Healthiness from Duality

Healthiness is a good old question in program logics that dates back to Dijkstra. It asks for an intrinsic characterization of those predicate transformers which arise as the (backward) interpretation of a certain class of programs. There are several results known for healthiness conditions: for deterministic programs, nondeterministic ones, probabilistic ones, etc. Building upon our previous works on so-called state-and-effect triangles, we contribute a unified categorical framework for investigating healthiness conditions. We find the framework to be centered around a dual adjunction induced by a dualizing object, together with our notion of relative Eilenberg-Moore algebra playing fundamental roles too. The latter notion seems interesting in its own right in the context of monads, Lawvere theories and enriched categories.Comment: 13 pages, Extended version with appendices of a paper accepted to LICS 201

Interacting scalar and spinor fields in Bianchi type I universe filled with magneto-fluid

Self-consistent system of spinor, scalar and BI gravitational fields in presence of magneto-fluid and $\Lambda$-term is considered. Assuming that the expansion of the BI universe is proportional to the $\sigma_1^1$ component of the shear tensor, exact solutions for the metric functions, as well as for scalar and spinor fields are obtained. For a non-positive $\Lambda$ the initially anisotropic space-time becomes isotropic one in the process of expansion, whereas, for $\Lambda > 0$ an oscillatory mode of expansion of the BI model occurs.Comment: RevTex4, 8 pages, no figure

Experimental Demonstration of a Quantum Circuit using Linear Optics Gates

One of the main advantages of an optical approach to quantum computing is the fact that optical fibers can be used to connect the logic and memory devices to form useful circuits, in analogy with the wires of a conventional computer. Here we describe an experimental demonstration of a simple quantum circuit of that kind in which two probabilistic exclusive-OR (XOR) logic gates were combined to calculate the parity of three input qubits.Comment: v2 is final PRA versio

The Minimum Wiener Connector

The Wiener index of a graph is the sum of all pairwise shortest-path distances between its vertices. In this paper we study the novel problem of finding a minimum Wiener connector: given a connected graph $G=(V,E)$ and a set $Q\subseteq V$ of query vertices, find a subgraph of $G$ that connects all query vertices and has minimum Wiener index. We show that The Minimum Wiener Connector admits a polynomial-time (albeit impractical) exact algorithm for the special case where the number of query vertices is bounded. We show that in general the problem is NP-hard, and has no PTAS unless $\mathbf{P} = \mathbf{NP}$. Our main contribution is a constant-factor approximation algorithm running in time $\widetilde{O}(|Q||E|)$. A thorough experimentation on a large variety of real-world graphs confirms that our method returns smaller and denser solutions than other methods, and does so by adding to the query set $Q$ a small number of important vertices (i.e., vertices with high centrality).Comment: Published in Proceedings of the 2015 ACM SIGMOD International Conference on Management of Dat

Combinatorial models of rigidity and renormalization

We first introduce the percolation problems associated with the graph theoretical concepts of $(k,l)$-sparsity, and make contact with the physical concepts of ordinary and rigidity percolation. We then devise a renormalization transformation for $(k,l)$-percolation problems, and investigate its domain of validity. In particular, we show that it allows an exact solution of $(k,l)$-percolation problems on hierarchical graphs, for $k\leq l<2k$. We introduce and solve by renormalization such a model, which has the interesting feature of showing both ordinary percolation and rigidity percolation phase transitions, depending on the values of the parameters.Comment: 22 pages, 6 figure

Antibody localization in horse, rabbit, and goat antilymphocyte sera

The localization of antibodies was studied in rabbit, goat, and horse ALS raised by weekly immunization with canine or human spleen cells for 4 to 12 weeks. A combination of analytic techniques was used including column chromatography, electrophoresis, immunoelectrophoresis, determination of protein concentration, and measurement of antibody titers. In the rabbit and goat ALS, virtually all of the leukoagglutinins and lymphocytotoxins were in the easily separable IgG; accidentally induced thromboagglutinins were in the same location. In the rabbit hemagglutinins were found in both the IgG and IgM, whereas in the goat these were almost exclusively in the IgM. The antiwhite cell antibodies were most widely distributed in the horse. The cytotoxins were primarily in the IgG, but the leukoagglutinins were most heavily concentrated in the T-equine globulin which consists mostly of IgA. By differential ammonium sulfate precipitation of a horse antidoglymphocyte serum, fractions were prepared that were rich in IgG and IgA. Both were able to delay the rejection of canine renal homografts, the IgA-rich preparation to a somewhat greater degree. The findings in this study have been discussed in relation to the refining techniques that have been used for the production of globulin from heterologous ALS. © 1970

Anomalous Density-of-States Fluctuations in Two-Dimensional Clean Metals

It is shown that density-of-states fluctuations, which can be interpreted as the order-parameter susceptibility \chi_OP in a Fermi liquid, are anomalously strong as a result of the existence of Goldstone modes and associated strong fluctuations. In a 2-d system with a long-range Coulomb interaction, a suitably defined \chi_OP diverges as 1/T^2 as a function of temperature in the limit of small wavenumber and frequency. In contrast, standard statistics suggest \chi_OP = O(T), a discrepancy of three powers of T. The reasons behind this surprising prediction, as well as ways to observe it, are discussed.Comment: 4 pp, revised version contains a substantially expanded derivatio