Exact solution in the Heisenberg picture and annihilation-creation operators

The annihilation-creation operators of the harmonic oscillator, the basic and most important tools in quantum physics, are generalised to most solvable quantum mechanical systems of single degree of freedom including the so-called `discrete' quantum mechanics. They admit exact Heisenberg operator solution. We present unified definition of the annihilation-creation operators (a^{(\pm)}) as the positive/negative frequency parts of the exact Heisenberg operator solution.Comment: 10 pages, no figures. Abstract, Introduction revised; Conclusion added; Document-class changed. To appear in Phys. Lett.

Constraints to the Growth of Small Firms in Northern Myanmar

This paper uses survey data collected from Kalaymyo, a small urban city in North West Myanmar, to characterize firms and analyze the constraints limiting their growth. The level of firm ownership is very high but most firms are small, informal, operated out of the home, earning low income and with no employees. The most binding constraints are related to financing constraints, especially lack of access to informal credit. This is followed by the high degree of competition as the majority of firms are small retailers selling non-differentiated goods. This lack of credit combined with an apparent aversion to debt, limits the ability of entrepreneurs to take advantage of the high returns available on investment. We find that firms that made a capital investment over the last three years are significantly more profitable than those that did not

Variable and value elimination in binary constraint satisfaction via forbidden patterns

Variable or value elimination in a constraint satisfaction problem (CSP) can be used in preprocessing or during search to reduce search space size. A variable elimination rule (value elimination rule) allows the polynomial-time identification of certain variables (domain elements) whose elimination, without the introduction of extra compensatory constraints, does not affect the satisfiability of an instance. We show that there are essentially just four variable elimination rules and three value elimination rules defined by forbidding generic sub-instances, known as irreducible existential patterns, in arc-consistent CSP instances. One of the variable elimination rules is the already-known Broken Triangle Property, whereas the other three are novel. The three value elimination rules can all be seen as strict generalisations of neighbourhood substitution.Comment: A full version of an IJCAI'13 paper to appear in Journal of Computer and System Sciences (JCSS

On Broken Triangles (IJCAI 2016)

International audienceA binary CSP instance satisfying the broken-triangle property (BTP) can be solved in polynomial time. Unfortunately, in practice, few instances satisfy the BTP. We show that a local version of the BTP allows the merging of domain values in binary CSPs, thus providing a novel polynomial-time reduction operation. Experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems. We show that BTP-merging can be generalised to instances with constraints of arbitrary arity. A directional version of the general-arity BTP then allows us to extend the BTP tractable class previously defined only for binary CSP

Autour des Triangles Cassés

National audienceUne instance CSP binaire qui satisfait la propriété des triangles cassés (BTP) peut etre résolue en temps polynomial. Malheureusement, en pratique, peu d'ins-tances satisfont cette propriété. Nous montrons qu'une version locale de BTP permet de fusionner des valeurs dans les domaines d'instances binaires quelconques. Des expérimentations démontrent la diminution significative de la taille de l'instance pour certaines classes de pro-bì emes. Ensuite, nous proposons une généralisation de cette fusion a des contraintes d'arité quelconque. En-fin, une version orientée nous permet d'´ etendre la classe polynomiale BTP. Ce papier est un résumé de l'article M. C. Cooper, A. El Mouelhi, C. Terrioux et B. Zanuttini. On Broken Triangles In Proceedings of CP,LNCS 8656, 9–24, 2014

On Broken Triangles

A binary CSP instance satisfying the broken-triangle property (BTP) can be solved in polynomial time. Unfortunately, in practice, few instances satisfy the BTP. We show that a local version of the BTP allows the merging of domain values in binary CSPs, thus providing a novel polynomial-time reduction operation. Experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems. We show that BTP-merging can be generalised to instances with constraints of arbitrary arity. A directional version of the general-arity BTP then allows us to extend the BTP tractable class previously defined only for binary CSP