A Quantitative Version of Simple Types

This work introduces a quantitative version of the simple type assignment system, starting from a suitable restriction of non-idempotent intersection types. The resulting system is decidable and has the same typability power as the simple type system; thus, assigning types to terms supplies the very same qualitative information given by simple types, but at the same time can provide some interesting quantitative information. It is well known that typability for simple types is equivalent to unification; we prove a similar result for the newly introduced system. More precisely, we show that typability is equivalent to a unification problem which is a non-trivial extension of the classical one: in addition to unification rules, our typing algorithm makes use of an expansion operation that increases the cardinality of multisets whenever needed

CALCULATING PRIVACY PRESERVING REACH USING HYPERLOGLOG SKETCHES

Methods for measuring cross media content exposure across multiple publishers in a privacy preserving way are disclosed. The solutions described can accommodate publishing platforms that vary in size and computational resources without hindering performance or accuracy. Proposed is a solution to implement a privacy-safe HyperLogLog sketch implementation that can be applied to the cross media content exposure problem, as well as other problems that require privacy safe multi-set cardinality estimation. The processes described herein include publishers constructing encrypted HyperLogLog sketches and transmitting the encrypted sketches to worker computing devices, the worker computing devices joining the encrypted sketches, the worker computing devices finding the minimum value of each register in the joined sketch, and summing the registers to compute the multi-set cardinality estimate

P and dP Automata: A Survey

This is a quick survey of basic notions and results related to P automata (P systems with symport/antiport rules working in the accepting mode), with some emphasis on the recently introduced dP automata (a distributed version of the standard P automata), ending with some open problems and research topics which we find of interest in this area.Junta de Andalucía P08 – TIC 0420

Types as Resources for Classical Natural Deduction

We define two resource aware typing systems for the lambda-mu-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial arguments - based on decreasing measures of type derivations - to characterize head and strongly normalizing terms. Moreover, typability provides upper bounds for the length of head-reduction sequences and maximal reduction sequences

Reduction of attribute space dimensionality: the SOCRATES method

The new SOCRATES (ShOrtening CRiteria and ATtributES) method for reducing the dimensionality of attribute space is described. In this method, a large number of initial numerical and/or verbal characteristics of objects are aggregated into a single integral index or several composite indicators with small scales of qualitative estimates. Multiattribute objects are represented as multisets of object propertie

A Transfer Principle for Branched Rough Paths

A branched rough path $X$ consists of a rough integral calculus for $X \colon [0, T] \to \mathbb R^d$ which may fail to satisfy integration by parts. Using Kelly's bracket extension [Kel12], we define a notion of pushforward of branched rough paths through smooth maps, which leads naturally to a definition of branched rough path on a smooth manifold. Once a covariant derivative is fixed, we are able to give a canonical, coordinate-free definition of integral against such rough paths. After characterising quasi-geometric rough paths in terms of their bracket extension, we use the same framework to define manifold-valued rough differential equations (RDEs) driven by quasi-geometric rough paths. These results extend previous work on $3 > p$-rough paths [ABCRF22], itself a generalisation of the Ito calculus on manifolds developed by Meyer and Emery [Mey81, E89, E90], to the setting of non-geometric rough calculus of arbitrarily low regularity