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TheβPictoris system is the closest known stellar system with directly detected gas giant planets, an edge-on circumstellar disc, and evidence of falling sublimating bodies and transiting exocomets. The inner planet,βPictoris c, has also been indirectly detected with radial velocity (RV) measurements. The star is a knownδScuti pulsator, and the long-term stability of these pulsations opens up the possibility of indirectly detecting the gas giant planets through time delays of the pulsations due to a varying light travel time. We search for phase shifts in theδScuti pulsations consistent with the known planetsβPictoris b and c and carry out an analysis of the stellar pulsations ofβPictoris over a multi-year timescale. We used photometric data collected by the BRITE-Constellation, bRing, ASTEP, and TESS to derive a list of the strongest and most significantδScuti pulsations. We carried out an analysis with the open-source python package maelstrom to study the stability of the pulsation modes ofβPictoris in order to determine the long-term trends in the observed pulsations. We did not detect the expected signal forβPictoris b orβPictoris c. The expected time delay is 6 s forβPictoris c and 24 s forβPictoris b. With simulations, we determined that the photometric noise in all the combined data sets cannot reach the sensitivity needed to detect the expected timing drifts. An analysis of the pulsational modes ofβPictoris using maelstrom showed that the modes themselves drift on the timescale of a year, fundamentally limiting our ability to detect exoplanets aroundβPictoris via pulsation timing. 

We present a computer interface to visualize and interact with mathematical knots, i.e., the embeddings of closed circles in 3-dimensional Euclidean space. Mathematical knots are slightly different than everyday knots in that they are infinitely stretchy and flexible when being deformed into their topological equivalence. In this work, we design a visualization interface to depict mathematical knots as closed node-link diagrams with energies charged at each node, so that highly-tangled knots can evolve by themselves from high-energy states to minimal (or lower) energy states. With a family of interactive methods and supplementary user interface elements, out tool allows one to sketch, edit, and experiment with mathematical knots, and observe their topological evolution towards optimal embeddings. In addition, out interface can extract from the entire knot evolution those key moments where successive terms in the sequence differ by critical change; this provides a clear and intuitive way to understand and trace mathematical evolution with a minimal number of visual frames. Finally out interface is adapted and extended to support the depiction of mathematical links and braids, whose mathematical concepts and interactions are just similar to our intuition about knots. All these combine to show a mathematically rich interface to help us explore and understand a family of fundamental geometric and topological problems.