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===========================================================================================================================** FRIDAY, MARCH 27: ** Ralph Kopperman will discuss "Decimals and Aspigories".
At CCNY; tea 12:30 p.m. at NAC 8/130, talk 1:00 to 2:00 p.m. at NAC 5/150. For more information, contact Ralph Kopperman,
rdkcc@ccny.cuny.edu.

__ SCHEDULE__:

11 a.m. - 12 noon, Michael Bukatin, Nokia Corporation, will discuss "Topics in bicontinuity, partial inconsistency,
and vector semantics".

12 noon - 12:30 p.m., tea.

12:30 p.m. - 1:30 p.m., Steve Matthews, University of Warwick, will speak on "Intensional
Partial Metric Spaces".

1:30 p.m. - 2 p.m., tea.

__ABSTRACTS__:

__Michael Bukatin, Nokia, "Topics in bicontinuity, partial inconsistency, and vector
semantics"__

The Scott topology allows modeling the meaning of programs with continuous functions.
Admitting the elements expressing partial contradictions, such as negative probabilities and segments of negative length,
allows us to bridge the gap between Scott domains and vector spaces, raising hopes that standard methods of applied
mathematics will become applicable to the tasks of program learning, program transformation, and program synthesis.

In this talk I hope to cover three topics within this context.

1) Bicontinuity and the domain of arrows. A partially ordered set D is a bicontinuous domain,
if both D and D^* (D with the reverse order) are continuous domains. The domain of arrows, D^* \times D, is a remarkably
interesting structure. Our original inspiration for the domain of arrows came from the desire to consider limits and
continuity in the intensional partial metric spaces (functors into a category of partial metrics) proposed by Steve Matthews.
Important constructions on the domain of arrows resemble distributors (profunctors) and hopefully can be lifted back to the
context of intensional spaces.

2) Negative probability and quantum algorithms. The phase space formulation of quantum
mechanics uses the Wigner quasiprobability distribution rather than complex amplitude. There is a body of research
reformulating quantum algorithms in terms of quasiprobabilities. At the same time there are surprising parallels between
Grover's quantum algorithm and a scheme of computations in the domain of arrows involving a mixture of monotonic steps and
order-reversing involutions.

3) Linear combinations of computations. I am aware of two large classes of computations which
admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. Working with those
types of computations seems to give the most direct shot at the practical use of vector semantics in the tasks of program
learning, program transformation, and program synthesis.

__Steve Matthews, University of Warwick, "Intensional Partial Metric Spaces"__

Partial metric spaces [4,5] generalise metric spaces [1] by allowing self-distance to be a
non-negative number. Originally motivated by the goal to reconcile metric space topology with the logic of computable
functions and Dana Scott's innovative theory of topological domains, they are now too rigid a form of mathematics to be of
use in modelling contemporary applications software (aka Apps) which is increasingly concurrent, pragmatic, interactive,
rapidly changing, and inconsistent in nature.

This presentation aims to further develop partial metric spaces in order to catch up with
the modern computer science of Apps. Our illustrative working example is that of the Lucid programming language [2,3] and a
temporal generalisation using Wadge's hiaton, an innovative notion of pause in a computation.

References:

[1] M. Fr\'{e}chet, "Sur quelques points du calcul fonctionnel", Rend.Circ. Mat. Palermo 22
(1906), pp. 1-74.

[2] E.A. Ashcroft \& W.W. Wadge, "Lucid, a nonprocedural language with iteration", Comm.
ACM 20, (1977), pp. 519-526.

[3] W.W. Wadge \& E.A. Ashcroft, "Lucid, the Dataflow Programming Language", APIC Studies in
Data Processing 22, Academic Press (1985).

[4] S.G. Matthews, "Partial metric topology", in General Topology \& its Applications, Proc.
8th Summer Conf. Queen's College (1992), Annals of the New York Academy of Science, eds. Andima, S. et al, Vol 728, (1994),
pp. 183-197.

[5] M. Bukatin, R. Kopperman, S. Matthews, \& H. Pajoohesh, "Partial Metric Spaces", American
Mathematical Monthly, Vol. 116, No. 8 (2009), pp. 708-718.

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** THURSDAY, APRIL 23: ** Aaron R. Todd, Baruch College, CUNY, will discuss "The Separable Quotient
Problem, Barrelled Spaces and C

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** FRIDAY, MAY 8: ** Daniel R. Patten, Syracuse University, will speak on "Differential calculus on
discrete structures". At CCNY; tea 12:30 p.m. NAC 8/130, talk 1 p.m. NAC 5/150. For more information, contact Ralph
Kopperman, rdkcc@ccny.cuny.edu.

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__For more information, contact:__

CCNY: R. Kopperman (845-915-0914), S. Popvassilev (646-257-7197)

College of Staten Island (718-982-3626): P. R. Misra

Baruch College (646-312-4136): A. Todd

LIU C. W. Post Center (516-299-2447): S. Andima

Medgar Evers College, (718-270-6416): H. Pajoohesh

Queensborough Community College, (718-281-5291): F. Jordan