Lipschitz Robustness of Finite-state Transducers

We investigate the problem of checking if a finite-state transducer is robust to uncertainty in its input. Our notion of robustness is based on the analytic notion of Lipschitz continuity --- a transducer is K-(Lipschitz) robust if the perturbation in its output is at most K times the perturbation in its input. We quantify input and output perturbation using similarity functions. We show that K-robustness is undecidable even for deterministic transducers. We identify a class of functional transducers, which admits a polynomial time automata-theoretic decision procedure for K-robustness. This class includes Mealy machines and functional letter-to-letter transducers. We also study K-robustness of nondeterministic transducers. Since a nondeterministic transducer generates a set of output words for each input word, we quantify output perturbation using set-similarity functions. We show that K-robustness of nondeterministic transducers is undecidable, even for letter-to-letter transducers. We identify a class of set-similarity functions which admit decidable K-robustness of letter-to-letter transducers.Comment: In FSTTCS 201

Characterization of pyridine nucleotide binding site of UDP-glucose 4-epimerase from Saccharomyces fragilis

UDP-glucose 4-epimerase from Saccharomyces fragilis has 1 mol of NAD firmly bound per mol of the dimeric apoenzyme. This prevents a direct study of the coenzyme binding site of the protein. Dissociation of the dimer with p-chloromercuribenzoate and its reconstitution with exogenous NAD or one of its analogues and 2-mercaptoethanol provides an indirect method of study of the site. Depending on the reconstitution properties, the analogues can be classified in the following groups: (i) analogues that have no affinity for the site; (ii) analogues that have affinity but are not incorporated into the apoenzyme; (iii) analogues that produce catalytically inactive holoenzymes; and (iv) analogues that produce catalytically active holoenzymes. Minimum structural requirements that lead to affinity for the coenzyme site and to binding to the apoenzyme can also be discerned from these studies. Reconstitution with etheno-NAD, a fluorescent analogue of NAD, indicates the presence of a hydrophobic pocket for the adenosine subsite

Study on Noncommutative Representations of Galilean Generators

The representations of Galilean generators are constructed on a space where both position and momentum coordinates are noncommutating operators. A dynamical model invariant under noncommutative phase space transformations is constructed. The Dirac brackets of this model reproduce the original noncommutative algebra. Also, the generators in terms of noncommutative phase space variables are abstracted from this model in a consistent manner. Finally, the role of Jacobi identities is emphasised to produce the noncommuting structure that occurs when an electron is subjected to a constant magnetic field and Berry curvature.Comment: Title changed, new references added, published in Int. J. Mod. Phys.