Hypergraph Acyclicity and Propositional Model Counting

We show that the propositional model counting problem #SAT for CNF- formulas with hypergraphs that allow a disjoint branches decomposition can be solved in polynomial time. We show that this class of hypergraphs is incomparable to hypergraphs of bounded incidence cliquewidth which were the biggest class of hypergraphs for which #SAT was known to be solvable in polynomial time so far. Furthermore, we present a polynomial time algorithm that computes a disjoint branches decomposition of a given hypergraph if it exists and rejects otherwise. Finally, we show that some slight extensions of the class of hypergraphs with disjoint branches decompositions lead to intractable #SAT, leaving open how to generalize the counting result of this paper

Pose Induction for Novel Object Categories

We address the task of predicting pose for objects of unannotated object categories from a small seed set of annotated object classes. We present a generalized classifier that can reliably induce pose given a single instance of a novel category. In case of availability of a large collection of novel instances, our approach then jointly reasons over all instances to improve the initial estimates. We empirically validate the various components of our algorithm and quantitatively show that our method produces reliable pose estimates. We also show qualitative results on a diverse set of classes and further demonstrate the applicability of our system for learning shape models of novel object classes

Towards a More Well-Founded Cosmology

First, this paper broaches the definition of science and the epistemic yield of tenets and approaches: phenomenological (descriptive only), well-founded (solid first principles, conducive to deep understanding), provisional (falsifiable if universal, verifiable if existential), and imaginary (fictitious entities or processes, conducive to empirically unsupported beliefs). The Big-Bang pardigm and the {\Lambda}CDM "concordance model" involve such beliefs: the emanation of the universe out of a non-physical stage, cosmic inflation (invented ad hoc), {\Lambda} (fictitious energy), and exotic dark matter. They fail in the confidence check that is required in empirical science. They also face a problem in delimiting what expands from what does not. In the more well-founded cosmology that emerges, energy is conserved, the universe is persistent (not transient) and the 'perfect cosmological principle' holds. Waves and other perturbations that propagate at c (the escape velocity from the universe) expand exponentially with distance. This dilatation results from gravitation. The cosmic web of galaxies does not expand. Potential {\Phi} varies as -H/(cz) instead of -1/r. Inertial forces arise from gravitational interaction with the rest of the universe (not with space). They are increased where the universe appears blueshifted and decreased more than proportionately at very low accelerations. A cut-off acceleration a0 = 0.168 cH is deduced. This explains the successful description of galaxy rotation curves by MoND. A fully elaborated physical theory is still pending. The recycling of energy via a cosmic ocean filled with photons (the CMB), neutrinos and gravitons, and wider implications for science, are briefly discussed