Deciding regular grammar logics with converse through first-order logic

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. A consequence of the translation is that the general satisfiability problem for regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Using the same method, we show how some other modal logics can be naturally translated into GF2, including nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed point-operators.Comment: 34 page

Structured Dropout for Weak Label and Multi-Instance Learning and Its Application to Score-Informed Source Separation

Many success stories involving deep neural networks are instances of supervised learning, where available labels power gradient-based learning methods. Creating such labels, however, can be expensive and thus there is increasing interest in weak labels which only provide coarse information, with uncertainty regarding time, location or value. Using such labels often leads to considerable challenges for the learning process. Current methods for weak-label training often employ standard supervised approaches that additionally reassign or prune labels during the learning process. The information gain, however, is often limited as only the importance of labels where the network already yields reasonable results is boosted. We propose treating weak-label training as an unsupervised problem and use the labels to guide the representation learning to induce structure. To this end, we propose two autoencoder extensions: class activity penalties and structured dropout. We demonstrate the capabilities of our approach in the context of score-informed source separation of music

Extending emission line Doppler tomography ; mapping modulated line flux

Emission line Doppler tomography is a powerful tool that resolves the accretion flow in binaries on micro-arcsecond scales using time-resolved spectroscopy. I present an extension to Doppler tomography that relaxes one of its fundamental axioms and permits the mapping of time-dependent emission sources. Significant variability on the orbital period is a common characteristic of the emission sources that are observed in the accretion flows of cataclysmic variables and X-ray binaries. Modulation Doppler tomography maps sources varying harmonically as a function of the orbital period through the simultaneous reconstruction of three Doppler tomograms. One image describes the average flux distribution like in standard tomography, while the two additional images describe the variable component in terms of its sine and cosine amplitudes. I describe the implementation of such an extension in the form of the maximum entropy based fitting code MODMAP. Test reconstructions of synthetic data illustrate that the technique is robust and well constrained. Artifact free reconstructions of complex emission distributions can be achieved under a wide range of signal to noise levels. An application of the technique is illustrated by mapping the orbital modulations of the asymmetric accretion disc emission in the dwarf nova IP Pegasi.Comment: 8 pages, 4 figures; accepted for publication in MNRA

Higgs bundles and local systems on Riemann surfaces

Lecture notes from the Third International School on Geometry and Physics at the Centre de Recerca Matematica in Barcelona, March 26--30, 2012.Comment: Final version. To appear in the collection CRM Advanced Courses in Mathematic

The infinite random simplicial complex

We study the Fraisse limit of the class of all finite simplicial complexes. Whilst the natural model-theoretic setting for this class uses an infinite language, a range of results associated with Fraisse limits of structures for finite languages carry across to this important example. We introduce the notion of a local class, with the class of finite simplicial complexes as an archetypal example, and in this general context prove the existence of a 0-1 law and other basic model-theoretic results. Constraining to the case where all relations are symmetric, we show that every direct limit of finite groups, and every metrizable profinite group, appears as a subgroup of the automorphism group of the Fraisse limit. Finally, for the specific case of simplicial complexes, we show that the geometric realisation is topologically surprisingly simple: despite the combinatorial complexity of the Fraisse limit, its geometric realisation is homeomorphic to the infinite simplex.Comment: 33 page