7,974 research outputs found
Phase transition and landscape statistics of the number partitioning problem
The phase transition in the number partitioning problem (NPP), i.e., the
transition from a region in the space of control parameters in which almost all
instances have many solutions to a region in which almost all instances have no
solution, is investigated by examining the energy landscape of this classic
optimization problem. This is achieved by coding the information about the
minimum energy paths connecting pairs of minima into a tree structure, termed a
barrier tree, the leaves and internal nodes of which represent, respectively,
the minima and the lowest energy saddles connecting those minima. Here we apply
several measures of shape (balance and symmetry) as well as of branch lengths
(barrier heights) to the barrier trees that result from the landscape of the
NPP, aiming at identifying traces of the easy/hard transition. We find that it
is not possible to tell the easy regime from the hard one by visual inspection
of the trees or by measuring the barrier heights. Only the {\it difficulty}
measure, given by the maximum value of the ratio between the barrier height and
the energy surplus of local minima, succeeded in detecting traces of the phase
transition in the tree. In adddition, we show that the barrier trees associated
with the NPP are very similar to random trees, contrasting dramatically with
trees associated with the spin-glass and random energy models. We also
examine critically a recent conjecture on the equivalence between the NPP and a
truncated random energy model
Latent class analysis for segmenting preferences of investment bonds
Market segmentation is a key component of conjoint analysis which addresses consumer
preference heterogeneity. Members in a segment are assumed to be homogenous in their
views and preferences when worthing an item but distinctly heterogenous to members of other
segments. Latent class methodology is one of the several conjoint segmentation procedures
that overcome the limitations of aggregate analysis and a-priori segmentation. The main
benefit of Latent class models is that market segment membership and regression parameters
of each derived segment are estimated simultaneously. The Latent class model presented in
this paper uses mixtures of multivariate conditional normal distributions to analyze rating
data, where the likelihood is maximized using the EM algorithm. The application focuses on
customer preferences for investment bonds described by four attributes; currency, coupon
rate, redemption term and price. A number of demographic variables are used to generate
segments that are accessible and actionable.peer-reviewe
BARD: Better Automated Redistricting
BARD is the first (and at time of writing, only) open source software package for general redistricting and redistricting analysis. BARD provides methods to create, display, compare, edit, automatically refine, evaluate, and profile political districting plans. BARD aims to provide a framework for scientific analysis of redistricting plans and to facilitate wider public participation in the creation of new plans. BARD facilitates map creation and refinement through command-line, graphical user interface, and automatic methods. Since redistricting is a computationally complex partitioning problem not amenable to an exact optimization solution, BARD implements a variety of selectable metaheuristics that can be used to refine existing or randomly-generated redistricting plans based on user-determined criteria. Furthermore, BARD supports automated generation of redistricting plans and profiling of plans by assigning different weights to various criteria, such as district compactness or equality of population. This functionality permits exploration of trade-offs among criteria. The intent of a redistricting authority may be explored by examining these trade-offs and inferring which reasonably observable plans were not adopted. Redistricting is a computationally-intensive problem for even modest-sized states. Performance is thus an important consideration in BARD's design and implementation. The program implements performance enhancements such as evaluation caching, explicit memory management, and distributed computing across snow clusters.
- ā¦