We introduce and study two new classes of unital quantum channels. The first class describes a 2-parameter family channels given by completely positive (CP) maps $M_3({\bf C}) \mapsto M_3({\bf C})$ which are both trace-preserving. Almost every member this is factorizable extreme in the set CP trace-preserving, but not either or trace-preserving maps. also large generalize Werner-Holevo channel ...

The CEGAR loop in software model checking notoriously diverges when the abstraction refinement procedure does not derive a loop invariant. An abstraction refinement procedure based on an SMT solver is applied to a trace, i.e., a restricted form of a program (without loops). In this paper, we present a new abstraction refinement procedure that aims at circumventing this restriction whenever poss...

Three strains of heterotrophic denitrifying bacteria were cultured in artificial seawater medium under trace metal clean conditions to investigate their physiological response to changes in copper concentration. Decreasing the copper concentration in cultures of Pseudomonas stutzeri and Paracoccus denitrificans resulted in accumulation of nitrous oxide (N2O) gas compared to copper-replete cultu...

The prefrontal cortex has been shown to participate in the association of events separated by time. However, it is not known whether the prefrontal cortex stores the memory for these relationships. Trace conditioning is a form of classical conditioning in which a time gap separates the conditioned stimulus (CS) from the unconditioned stimulus (US), the association of which has been shown to dep...

is then a unitary representation of G(F) X G(F) on L2(G(F)). Kazhdan has suggested that there should be a local trace formula attached to R which is analogous to the global trace formula for automorphic forms. The purpose of this note is to discuss how one might go about proving such an identity, and to describe the ultimate form the identity is likely to take. To see the analogy with automorph...

Symplectic eigenvalues are conventionally defined for symmetric positive-definite matrices via Williamson's diagonal form. Many properties of standard eigenvalues, including the trace minimization theorem, have been extended to case symplectic eigenvalues. In this note, we will generalize form positive-semidefinite matrices, which allows us define and prove theorem in new setting.

desired physical form of cities has been noticeable since the beginning of urbanization, from old patterns of early civilizations to the latest urbanism’s theories, which offered to build better cities. the opinions in recent decades have expressed that compact physical form of cities is a better form than sprawl form to achieve urban sustainability. the form of the city is the embodiment of it...