253 research outputs found
Structure and Interpretation of Dual-Feasible Functions
We study two techniques to obtain new families of classical and general
Dual-Feasible Functions: A conversion from minimal Gomory--Johnson functions;
and computer-based search using polyhedral computation and an automatic
maximality and extremality test.Comment: 6 pages extended abstract to appear in Proc. LAGOS 2017, with 21
pages of appendi
Software for cut-generating functions in the Gomory--Johnson model and beyond
We present software for investigations with cut generating functions in the
Gomory-Johnson model and extensions, implemented in the computer algebra system
SageMath.Comment: 8 pages, 3 figures; to appear in Proc. International Congress on
Mathematical Software 201
New computer-based search strategies for extreme functions of the Gomory--Johnson infinite group problem
We describe new computer-based search strategies for extreme functions for
the Gomory--Johnson infinite group problem. They lead to the discovery of new
extreme functions, whose existence settles several open questions.Comment: 54 pages, many figure
Holographic entanglement entropy of semi-local quantum liquids
We consider the holographic entanglement entropy of -dimensional
semi-local quantum liquids, for which the dual gravity background in the deep
interior is multiplied by a warp factor which
depends on the radial coordinate. The entropy density of this geometry goes to
zero in the extremal limit. The thermodynamics associated with this semi-local
background is discussed via dimensional analysis and scaling arguments. For the
case of an asymptotically AdS UV completion of this geometry, we show that the
entanglement entropy of a strip and an annulus exhibits a phase transition as a
typical length of the different shapes is varied, while there is no sign of
such a transition for the entanglement entropy of a sphere. Moreover, for the
spherical entangling region, the leading order contribution to the entanglement
entropy in the IR is calculated analytically. It exhibits an area law behaviour
and agrees with the numerical result.Comment: 33 pages, 24 figure
Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness
Hedonic pricing with quasi-linear preferences is shown to be equivalent to stable matching with transferable utilities and a participation constraint, and to an optimal transportation (Monge-Kantorovich) linear programming problem. Optimal assignments in the latter correspond to stable matchings, and to hedonic equilibria. These assignments are shown to exist in great generality; their marginal indirect payoffs with respect to agent type are shown to be unique whenever direct payoffs vary smoothly with type. Under a generalized Spence-Mirrlees condition (also known as a twist condition) the assignments are shown to be unique and to be pure, meaning the matching is one-to-one outside a negligible set. For smooth problems set on compact, connected type spaces such as the circle, there is a topological obstruction to purity, but we give a weaker condition still guaranteeing uniqueness of the stable match
On duality and fractionality of multicommodity flows in directed networks
In this paper we address a topological approach to multiflow (multicommodity
flow) problems in directed networks. Given a terminal weight , we define a
metrized polyhedral complex, called the directed tight span , and
prove that the dual of -weighted maximum multiflow problem reduces to a
facility location problem on . Also, in case where the network is
Eulerian, it further reduces to a facility location problem on the tropical
polytope spanned by . By utilizing this duality, we establish the
classifications of terminal weights admitting combinatorial min-max relation
(i) for every network and (ii) for every Eulerian network. Our result includes
Lomonosov-Frank theorem for directed free multiflows and
Ibaraki-Karzanov-Nagamochi's directed multiflow locking theorem as special
cases.Comment: 27 pages. Fixed minor mistakes and typos. To appear in Discrete
Optimizatio
Non-extremal Black Hole Microstates: Fuzzballs of Fire or Fuzzballs of Fuzz ?
We construct the first family of microstate geometries of near-extremal black
holes, by placing metastable supertubes inside certain scaling supersymmetric
smooth microstate geometries. These fuzzballs differ from the classical black
hole solution macroscopically at the horizon scale, and for certain probes the
fluctuations between various fuzzballs will be visible as thermal noise far
away from the horizon. We discuss whether these fuzzballs appear to infalling
observers as fuzzballs of fuzz or as fuzzballs of fire. The existence of these
solutions suggests that the singularity of non-extremal black holes is resolved
all the way to the outer horizon and this "backwards in time" singularity
resolution can shed light on the resolution of spacelike cosmological
singularities.Comment: 34 pages, 10 figure
Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness
Hedonic pricing with quasilinear preferences is shown to be equivalent to stable matching with transferable utilities and a participation constraint, and to an optimal transportation (Monge-Kantorovich) linear programming problem. Optimal assignments in the latter correspond to stable matchings, and to hedonic equilibria. These assignments are shown to exist in great generality; their marginal indirect payoffs with respect to agent type are shown to be unique whenever direct payoffs vary smoothly with type. Under a generalized Spence-Mirrlees condition the assignments are shown to be unique and to be pure, meaning the matching is one-to-one outside a negligible set. For smooth problems set on compact, connected type spaces such as the circle, there is a topological obstruction to purity, but we give a weaker condition still guaranteeing uniqueness of the stable match. An appendix resolves an old problem (# 111) of Birkhoff in probability and statistics [5], by giving a necessary and sufficient condition on the support of a joint probability to guarantee extremality among all joint measures with the same marginals.
- …