84,208 research outputs found
Prices, Profits, Proxies, and Production
This paper studies nonparametric identification and counterfactual bounds for
heterogeneous firms that can be ranked in terms of productivity. Our approach
works when quantities and prices are latent rendering standard approaches
inapplicable. Instead, we require observation of profits or other
optimizing-values such as costs or revenues, and either prices or price proxies
of flexibly chosen variables. We extend classical duality results for
price-taking firms to a setup with discrete heterogeneity, endogeneity, and
limited variation in possibly latent prices. Finally, we show that convergence
results for nonparametric estimators may be directly converted to convergence
results for production sets.Comment: This paper was previously circulated with the title "Prices, Profits,
and Production
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
Semiclassical regime of Regge calculus and spin foams
Recent attempts to recover the graviton propagator from spin foam models
involve the use of a boundary quantum state peaked on a classical geometry. The
question arises whether beyond the case of a single simplex this suffices for
peaking the interior geometry in a semiclassical configuration. In this paper
we explore this issue in the context of quantum Regge calculus with a general
triangulation. Via a stationary phase approximation, we show that the boundary
state succeeds in peaking the interior in the appropriate configuration, and
that boundary correlations can be computed order by order in an asymptotic
expansion. Further, we show that if we replace at each simplex the exponential
of the Regge action by its cosine -- as expected from the semiclassical limit
of spin foam models -- then the contribution from the sign-reversed terms is
suppressed in the semiclassical regime and the results match those of
conventional Regge calculus.Comment: 30 pages, no figures. Updated version with minor corrections, one
reference adde
Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
The physical interpretation and eventual fate of gravitational singularities
in a theory surpassing classical general relativity are puzzling questions that
have generated a great deal of interest among various quantum gravity
approaches. In the context of loop quantum gravity (LQG), one of the major
candidates for a non-perturbative background-independent quantisation of
general relativity, considerable effort has been devoted to construct effective
models in which these questions can be studied. In these models, classical
singularities are replaced by a "bounce" induced by quantum geometry
corrections. Undesirable features may arise however depending on the details of
the model. In this paper, we focus on Schwarzschild black holes and propose a
new effective quantum theory based on polymerisation of new canonical phase
space variables inspired by those successful in loop quantum cosmology. The
quantum corrected spacetime resulting from the solutions of the effective
dynamics is characterised by infinitely many pairs of trapped and anti-trapped
regions connected via a space-like transition surface replacing the central
singularity. Quantum effects become relevant at a unique mass independent
curvature scale, while they become negligible in the low curvature region near
the horizon. The effective quantum metric describes also the exterior regions
and asymptotically classical Schwarzschild geometry is recovered. We however
find that physically acceptable solutions require us to select a certain subset
of initial conditions, corresponding to a specific mass (de-)amplification
after the bounce. We also sketch the corresponding quantum theory and
explicitly compute the kernel of the Hamiltonian constraint operator.Comment: 50 pages, 10 figures; v2: journal version, minor comment and
references added; v3: minor corrections in section 5.3 to match journal
versio
- …