in this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. in particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. then we study fuzzy...

Individual-based models describing the migration and proliferation of a population of cells frequently restrict the cells to a predefined lattice. An implicit assumption of this type of lattice-based model is that a proliferative population will always eventually fill the lattice. Here, we develop a new lattice-free individual-based model that incorporates cell-to-cell crowding effects. We also...

Coordinate transformation is essential in many georeferencing applications. Level-wised transformation can be considered as a regression problem and done by machine-learning approaches. However, inaccurate and biased results are usually derived when training data do not uniformly distribute. In this paper, the performance of regression-based coordinate transformation for GPS applications is dis...

Belief propagation (BP) is a message-passing method for solving probabilistic graphical models. It is very successful in treating disordered models (such as spin glasses) on random graphs. On the other hand, finite-dimensional lattice models have an abundant number of short loops, and the BP method is still far from being satisfactory in treating the complicated loop-induced correlations in the...

We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, it then gets promoted to a quantum group gauge symmetry. The theory depends on two parameters-the deformation parameter and the lattice spacing a. We show that the system of Kogut and Susskind is ...

There is an inherent difficulty in building 3-move ID schemes based on combinatorial problems without much algebraic structure. A consequence of this, is that most standard ID schemes today are based on the hardness of number theory problems. Not having schemes based on alternate assumptions is a cause for concern since improved number theoretic algorithms or the realization of quantum computin...

We present a new open source model checker, opaal, for automatic verification of models using lattice automata. Lattice automata allow the users to incorporate abstractions of a model into the model itself. This provides an efficient verification procedure, while giving the user fine-grained control of the level of abstraction by using a method similar to Counter-Example Guided Abstraction Refi...