4,701 research outputs found
Enumerating Polytropes
Polytropes are both ordinary and tropical polytopes. We show that tropical
types of polytropes in are in bijection with cones of a
certain Gr\"{o}bner fan in restricted
to a small cone called the polytrope region. These in turn are indexed by
compatible sets of bipartite and triangle binomials. Geometrically, on the
polytrope region, is the refinement of two fans: the fan of
linearity of the polytrope map appeared in \cite{tran.combi}, and the bipartite
binomial fan. This gives two algorithms for enumerating tropical types of
polytropes: one via a general Gr\"obner fan software such as \textsf{gfan}, and
another via checking compatibility of systems of bipartite and triangle
binomials. We use these algorithms to compute types of full-dimensional
polytropes for , and maximal polytropes for .Comment: Improved exposition, fixed error in reporting the number maximal
polytropes for , fixed error in definition of bipartite binomial
HodgeRank is the limit of Perron Rank
We study the map which takes an elementwise positive matrix to the k-th root
of the principal eigenvector of its k-th Hadamard power. We show that as
tends to 0 one recovers the row geometric mean vector and discuss the geometric
significance of this convergence. In the context of pairwise comparison
ranking, our result states that HodgeRank is the limit of Perron Rank, thereby
providing a novel mathematical link between two important pairwise ranking
methods
Learning Technological Capability for Vietnam's Industrial Upgrading: Challenges of the Globalization.
The paper discusses technological capabilities in Vietnamese industry considering mainly the role of foreign companies. The support of technological change is limited by specific disadvantages of Vietnamese environment, mainly insufficient organizational and legal shortcomings. Thus the connections between foreign and local companies did not produce expected results. The diffusion of technological skills takes place via training process, transfer of tacit and codified knowledge, spillover to local partners and influence absorption capacity of the local market. The cases of ten foreign companies from five different countries are presented. Major conclusions underline the threats of global operations of international companies when they are not supported by enlightened policies of companies and governments in host countries on one side and present the opportunities for these countries economy on the other.FDI; Joint-ventures; technology spillover; technological capabilities; tacit knowledge; low-cost-labor-trap; value chain; technical change
Model Selection with the Loss Rank Principle
A key issue in statistics and machine learning is to automatically select the
"right" model complexity, e.g., the number of neighbors to be averaged over in
k nearest neighbor (kNN) regression or the polynomial degree in regression with
polynomials. We suggest a novel principle - the Loss Rank Principle (LoRP) -
for model selection in regression and classification. It is based on the loss
rank, which counts how many other (fictitious) data would be fitted better.
LoRP selects the model that has minimal loss rank. Unlike most penalized
maximum likelihood variants (AIC, BIC, MDL), LoRP depends only on the
regression functions and the loss function. It works without a stochastic noise
model, and is directly applicable to any non-parametric regressor, like kNN.Comment: 31 LaTeX pages, 1 figur
Antibiotics Time Machine is NP-hard
The antibiotics time machine is an optimization question posed by Mira
\latin{et al.} on the design of antibiotic treatment plans to minimize
antibiotic resistance. The problem is a variation of the Markov decision
process. These authors asked if the problem can be solved efficiently. In this
paper, we show that this problem is NP-hard in general.Comment: 5 page
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