Proving Safety with Trace Automata and Bounded Model Checking

Loop under-approximation is a technique that enriches C programs with additional branches that represent the effect of a (limited) range of loop iterations. While this technique can speed up the detection of bugs significantly, it introduces redundant execution traces which may complicate the verification of the program. This holds particularly true for verification tools based on Bounded Model Checking, which incorporate simplistic heuristics to determine whether all feasible iterations of a loop have been considered. We present a technique that uses \emph{trace automata} to eliminate redundant executions after performing loop acceleration. The method reduces the diameter of the program under analysis, which is in certain cases sufficient to allow a safety proof using Bounded Model Checking. Our transformation is precise---it does not introduce false positives, nor does it mask any errors. We have implemented the analysis as a source-to-source transformation, and present experimental results showing the applicability of the technique

Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton - Jacobi Formalism

We obtain the band edge eigenfunctions and the eigenvalues of solvable periodic potentials using the quantum Hamilton - Jacobi formalism. The potentials studied here are the Lam{\'e} and the associated Lam{\'e} which belong to the class of elliptic potentials. The formalism requires an assumption about the singularity structure of the quantum momentum function $p$, which satisfies the Riccati type quantum Hamilton - Jacobi equation, $p^{2} -i \hbar \frac{d}{dx}p = 2m(E- V(x))$ in the complex $x$ plane. Essential use is made of suitable conformal transformations, which leads to the eigenvalues and the eigenfunctions corresponding to the band edges in a simple and straightforward manner. Our study reveals interesting features about the singularity structure of $p$, responsible in yielding the band edge eigenfunctions and eigenvalues.Comment: 21 pages, 5 table

Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation

In this paper we classify Weingarten surfaces integrable in the sense of soliton theory. The criterion is that the associated Gauss equation possesses an sl(2)-valued zero curvature representation with a nonremovable parameter. Under certain restrictions on the jet order, the answer is given by a third order ordinary differential equation to govern the functional dependence of the principal curvatures. Employing the scaling and translation (offsetting) symmetry, we give a general solution of the governing equation in terms of elliptic integrals. We show that the instances when the elliptic integrals degenerate to elementary functions were known to nineteenth century geometers. Finally, we characterize the associated normal congruences

Quantum Inozemtsev model, quasi-exact solvability and N-fold supersymmetry

Inozemtsev models are classically integrable multi-particle dynamical systems related to Calogero-Moser models. Because of the additional q^6 (rational models) or sin^2(2q) (trigonometric models) potentials, their quantum versions are not exactly solvable in contrast with Calogero-Moser models. We show that quantum Inozemtsev models can be deformed to be a widest class of partly solvable (or quasi-exactly solvable) multi-particle dynamical systems. They posses N-fold supersymmetry which is equivalent to quasi-exact solvability. A new method for identifying and solving quasi-exactly solvable systems, the method of pre-superpotential, is presented.Comment: LaTeX2e 28 pages, no figure

Representations of sl(2,?) in category O and master symmetries

We show that the indecomposable sl(2,?)-modules in the Bernstein-Gelfand-Gelfand category O naturally arise for homogeneous integrable nonlinear evolution systems. We then develop a new approach called the O scheme to construct master symmetries for such integrable systems. This method naturally allows computing the hierarchy of time-dependent symmetries. We finally illustrate the method using both classical and new examples. We compare our approach to the known existing methods used to construct master symmetries. For new integrable equations such as a Benjamin-Ono-type equation, a new integrable Davey-Stewartson-type equation, and two different versions of (2+1)-dimensional generalized Volterra chains, we generate their conserved densities using their master symmetries

Universal Lax pairs for Spin Calogero-Moser Models and Spin Exchange Models

For any root system $\Delta$ and an irreducible representation ${\cal R}$ of the reflection (Weyl) group $G_\Delta$ generated by $\Delta$, a {\em spin Calogero-Moser model} can be defined for each of the potentials: rational, hyperbolic, trigonometric and elliptic. For each member $\mu$ of ${\cal R}$, to be called a "site", we associate a vector space ${\bf V}_{\mu}$ whose element is called a "spin". Its dynamical variables are the canonical coordinates $\{q_j,p_j\}$ of a particle in ${\bf R}^r$, ($r=$ rank of $\Delta$), and spin exchange operators $\{\hat{\cal P}_\rho\}$ ($\rho\in\Delta$) which exchange the spins at the sites $\mu$ and $s_{\rho}(\mu)$. Here $s_\rho$ is the reflection generated by $\rho$. For each $\Delta$ and ${\cal R}$ a {\em spin exchange model} can be defined. The Hamiltonian of a spin exchange model is a linear combination of the spin exchange operators only. It is obtained by "freezing" the canonical variables at the equilibrium point of the corresponding classical Calogero-Moser model. For $\Delta=A_r$ and ${\cal R}=$ vector representation it reduces to the well-known Haldane-Shastry model. Universal Lax pair operators for both spin Calogero-Moser models and spin exchange models are presented which enable us to construct as many conserved quantities as the number of sites for {\em degenerate} potentials.Comment: 18 pages, LaTeX2e, no figure

Physics and Mathematics of Calogero particles

We give a review of the mathematical and physical properties of the celebrated family of Calogero-like models and related spin chains.Comment: Version to appear in Special Issue of Journal of Physics A: Mathematical and Genera

Design of synthetic bacterial communities for predictable plant phenotypes

Specific members of complex microbiota can influence host phenotypes, depending on both the abiotic environment and the presence of other microorganisms. Therefore, it is challenging to define bacterial combinations that have predictable host phenotypic outputs. We demonstrate that plant–bacterium binary-association assays inform the design of small synthetic communities with predictable phenotypes in the host. Specifically, we constructed synthetic communities that modified phosphate accumulation in the shoot and induced phosphate starvation–responsive genes in a predictable fashion. We found that bacterial colonization of the plant is not a predictor of the plant phenotypes we analyzed. Finally, we demonstrated that characterizing a subset of all possible bacterial synthetic communities is sufficient to predict the outcome of untested bacterial consortia. Our results demonstrate that it is possible to infer causal relationships between microbiota membership and host phenotypes and to use these inferences to rationally design novel communities

Artificial reefs: from ecological processes to fishing enhancement tools

info:eu-repo/semantics/publishedVersio