8,937 research outputs found
A cost function for similarity-based hierarchical clustering
The development of algorithms for hierarchical clustering has been hampered
by a shortage of precise objective functions. To help address this situation,
we introduce a simple cost function on hierarchies over a set of points, given
pairwise similarities between those points. We show that this criterion behaves
sensibly in canonical instances and that it admits a top-down construction
procedure with a provably good approximation ratio
The persistence of wishful thinking: Response to "Updated thinking on positivity ratios"
This is a response to Barbara Fredrickson's comment [American Psychologist
68, 814-822 (2013)] on our article arXiv:1307.7006.
We analyze critically the renewed claims made by Fredrickson (2013)
concerning positivity ratios and "flourishing", and attempt to disentangle some
conceptual confusions; we also address the alleged empirical evidence for
nonlinear effects. We conclude that there is no evidence whatsoever for the
existence of any "tipping points", and only weak evidence for the existence of
any nonlinearity of any kind. Our original concern, that the application of
advanced mathematical techniques in psychology and related disciplines may not
always be appropriate, remains undiminished.Comment: LaTeX2e, 10 pages including 6 Postscript figure
Positive psychology and romantic scientism: Reply to comments on Brown, Sokal, & Friedman (2013)
This is a response to five comments [American Psychologist 69, 626-629 and
632-635 (2014)] on our article arXiv:1307.7006.Comment: PDF, 9 page
Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions
We present Monte Carlo simulations of the spanning-forest model (q \to 0
limit of the ferromagnetic Potts model) in spatial dimensions d=3,4,5. We show
that, in contrast to the two-dimensional case, the model has a "ferromagnetic"
second-order phase transition at a finite positive value w_c. We present
numerical estimates of w_c and of the thermal and magnetic critical exponents.
We conjecture that the upper critical dimension is 6.Comment: LaTex2e, 4 pages; includes 6 Postscript figures; Version 2 has
expanded title as published in PR
Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm
We study the dynamic critical behavior of the Chayes-Machta dynamics for the
Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang
dynamics for the q-state Potts model to noninteger q, in two and three spatial
dimensions, by Monte Carlo simulation. We show that the Li-Sokal bound z \ge
\alpha/\nu is close to but probably not sharp in d=2, and is far from sharp in
d=3, for all q. The conjecture z \ge \beta/\nu is false (for some values of q)
in both d=2 and d=3.Comment: Revtex4, 4 pages including 4 figure
Cluster simulations of loop models on two-dimensional lattices
We develop cluster algorithms for a broad class of loop models on
two-dimensional lattices, including several standard O(n) loop models at n \ge
1. We show that our algorithm has little or no critical slowing-down when 1 \le
n \le 2. We use this algorithm to investigate the honeycomb-lattice O(n) loop
model, for which we determine several new critical exponents, and a
square-lattice O(n) loop model, for which we obtain new information on the
phase diagram.Comment: LaTex2e, 4 pages; includes 1 table and 2 figures. Totally rewritten
in version 2, with new theory and new data. Version 3 as published in PR
Completeness of the classical 2D Ising model and universal quantum computation
We prove that the 2D Ising model is complete in the sense that the partition
function of any classical q-state spin model (on an arbitrary graph) can be
expressed as a special instance of the partition function of a 2D Ising model
with complex inhomogeneous couplings and external fields. In the case where the
original model is an Ising or Potts-type model, we find that the corresponding
2D square lattice requires only polynomially more spins w.r.t the original one,
and we give a constructive method to map such models to the 2D Ising model. For
more general models the overhead in system size may be exponential. The results
are established by connecting classical spin models with measurement-based
quantum computation and invoking the universality of the 2D cluster states.Comment: 4 pages, 1 figure. Minor change
Correction-to-scaling exponents for two-dimensional self-avoiding walks
We study the correction-to-scaling exponents for the two-dimensional
self-avoiding walk, using a combination of series-extrapolation and Monte Carlo
methods. We enumerate all self-avoiding walks up to 59 steps on the square
lattice, and up to 40 steps on the triangular lattice, measuring the
mean-square end-to-end distance, the mean-square radius of gyration and the
mean-square distance of a monomer from the endpoints. The complete endpoint
distribution is also calculated for self-avoiding walks up to 32 steps (square)
and up to 22 steps (triangular). We also generate self-avoiding walks on the
square lattice by Monte Carlo, using the pivot algorithm, obtaining the
mean-square radii to ~0.01% accuracy up to N = 4000. We give compelling
evidence that the first non-analytic correction term for two-dimensional
self-avoiding walks is Delta_1 = 3/2. We compute several moments of the
endpoint distribution function, finding good agreement with the field-theoretic
predictions. Finally, we study a particular invariant ratio that can be shown,
by conformal-field-theory arguments, to vanish asymptotically, and we find the
cancellation of the leading analytic correction.Comment: LaTeX 2.09, 56 pages. Version 2 adds a renormalization-group
discussion near the end of Section 2.2, and makes many small improvements in
the exposition. To be published in the Journal of Statistical Physic
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