7,194 research outputs found
A proof of the set-theoretic version of the salmon conjecture
We show that the irreducible variety of 4 x 4 x 4 complex valued tensors of
border rank at most 4 is the zero set of polynomial equations of degree 5 (the
Strassen commutative conditions), of degree 6 (the Landsberg-Manivel
polynomials), and of degree 9 (the symmetrization conditions).Comment: 7 page
Ranks and Symmetric Ranks of Cubic Surfaces
We study cubic surfaces as symmetric tensors of format .
We consider the non-symmetric tensor rank and the symmetric Waring rank of
cubic surfaces, and show that the two notions coincide over the complex
numbers. The corresponding algebraic problem concerns border ranks. We show
that the non-symmetric border rank coincides with the symmetric border rank for
cubic surfaces. As part of our analysis, we obtain minimal ideal generators for
the symmetric analogue to the secant variety from the salmon conjecture. We
also give a test for symmetric rank given by the non-vanishing of certain
discriminants. The results extend to order three tensors of all sizes, implying
the equality of rank and symmetric rank when the symmetric rank is at most
seven, and the equality of border rank and symmetric border rank when the
symmetric border rank is at most five. We also study real ranks via the real
substitution method.Comment: 16 page
A practical fpt algorithm for Flow Decomposition and transcript assembly
The Flow Decomposition problem, which asks for the smallest set of weighted
paths that "covers" a flow on a DAG, has recently been used as an important
computational step in transcript assembly. We prove the problem is in FPT when
parameterized by the number of paths by giving a practical linear fpt
algorithm. Further, we implement and engineer a Flow Decomposition solver based
on this algorithm, and evaluate its performance on RNA-sequence data.
Crucially, our solver finds exact solutions while achieving runtimes
competitive with a state-of-the-art heuristic. Finally, we contextualize our
design choices with two hardness results related to preprocessing and weight
recovery. Specifically, -Flow Decomposition does not admit polynomial
kernels under standard complexity assumptions, and the related problem of
assigning (known) weights to a given set of paths is NP-hard.Comment: Introduces software package Toboggan: Version 1.0.
http://dx.doi.org/10.5281/zenodo.82163
The Age-Specific Force of Natural Selection and Walls of Death
W. D. Hamilton's celebrated formula for the age-specific force of natural
selection furnishes predictions for senescent mortality due to mutation
accumulation, at the price of reliance on a linear approximation. Applying to
Hamilton's setting the full non-linear demographic model for mutation
accumulation of Evans et al. (2007), we find surprising differences. Non-linear
interactions cause the collapse of Hamilton-style predictions in the most
commonly studied case, refine predictions in other cases, and allow Walls of
Death at ages before the end of reproduction. Haldane's Principle for genetic
load has an exact but unfamiliar generalization.Comment: 27 page
Stewardship and Risk: An Empirically Grounded Theory of Organic Fish Farming in Scotland
It has long been assumed ownership gives farmers incentives to act as stewards for the land. On this basis, quasi-property rights are granted to fish farmers to encourage them to manage risks to the aquatic environment. This paper offers an empirically grounded theorization of fish farmersâ perspectives on these issues. Data were gathered via field research with Scottish salmon farmers who had switched from conventional to organic fish farmersâ risk management strategies offer little support for the view that property rights automatically create incentives for stewardship of the marine environment.Risk, organic, fish farming, grounded theory, Agricultural and Food Policy,
On the Truly Noncooperative Game of Island Life II: Evolutionary Stable Economic Development Strategy in Brief
This paper offers a solution to 'The Problem of Sustainable Economic Development' on islands. This hypothesis offers a foundational, sub-game solution to The Island Survival Game, a counterintuitive, dominant economic development strategy for âislandsâ (and relatively insular states). This discourse also tables conceptual building blocks, prerequisite analytical tools, and a guiding principle for The Earth Island Survival Game, a bounded delay supergame which models 'The Problem of Sustainable Economic Development' at the global level. We begin our exploration with an introduction to The Principle of Relative Insularity, a postulate which informs ESS for âislandâ and âcontinentalâ players alike. Next, we model âislandâ economic development with two bio-geo-politico-economic models and respective strategies: The Mustique Co. Development Plan, and The Prince Edward Island Federal-Provincial Program for Social and Economic Advancement. These diametrically opposed strategies offer an extraordinary comparative study. One island serves as a highly descriptive model for 'The Problem of Sustainable Economic Development'; the other model informs ESS. 'The Earth Island Survival Game' serves as a remarkable learning tool, offering lessons which promote islander survival, resource holding power, cooperative behaviour, and independence by illuminating the illusive path toward sustainable economic development.Non-cooperative games, evolutionary game theory, relative insularity, islands, tragedy of the commons, sustainable economic development, theory of value, resource holding power, evolutionary stable strategy, natural selection, long distance dispersal
Inclusion of Experimental Information in First Principles Modeling of Materials
We propose a novel approach to model amorphous materials using a first
principles density functional method while simultaneously enforcing agreement
with selected experimental data. We illustrate our method with applications to
amorphous silicon and glassy GeSe. The structural, vibrational and
electronic properties of the models are found to be in agreement with
experimental results. The method is general and can be extended to other
complex materials.Comment: 11 pages, 8 PostScript figures, submitted to J. Phys.: Condens.
Matter in honor of Mike Thorpe's 60th birthda
- âŠ