46,158 research outputs found
A fixed-parameter perspective on #BIS
The problem of (approximately) counting the independent sets of a bipartite
graph (#BIS) is the canonical approximate counting problem that is complete in
the intermediate complexity class #RH\Pi_1. It is believed that #BIS does not
have an efficient approximation algorithm but also that it is not NP-hard. We
study the robustness of the intermediate complexity of #BIS by considering
variants of the problem parameterised by the size of the independent set. We
exhaustively map the complexity landscape for three problems, with respect to
exact computation and approximation and with respect to conventional and
parameterised complexity. The three problems are counting independent sets of a
given size, counting independent sets with a given number of vertices in one
vertex class and counting maximum independent sets amongst those with a given
number of vertices in one vertex class. Among other things, we show that all of
these problems are NP-hard to approximate within any polynomial ratio. (This is
surprising because the corresponding problems without the size parameter are
complete in #RH\Pi_1, and hence are not believed to be NP-hard.) We also show
that the first problem is #W[1]-hard to solve exactly but admits an FPTRAS,
whereas the other two are W[1]-hard to approximate even within any polynomial
ratio. Finally, we show that, when restricted to graphs of bounded degree, all
three problems have efficient exact fixed-parameter algorithms.Comment: to appear in Algorithmic
Supply driven mortgage choice
Variable mortgage contracts dominate the UK mortgage market (Miles, 2004). The dominance of the variable rate mortgage contracts has important consequences for the transmission mechanism of monetary policy decisions and systemic risks (Khandani et al., 2012; Fuster and Vickery, 2013). This raises an obvious concern that a mortgage market such as that in the UK, where the major proportion of mortgage debt is either at a variable or fixed for less than two years rate (Badarinza, et al., 2013; CML, 2012), is vulnerable to alterations in the interest rate regime. Theoretically, mortgage choice is determined by demand and supply factors. So far, most of the existing literature has focused on the demand side perspective, and what is limited is consideration of supply side factors in empirical investigation on mortgage choice decisions. This paper uniquely explores whether supply side factors may partially explain observed/ex-post mortgage type decisions. Empirical results detect that lenders’ profit motives and mortgage funding/pricing issues may have assisted in preferences toward variable rate contracts. Securitisation is found to positively impact upon gross mortgage lending volumes while negatively impacting upon the share of variable lending flows. This shows that an increase in securitisation not only improves liquidity in the supply of mortgage funds, but also has the potential to shift mortgage choices toward fixed mortgage debt. The policy implications may involve a number of measures, including reconsideration of the capital requirements for the fixed, as opposed to the variable rate mortgage debt, growing securitisation and optimisation of the mortgage pricing policies
Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies
Many practical studies rely on hypothesis testing procedures applied to data
sets with missing information. An important part of the analysis is to
determine the impact of the missing data on the performance of the test, and
this can be done by properly quantifying the relative (to complete data) amount
of available information. The problem is directly motivated by applications to
studies, such as linkage analyses and haplotype-based association projects,
designed to identify genetic contributions to complex diseases. In the genetic
studies the relative information measures are needed for the experimental
design, technology comparison, interpretation of the data, and for
understanding the behavior of some of the inference tools. The central
difficulties in constructing such information measures arise from the multiple,
and sometimes conflicting, aims in practice. For large samples, we show that a
satisfactory, likelihood-based general solution exists by using appropriate
forms of the relative Kullback--Leibler information, and that the proposed
measures are computationally inexpensive given the maximized likelihoods with
the observed data. Two measures are introduced, under the null and alternative
hypothesis respectively. We exemplify the measures on data coming from mapping
studies on the inflammatory bowel disease and diabetes. For small-sample
problems, which appear rather frequently in practice and sometimes in disguised
forms (e.g., measuring individual contributions to a large study), the robust
Bayesian approach holds great promise, though the choice of a general-purpose
"default prior" is a very challenging problem.Comment: Published in at http://dx.doi.org/10.1214/07-STS244 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Quantum information analysis of electronic states at different molecular structures
We have studied transition metal clusters from a quantum information theory
perspective using the density-matrix renormalization group (DMRG) method. We
demonstrate the competition between entanglement and interaction localization.
We also discuss the application of the configuration interaction based
dynamically extended active space procedure which significantly reduces the
effective system size and accelerates the speed of convergence for complicated
molecular electronic structures to a great extent. Our results indicate the
importance of taking entanglement among molecular orbitals into account in
order to devise an optimal orbital ordering and carry out efficient
calculations on transition metal clusters. We propose a recipe to perform DMRG
calculations in a black-box fashion and we point out the connections of our
work to other tensor network state approaches
Fixed versus Flexible: Lessons from EMS Order Flow
This paper addresses the puzzle of regime-dependent volatility in foreign exchange. We extend the literature in two ways. First, our microstructural model provides a qualitatively new explanation for the puzzle. Second, we test implications of our model using Europe's recent shift to rigidly fixed rates (EMS to EMU). In the model, shocks to order flow induce volatility under flexible rates because they have portfolio-balance effects on price, whereas under fixed rates the same shocks do not have portfolio-balance effects. These effects arise in one regime and not the other because the elasticity of speculative demand for foreign exchange is (endogenously) regime-dependent: low elasticity under flexible rates magnifies portfolio-balance effects; under credibly fixed rates, elasticity of speculative demand is infinite, eliminating portfolio-balance effects. New data on FF/DM transactions show that order flow had persistent effects on the exchange rate before EMU parities were announced. After announcement, determination of the FF/DM rate was decoupled from order flow, as predicted by the model.
Black Hole Electromagnetic Duality
After defining the concept of duality in the context of general -form
abelian gauge fields in 2 dimensions, we show by explicit example the
difference between apparent but unrealizable duality transformations, namely
those in , and those, in , that can be implemented by explicit
dynamical generators. We then consider duality transformations in Maxwell
theory in the presence of gravitation, particularly electrically and
magnetically charged black hole geometries. By comparing actions in which both
the dynamical variables and the charge parameters are "rotated," we show their
equality for equally charged electric and magnetic black holes, thus
establishing their equivalence for semiclassical processes which depend on the
value of the action itself.Comment: 9 pages, aipproc.sty, Lecture at I Latin American Symposium on High
Energy Physics, Merida, Mexico, Nov. 5, 199
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