3,139 research outputs found
Convex Calibration Dimension for Multiclass Loss Matrices
We study consistency properties of surrogate loss functions for general
multiclass learning problems, defined by a general multiclass loss matrix. We
extend the notion of classification calibration, which has been studied for
binary and multiclass 0-1 classification problems (and for certain other
specific learning problems), to the general multiclass setting, and derive
necessary and sufficient conditions for a surrogate loss to be calibrated with
respect to a loss matrix in this setting. We then introduce the notion of
convex calibration dimension of a multiclass loss matrix, which measures the
smallest `size' of a prediction space in which it is possible to design a
convex surrogate that is calibrated with respect to the loss matrix. We derive
both upper and lower bounds on this quantity, and use these results to analyze
various loss matrices. In particular, we apply our framework to study various
subset ranking losses, and use the convex calibration dimension as a tool to
show both the existence and non-existence of various types of convex calibrated
surrogates for these losses. Our results strengthen recent results of Duchi et
al. (2010) and Calauzenes et al. (2012) on the non-existence of certain types
of convex calibrated surrogates in subset ranking. We anticipate the convex
calibration dimension may prove to be a useful tool in the study and design of
surrogate losses for general multiclass learning problems.Comment: Accepted to JMLR, pending editin
Collective stochastic resonance in shear-induced melting of sliding bilayers
The far-from-equilibrium dynamics of two crystalline two-dimensional
monolayers driven past each other is studied using Brownian dynamics
simulations. While at very high and low driving rates the layers slide past one
another retaining their crystalline order, for intermediate range of drives the
system alternates irregularly between the crystalline and fluid-like phases. A
dynamical phase diagram in the space of interlayer coupling and drive is
obtained. A qualitative understanding of this stochastic alternation between
the liquid-like and crystalline phases is proposed in terms of a reduced model
within which it can be understood as a stochastic resonance for the dynamics of
collective order parameter variables. This remarkable example of stochastic
resonance in a spatially extended system should be seen in experiments which we
propose in the paper.Comment: 12 pages, 18 eps figures, minor changes in text and labelling of
figures, accepted for publication in Phys. Rev.
Depletion of chondrocyte primary cilia reduces the compressive modulus of articular cartilage
Primary cilia are slender, microtubule based structures found in the majority of cell types with one cilium per cell. In articular cartilage, primary cilia are required for chondrocyte mechanotransduction and the development of healthy tissue. Loss of primary cilia in Col2aCre;ift88(fl/fl) transgenic mice results in up-regulation of osteoarthritic (OA) markers and development of OA like cartilage with greater thickness and reduced mechanical stiffness. However no previous studies have examined whether loss of primary cilia influences the intrinsic mechanical properties of articular cartilage matrix in the form of the modulus or just the structural properties of the tissue. The present study describes a modified analytical model to derive the viscoelastic moduli based on previous experimental indentation data. Results show that the increased thickness of the articular cartilage in the Col2aCre;ift88(fl/fl) transgenic mice is associated with a reduction in both the instantaneous and equilibrium moduli at indentation strains of greater than 20%. This reveals that the loss of primary cilia causes a significant reduction in the mechanical properties of cartilage particularly in the deeper zones and possibly the underlying bone. This is consistent with histological analysis and confirms the importance of primary cilia in the development of a mechanically functional articular cartilage
Flow-induced currents in nanotubes: a Brownian dynamics approach
Motivated by recent experiments [Science {\bf 299}, 1042 (2003)] reporting
that carbon nanotubes immersed in a flowing fluid displayed an electric current
and voltage, we numerically study the behaviour of a collection of Brownian
particles in a channel, in the presence of a flow field applied on similar but
slower particles in a wide chamber in contact with the channel. For a suitable
range of shear rates, we find that the flow field induces a unidirectional
drift in the confined particles, and is stronger for narrower channels. The
average drift velocity initially rises with increasing shear rate, then shows
saturation for a while, thereafter starts decreasing, in qualitative agreement
with recent theoretical studies [Phys. Rev. B {\bf 70}, 205423 (2004)] based on
Brownian drag and ``loss of grip''. Interestingly, if the sign of the
interspecies interaction is reversed, the direction of the induced drift
remains the same, but the flow-rate at which loss of grip occurs is lower, and
the level of fluctuations is higher.Comment: 7 pages, 9 figure
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