciplines such as nano-engineering, material science, electronic engineering and control systems engineering, to work together with computer science, physics, mathematics. It may sound like fantasy to create devices that are faster and smaller while requiring less energy, are easy to recycle and are made from ubiquitously available materials, but quantum engineering may well solve at least some of these problems.

Categories: Research | Tags: quantum engineering, quantum physics | No Comments

Matlab code performance testing

April 5th, 2010

Code to test the performance of matlab code and benchmark algorithms is now available here: perf. It uses the internal matlab walltime (tic/toc) and cputime functions as well as the PerformanceApplication Programming Interface (PAPI) using hardware counters for floating point operations, instructions, cycles and the PAPI real-time timer. It also counts m and builtin matlab function calls using matlab’s profiler. It’s mainly aimed at iterative algorithms.

See perf_test.m for some usage examples to collect the information and plot the results. Collecting information is done via perf_profile for the function call counters and perf_timing for the timers and PAPI counters. Use perf_profile_plot to plot and perf_timing_plot to plot the results. Iterative code needs to call perf_record_iteration(v) after each iteration to collect counters and timing information per iteration, where v is the value (vector) result for the current iteration.

The whole package still needs some detailed documentation and will be integrated with the Qyber package, mainly to test algorithms related to quantum engineering. For now this is an initial test version.

Categories: Research, Software | Tags: benchmark, matlab, performance | No Comments

Semantics vs Models

December 24th, 2008

The idea of a semantic web or just in general providing semantics is essentially to augment data with additional data providing more information about what the original data is about (and standardise this to enable communication/interfacing). This is supposed to enable algorithms to process the original data better and in some sense understand that data. Calling this meta data seems to be justified in as far as that the additional data is actually not directly used or useful to humans, but it is intended for the algorithms. Humans can go quite far with interpreting data without this additional information, as far as their knowledge, experience and intelligence actually allows them to.

However, in the semantic web context, it seems that this means the data provider also has to provide all useful semantic information and that appears impossible. The data provider can provide this information for the data in the original context, but the data itself may have a far wider use. This would be missed by any algorithm as it does not reinterpret the data in a new, unknown context, but only use the original interpretation(s). More generally it seems to suggest a purely extrinsic notion of understanding independent of the observer. While semantics information may be useful in a very narrowly defined, specific context, a single project or precisely defined subject area, in a wider context it seems hardly achievable or useful.

Instead, a system which builds models (of any sort, not just statistically, even if statistical models seem to be important, especially for human interpretation) based on the data available seems to enable reinterpretation of the data and enable using it in different contexts. The resulting models derived from the data may then still be augmented with semantics information to make them accessible. This would base semantics on actual data in combination with an interpretation instead of trying to make the data fit a particular view. But this is not always necessary or needed, depending simply on the use of the resulting models. Of course a certain bias can still be present depending on the type of models used. It also makes semantics more intrinsic, depending on the observer and how it/she/he builds the model. Many different models may even be build to explore concepts and these models may not be easily translatable into each other, if at all. Of course the question now becomes how to (reasonably quickly) build such models.

This is not just related to the semantic web, but also, say, to interpreting geometric models in the sense of describing it in terms that are meaningful to someone wishing to process (create, edit, analyse, etc.) the model. A fixed description of a model’s design intent in this context via history, geometric constraints, regularities, etc. seems to be restricting in a similar way than providing rather universal semantics to data on the web and does not allow for reinterpretation and with that reuse.

Categories: Research | Tags: DesignIntent, Semantics | No Comments

Identifying Non-Smooth Boundary Curve Segments

December 24th, 2008

Let $P$ be a closed, non-self-intersecting, piecewise linear curve given by the points $P_l$ , which lie on a continuous surface. We seek, in a simplified sense here, a closed, non-self-intersecting piecewise linear curve $Q$ given by the points $Q_l$ , which still lie on the surface $S$ (and $Q$ is within a small distance from the surface) such that $Q$ ‘s distance to $P$ on the outside of the region bounded by $P$ is at most $\epsilon^+$ and to the inside at most $\epsilon^-$ . $Q$ should be in some sense smoother or fairer than $P$ . One approach to compute $Q$ is to first identify non-smooth segments of $P$ which can then be improved by some algorithm. Also see http://www.langbein.org/research/curves/smoothing/boundary-smoothing/.

In general a smooth or fair curve can be characterised by having a minimal number of segments with monotonic curvature (in our case geodesic curvature), i.e. minimise inflection points. Furthermore, the curve should overall have rather low curvature, i.e. minimise the curvature energy $\int \kappa^2\;ds$ , as far as this can be achieved under the constraints (see Euler’s elastica where the curve is only constrained by its end-points).

For a piecewise-linear curve a discrete curvature can be defined via the turning angles at its vertices. The turning angle values, however, depend on the sampling density as they are effectively the integrals over the curvature ( $d\phi = \kappa ds$ ). Using Taylor expansion of the curve the curvature at a vertex can be approximated by $\hat{\kappa}_l = 2\phi_l / (\|P_l-P_{l-1}\|+\|P_{l+1}-P_l\|)$ , which is optimal for three-point approximations in the linear terms and converges of fourth order for elastica if all edges have equal length (Langer et al, 2005, http://tinyurl.com/a25thy).

Using the above approximation we can determine inflection points as sign changes and using a maximum (absolute) curvature limit can furthermore label curve vertices as non-smooth if they exceed the limit. However, this alone does not identify non-smoothness of a curve on a larger scale than the local sampling distance. Moreover, the sampling distance should be reasonably uniform, which may or may not be the case for $P$ . If $P$ is noisy it may also result in rather noisy local curvature estimates, which can over- and under-estimate the curvature behaviour on a larger scale.

One way of identifying non-smooth curve segments on a larger scale is to ask how far the curve can be smoothed within the tolerance zone set by $\epsilon^+$ and $\epsilon^-$ in terms of how much $\int \kappa^2\;ds$ can be minimised within the tolerance zone. An efficient way to do this without actually solving the optimisation problem may be to estimate how far $\hat{\kappa}_l$ can be minimised by moving the three $P_l$ within the tolerance zone. Obviously one can then always minimise this to 0 by arranging the points along a (very short) line segment, so further restrictions are needed. One can restrict to move only $P_{l-1}, P_{l+1}$ along the curve to a maximum distance and find the minimal curvature to estimate the improvement possible by taking the difference between the minimum and the actual local estimate. Or move the points “orthogonal” to the curve in the tolerance zone again to find the best improvement. Or possibly find the (approximately) longest line segment through $P_l$ lying inside the tolerance zone to set the scale along which $P_{l-1},P_{l+1}$ can be moved along the curve to estimate the curvature improvement.

In general estimating the variation of curvature possible over a certain length range seems to indicate quite well how much the curve may be smoothed locally under the constraints and hence either label vertices with high potential for smoothing as non-smooth or even derive a smoothing priority for the vertices. See the figures below where the curve is plotted in black, the maximal improvement of the absolute curvature in magenta and curve vertices which can be improved by more than a certain amount are marked blue. Underneath the estimated vertex curvature is plotted in red, the maximal and minimal curvature achieved by moving the two adjacent points along the curve a certain maximal distance are plotted in green and the mean curvature is plotted in blue. The range the points could be moved is about four times as big in the first figure compared to the second figure.