Structural Parsimony

Many metaphysicians often appeal to Hume’s dictum (HD), according to which there are no necessary connections between distinct entities (or states of entities), in order to resist theories that commit us to such connections. Some have argued that HD is an unsupported dogma of metaphysics. But theories that commit us to necessary connections between distinct goings-on can also be resisted by invoking a normative twist on HD, which I call the Humean Solvent (HS): “Do not connect distinct entities (or states of entities) beyond necessity”. HS is a principle of structural parsimony – assuming that a theory is structurally more parsimonious than another when the latter is committed to a more connected ontology than the former is. Just as Ockham’s ‘razor’ encourages us to cut down superfluous ontological commitments, the Humean ‘solvent’ encourages us to dissolve dispensable metaphysical glue: we ought not to glue elements of our ontology beyond necessity. HS has both a qualitative and a quantitative dimension: qualitatively, it encourages us to avoid using metaphysical glues that are unnecessarily strong, the strongest of which being metaphysically necessary connections; quantitatively, it encourages us not to metaphysically glue things that need no gluing. Thus, given HS, other things being equal, what is worst is a theory that entails that everything is metaphysically necessarily connected to anything else and what is best is a theory that leaves all things loose and separable. In this paper, I will first compare HD and HS as grounds for paradigmatic Humean doctrines in contemporary metaphysics, then I will argue that structural parsimony is neither a variety of ontological nor of ideological parsimony; finally, I will offer an argument for HS

On Computing the Maximum Parsimony Score of a Phylogenetic Network

Phylogenetic networks are used to display the relationship of different species whose evolution is not treelike, which is the case, for instance, in the presence of hybridization events or horizontal gene transfers. Tree inference methods such as Maximum Parsimony need to be modified in order to be applicable to networks. In this paper, we discuss two different definitions of Maximum Parsimony on networks, "hardwired" and "softwired", and examine the complexity of computing them given a network topology and a character. By exploiting a link with the problem Multicut, we show that computing the hardwired parsimony score for 2-state characters is polynomial-time solvable, while for characters with more states this problem becomes NP-hard but is still approximable and fixed parameter tractable in the parsimony score. On the other hand we show that, for the softwired definition, obtaining even weak approximation guarantees is already difficult for binary characters and restricted network topologies, and fixed-parameter tractable algorithms in the parsimony score are unlikely. On the positive side we show that computing the softwired parsimony score is fixed-parameter tractable in the level of the network, a natural parameter describing how tangled reticulate activity is in the network. Finally, we show that both the hardwired and softwired parsimony score can be computed efficiently using Integer Linear Programming. The software has been made freely available

Pure Parsimony Xor Haplotyping

The haplotype resolution from xor-genotype data has been recently formulated as a new model for genetic studies. The xor-genotype data is a cheaply obtainable type of data distinguishing heterozygous from homozygous sites without identifying the homozygous alleles. In this paper we propose a formulation based on a well-known model used in haplotype inference: pure parsimony. We exhibit exact solutions of the problem by providing polynomial time algorithms for some restricted cases and a fixed-parameter algorithm for the general case. These results are based on some interesting combinatorial properties of a graph representation of the solutions. Furthermore, we show that the problem has a polynomial time k-approximation, where k is the maximum number of xor-genotypes containing a given SNP. Finally, we propose a heuristic and produce an experimental analysis showing that it scales to real-world large instances taken from the HapMap project

Mod/Resc Parsimony Inference

We address in this paper a new computational biology problem that aims at understanding a mechanism that could potentially be used to genetically manipulate natural insect populations infected by inherited, intra-cellular parasitic bacteria. In this problem, that we denote by \textsc{Mod/Resc Parsimony Inference}, we are given a boolean matrix and the goal is to find two other boolean matrices with a minimum number of columns such that an appropriately defined operation on these matrices gives back the input. We show that this is formally equivalent to the \textsc{Bipartite Biclique Edge Cover} problem and derive some complexity results for our problem using this equivalence. We provide a new, fixed-parameter tractability approach for solving both that slightly improves upon a previously published algorithm for the \textsc{Bipartite Biclique Edge Cover}. Finally, we present experimental results where we applied some of our techniques to a real-life data set.Comment: 11 pages, 3 figure

The Perils of Parsimony

It is widely thought in philosophy and elsewhere that parsimony is a theoretical virtue in that if T1 is more parsimonious than T2, then T1 is preferable to T2, other things being equal. This thesis admits of many distinct precisifications. I focus on a relatively weak precisification on which preferability is a matter of probability, and argue that it is false. This is problematic for various alternative precisifications, and even for Inference to the Best Explanation as standardly understood

Information parsimony in collaborative interaction

We investigate the information processing cost associated with performing a collaborative dyadic task at a specific utility level. We build our approach on the Relevant Information formalism, which combines Shannon's Information Theory and Markov Decision Processes, for modelling a dyadic interaction scenario in which two agents with independent controllers move an object together with fully redundant control. Results show that increasing dyad's collaboration decreases the information intake and vice versa, antagonistic behavior puts a strain on the information bandwidth capacity. The key role of the particular embodiment of the environment in this trade-off is demonstrated in a series of simulations with informationally parsimonious optimal controllers.Peer reviewedFinal Published versio