Statistical relational learning with soft quantifiers

Quantification in statistical relational learning (SRL) is either existential or universal, however humans might be more inclined to express knowledge using soft quantifiers, such as ``most'' and ``a few''. In this paper, we define the syntax and semantics of PSL^Q, a new SRL framework that supports reasoning with soft quantifiers, and present its most probable explanation (MPE) inference algorithm. To the best of our knowledge, PSL^Q is the first SRL framework that combines soft quantifiers with first-order logic rules for modelling uncertain relational data. Our experimental results for link prediction in social trust networks demonstrate that the use of soft quantifiers not only allows for a natural and intuitive formulation of domain knowledge, but also improves the accuracy of inferred results

Stochastic switching circuit synthesis

Shannon in his 1938 Masterpsilas Thesis demonstrated that any Boolean function can be realized by a switching relay circuit, leading to the development of deterministic digital logic. Here, we replace each classical switch with a probabilistic switch (pswitch). We present algorithms for synthesizing circuits closed with a desired probability, including an algorithm that generates optimal size circuits for any binary fraction. We also introduce a new duality property for series-parallel stochastic switching circuits. Finally, we construct a universal probability generator which maps deterministic inputs to arbitrary probabilistic outputs. Potential applications exist in the analysis and design of stochastic networks in biology and engineering

COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS

The ability to simulate a biological organism by employing a computer is related to the ability of the computer to calculate the behavior of such a dynamical system, or the "computability" of the system.* However, the two questions of computability and simulation are not equivalent. Since the question of computability can be given a precise answer in terms of recursive functions, automata theory and dynamical systems, it will be appropriate to consider it first. The more elusive question of adequate simulation of biological systems by a computer will be then addressed and a possible connection between the two answers given will be considered. A conjecture is formulated that suggests the possibility of employing an algebraic-topological, "quantum" computer (Baianu, 1971b) for analogous and symbolic simulations of biological systems that may include chaotic processes that are not, in genral, either recursively or digitally computable. Depending on the biological network being modelled, such as the Human Genome/Cell Interactome or a trillion-cell Cognitive Neural Network system, the appropriate logical structure for such simulations might be either the Quantum MV-Logic (QMV) discussed in recent publications (Chiara, 2004, and references cited therein)or Lukasiewicz Logic Algebras that were shown to be isomorphic to MV-logic algebras (Georgescu et al, 2001)