The modularity of the partition generating function has many important consequences, for example asymptotics and congruences for p(n). In a series of papers the author and Ono [12, 13] connected the rank, a partition statistic introduced by Dyson, to weak Maass forms, a new class of functions which are related to modular forms and which were first considered in [11]. Here we do a further step t...

A novel Bayesian Augmented-Learning framework, quantifying the uncertainty of spectral representations stochastic processes in presence missing data, is developed. The approach combines additional information (prior domain knowledge) physical with real, yet incomplete, observations. deep learning models are trained to learn underlying process, probabilistically capturing temporal dynamics, from...

We have developed a new partial order planner called PSIPLAN for open world planning, where the agent does not have complete information about the world and must take actions both to acquire knowledge and to change the world. Incompleteness of the agent's knowledge means that it cannot use the Closed World Assumption (CWA) in the representation of the state and must rely on a diierent method fo...

Even under polynomial restrictions on plan length, conformant planning remains a very hard computational problem as plan verification itself can take exponential time. This heavy price cannot be avoided in general although in many cases conformant plans are verifiable efficiently by means of simple forms of disjunctive inference. This raises the question of whether it is possible to identify an...

UNLABELLED Henoch-Schönlein purpura, the most common primary vasculitis of the child, may cause, in some cases with atypical clinical picture, diagnostic difficulties with a significant prognosis impact, especially when occasionally "silent" renal symptoms coexist. The purpose of our study is, on one hand, to determine the histopathological investigation needs of Henoch-Schönlein purpura in chi...