Transformation design and nonlinear Hamiltonians

We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.Comment: Accepted for publication in Journal of Modern Optic

Counting, generating and sampling tree alignments

Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical sets of matches between identical pairs of trees. This ambiguity is uninformative, and detrimental to any probabilistic analysis.In this work, we consider tree alignments up to equivalence. Our first result is a precise asymptotic enumeration of tree alignments, obtained from a context-free grammar by mean of basic analytic combinatorics. Our second result focuses on alignments between two given ordered trees $S$ and $T$. By refining our grammar to align specific trees, we obtain a decomposition scheme for the space of alignments, and use it to design an efficient dynamic programming algorithm for sampling alignments under the Gibbs-Boltzmann probability distribution. This generalizes existing tree alignment algorithms, and opens the door for a probabilistic analysis of the space of suboptimal RNA secondary structures alignments.Comment: ALCOB - 3rd International Conference on Algorithms for Computational Biology - 2016, Jun 2016, Trujillo, Spain. 201

Reactive Control Improvisation

Reactive synthesis is a paradigm for automatically building correct-by-construction systems that interact with an unknown or adversarial environment. We study how to do reactive synthesis when part of the specification of the system is that its behavior should be random. Randomness can be useful, for example, in a network protocol fuzz tester whose output should be varied, or a planner for a surveillance robot whose route should be unpredictable. However, existing reactive synthesis techniques do not provide a way to ensure random behavior while maintaining functional correctness. Towards this end, we generalize the recently-proposed framework of control improvisation (CI) to add reactivity. The resulting framework of reactive control improvisation provides a natural way to integrate a randomness requirement with the usual functional specifications of reactive synthesis over a finite window. We theoretically characterize when such problems are realizable, and give a general method for solving them. For specifications given by reachability or safety games or by deterministic finite automata, our method yields a polynomial-time synthesis algorithm. For various other types of specifications including temporal logic formulas, we obtain a polynomial-space algorithm and prove matching PSPACE-hardness results. We show that all of these randomized variants of reactive synthesis are no harder in a complexity-theoretic sense than their non-randomized counterparts.Comment: 25 pages. Full version of a CAV 2018 pape

First evidence for Wollemi Pine-type pollen (Dilwynites: Araucariaceae) in South America

We report the first fossil pollen from South America of the lineage that includes the recently discovered, extremely rare Australian Wollemi Pine, Wollemia nobilis (Araucariaceae). The grains are from the late Paleocene to early middle Eocene Ligorio Márquez Formation of Santa Cruz, Patagonia, Argentina, and are assigned to Dilwynites, the fossil pollen type that closely resembles the pollen of modern Wollemia and some species of its Australasian sister genus, Agathis. Dilwynites was formerly known only from Australia, New Zealand, and East Antarctica. The Patagonian Dilwynites occurs with several taxa of Podocarpaceae and a diverse range of cryptogams and angiosperms, but not Nothofagus. The fossils greatly extend the known geographic range of Dilwynites and provide important new evidence for the Antarctic region as an early Paleogene portal for biotic interchange between Australasia and South America.Mike Macphail, Raymond J. Carpenter, Ari Iglesias, Peter Wil

Concentration of the intrinsic volumes of a convex body

The intrinsic volumes are measures of the content of a convex body. This paper applies probabilistic and information-theoretic methods to study the sequence of intrinsic volumes. The main result states that the intrinsic volume sequence concentrates sharply around a specific index, called the central intrinsic volume. Furthermore, among all convex bodies whose central intrinsic volume is fixed, an appropriately scaled cube has the intrinsic volume sequence with maximum entropy

How to generate all possible rational Wilf-Zeilberger pairs?

A Wilf--Zeilberger pair $(F, G)$ in the discrete case satisfies the equation $F(n+1, k) - F(n, k) = G(n, k+1) - G(n, k)$. We present a structural description of all possible rational Wilf--Zeilberger pairs and their continuous and mixed analogues.Comment: 17 pages, add the notion of pseudo residues in the differential case, and some related papers in the reference, ACMES special volume in the Fields Institute Communications series, 201