608 research outputs found
Uncertainty in Spatial Duopoly with Possibly Asymmetric Distributions: a State Space Approach
In spatial competition firms are likely to be uncertain about consumer locations when launching products either because of shifting demograph- ics or of asymmetric information about preferences. Realistically distri- butions of consumer locations should be allowed to vary over states and need not be uniform. However, the existing literature models location uncertainty as an additive shock to a uniform consumer distribution. The additive shock restricts uncertainty to the mean of the consumers loca- tions. We generalize this approach to a state space model in which a vector of parameters gives rise to different distributions of consumer tastes in dif- ferent states, allowing other moments (besides the mean) of the consumer distribution to be uncertain. We illustrate our model with an asymmetric consumer distribution and obtain a unique subgame perfect equilibrium with an explicit, closed-form solution. An equilibrium existence result is then given for the general case. For symmetric distributions, the unique subgame perfect equilibrium in the general case can be described by a simple closed-form solution.Location, Product Differentiation, Uncertainty, Hotelling
Spacial Equilibrium in a State Space Approach to Demand Uncertainty
Firms are likely to be uncertain about consumer preferences when launching products. The existing literature models preference uncertainty as an additive shock to the consumer distribution in a characteristic space model. The additive shock only shifts the mean of the consumers' ideal points. We generalize this approach to a state space model in which a vector of parameters can give rise to dierent distributions of consumer tastes in dierent states, allowing other moments of the consumer density to be uncertain. An equilibrium existence result is given. In the case of symmetric distributions, the unique subgame-perfect equilibrium can be described by a simple closed-form solution.Location; Product Dierentiation; Uncertainty; Hotelling
Protein folding and the robustness of cells
The intricate intracellular infrastructure of all known life forms is based on proteins. The folded shape of a protein determines both the proteinās function and the set of molecules it will bind to. This tight coupling between a proteinās function and its interconnections in the molecular interaction network has consequences for the molecular course of evolution. It is also counter to human engineering approaches. Here we report on a simulation study investigating the impact of random errors in an abstract metabolic network of 500 enzymes. Tight coupling between function and interconnectivity of nodes is compared to the case where these two properties are independent. Our results show that the model system under consideration is more robust if function and interconnection are intertwined. These findings are discussed in the context of nanosystems engineering
Faster Methods for Contracting Infinite 2D Tensor Networks
We revisit the corner transfer matrix renormalization group (CTMRG) method of
Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and
demonstrate that its performance can be substantially improved by determining
the tensors using an eigenvalue solver as opposed to the power method used in
CTMRG. We also generalize the variational uniform matrix product state (VUMPS)
ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer
matrices and discuss similarities with the corner methods. These two new
algorithms will be crucial to improving the performance of variational infinite
projected entangled pair state (PEPS) methods.Comment: 20 pages, 5 figures, V. Zauner-Stauber previously also published
under the name V. Zaune
Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries
We develop variational matrix product state (MPS) methods with symmetries to
determine dispersion relations of one dimensional quantum lattices as a
function of momentum and preset quantum number. We test our methods on the XXZ
spin chain, the Hubbard model and a non-integrable extended Hubbard model, and
determine the excitation spectra with a precision similar to the one of the
ground state. The formulation in terms of quantum numbers makes the topological
nature of spinons and holons very explicit. In addition, the method also
enables an easy and efficient direct calculation of the necessary magnetic
field or chemical potential required for a certain ground state magnetization
or particle density.Comment: 13 pages, 4 pages appendix, 8 figure
Transfer Matrices and Excitations with Matrix Product States
We investigate the relation between static correlation functions in the
ground state of local quantum many-body Hamiltonians and the dispersion
relations of the corresponding low energy excitations using the formalism of
tensor network states. In particular, we show that the Matrix Product State
Transfer Matrix (MPS-TM) - a central object in the computation of static
correlation functions - provides important information about the location and
magnitude of the minima of the low energy dispersion relation(s) and present
supporting numerical data for one-dimensional lattice and continuum models as
well as two-dimensional lattice models on a cylinder. We elaborate on the
peculiar structure of the MPS-TM's eigenspectrum and give several arguments for
the close relation between the structure of the low energy spectrum of the
system and the form of static correlation functions. Finally, we discuss how
the MPS-TM connects to the exact Quantum Transfer Matrix (QTM) of the model at
zero temperature. We present a renormalization group argument for obtaining
finite bond dimension approximations of MPS, which allows to reinterpret
variational MPS techniques (such as the Density Matrix Renormalization Group)
as an application of Wilson's Numerical Renormalization Group along the virtual
(imaginary time) dimension of the system.Comment: 39 pages (+8 pages appendix), 14 figure
Symmetry Breaking and the Geometry of Reduced Density Matrices
The concept of symmetry breaking and the emergence of corresponding local
order parameters constitute the pillars of modern day many body physics. The
theory of quantum entanglement is currently leading to a paradigm shift in
understanding quantum correlations in many body systems and in this work we
show how symmetry breaking can be understood from this wavefunction centered
point of view. We demonstrate that the existence of symmetry breaking is a
consequence of the geometric structure of the convex set of reduced density
matrices of all possible many body wavefunctions. The surfaces of those convex
bodies exhibit non-analytic behavior in the form of ruled surfaces, which turn
out to be the defining signatures for the emergence of symmetry breaking and of
an associated order parameter.
We illustrate this by plotting the convex sets arising in the context of
three paradigmatic examples of many body systems exhibiting symmetry breaking:
the quantum Ising model in transverse magnetic field, exhibiting a second order
quantum phase transition; the classical Ising model at finite temperature in
two dimensions, which orders below a critical temperature ; and a system
of free bosons at finite temperature in three dimensions, exhibiting the
phenomenon of Bose-Einstein condensation together with an associated order
parameter . Remarkably, these convex sets look all very
much alike. We believe that this wavefunction based way of looking at phase
transitions demystifies the emergence of order parameters and provides a unique
novel tool for studying exotic quantum phenomena.Comment: 5 pages, 3 figures, Appendix with 2 pages, 3 figure
The Shared Design Space
The Shared Design Space is a novel interface for enhancing face-to-
face collaboration using multiple displays and input surfaces.
The system supports natural gestures and paper-pen input and overcomes
the limitations of using traditional technology in co-located
meetings and brainstorming activities
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