105,636 research outputs found
Toward an Algebraic Theory of Systems
We propose the concept of a system algebra with a parallel composition
operation and an interface connection operation, and formalize
composition-order invariance, which postulates that the order of composing and
connecting systems is irrelevant, a generalized form of associativity.
Composition-order invariance explicitly captures a common property that is
implicit in any context where one can draw a figure (hiding the drawing order)
of several connected systems, which appears in many scientific contexts. This
abstract algebra captures settings where one is interested in the behavior of a
composed system in an environment and wants to abstract away anything internal
not relevant for the behavior. This may include physical systems, electronic
circuits, or interacting distributed systems.
One specific such setting, of special interest in computer science, are
functional system algebras, which capture, in the most general sense, any type
of system that takes inputs and produces outputs depending on the inputs, and
where the output of a system can be the input to another system. The behavior
of such a system is uniquely determined by the function mapping inputs to
outputs. We consider several instantiations of this very general concept. In
particular, we show that Kahn networks form a functional system algebra and
prove their composition-order invariance.
Moreover, we define a functional system algebra of causal systems,
characterized by the property that inputs can only influence future outputs,
where an abstract partial order relation captures the notion of "later". This
system algebra is also shown to be composition-order invariant and appropriate
instantiations thereof allow to model and analyze systems that depend on time
On Lorentzian causality with continuous metrics
We present a systematic study of causality theory on Lorentzian manifolds
with continuous metrics. Examples are given which show that some standard facts
in smooth Lorentzian geometry, such as light-cones being hypersurfaces, are
wrong when metrics which are merely continuous are considered. We show that
existence of time functions remains true on domains of dependence with
continuous metrics, and that differentiability of the metric suffices
for many key results of the smooth causality theory.Comment: Minor changes. Version to appear in Classical and Quantum Gravit
Distributional Robustness of K-class Estimators and the PULSE
Recently, in causal discovery, invariance properties such as the moment
criterion which two-stage least square estimator leverage have been exploited
for causal structure learning: e.g., in cases, where the causal parameter is
not identifiable, some structure of the non-zero components may be identified,
and coverage guarantees are available. Subsequently, anchor regression has been
proposed to trade-off invariance and predictability. The resulting estimator is
shown to have optimal predictive performance under bounded shift interventions.
In this paper, we show that the concepts of anchor regression and K-class
estimators are closely related. Establishing this connection comes with two
benefits: (1) It enables us to prove robustness properties for existing K-class
estimators when considering distributional shifts. And, (2), we propose a novel
estimator in instrumental variable settings by minimizing the mean squared
prediction error subject to the constraint that the estimator lies in an
asymptotically valid confidence region of the causal parameter. We call this
estimator PULSE (p-uncorrelated least squares estimator) and show that it can
be computed efficiently, even though the underlying optimization problem is
non-convex. We further prove that it is consistent. We perform simulation
experiments illustrating that there are several settings including weak
instrument settings, where PULSE outperforms other estimators and suffers from
less variability.Comment: 85 pages, 15 figure
Game Networks
We introduce Game networks (G nets), a novel representation for multi-agent
decision problems. Compared to other game-theoretic representations, such as
strategic or extensive forms, G nets are more structured and more compact; more
fundamentally, G nets constitute a computationally advantageous framework for
strategic inference, as both probability and utility independencies are
captured in the structure of the network and can be exploited in order to
simplify the inference process. An important aspect of multi-agent reasoning is
the identification of some or all of the strategic equilibria in a game; we
present original convergence methods for strategic equilibrium which can take
advantage of strategic separabilities in the G net structure in order to
simplify the computations. Specifically, we describe a method which identifies
a unique equilibrium as a function of the game payoffs, and one which
identifies all equilibria.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in
Artificial Intelligence (UAI2000
Conformal diagrams for the gravitational collapse of a spherical dust cloud
We present an algorithm for the construction of conformal coordinates in the
interior of a spherically symmetric, collapsing matter cloud in general
relativity. This algorithm is based on the numerical integration of the radial
null geodesics and a local analysis of their behavior close to the singularity.
As an application, we consider a collapsing spherical dust cloud, generate the
corresponding conformal diagram and analyze the structure of the resulting
singularity. A new bound on the initial data which guarantees that the
singularity is visible from future null infinity is also obtained.Comment: added a new subsection with a phase space analysis, 23 pages, 8
figure
Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes
The present work extends our short communication Phys. Rev. Lett. 95, 111102
(2005). For smooth marginally outer trapped surfaces (MOTS) in a smooth
spacetime we define stability with respect to variations along arbitrary
vectors v normal to the MOTS. After giving some introductory material about
linear non self-adjoint elliptic operators, we introduce the stability operator
L_v and we characterize stable MOTS in terms of sign conditions on the
principal eigenvalue of L_v. The main result shows that given a strictly stable
MOTS S contained in one leaf of a given reference foliation in a spacetime,
there is an open marginally outer trapped tube (MOTT), adapted to the reference
foliation, which contains S. We give conditions under which the MOTT can be
completed. Finally, we show that under standard energy conditions on the
spacetime, the MOTT must be either locally achronal, spacelike or null.Comment: 33 pages, no figures, typos corrected, minor changes in presentatio
No Simple Dual to the Causal Holographic Information?
In AdS/CFT, the fine grained entropy of a boundary region is dual to the area
of an extremal surface X in the bulk. It has been proposed that the area of a
certain 'causal surface' C - i.e. the 'causal holographic information' (CHI) -
corresponds to some coarse-grained entropy in the boundary theory. We construct
two kinds of counterexamples that rule out various possible duals, using (1)
vacuum rigidity and (2) thermal quenches. This includes the 'one-point entropy'
proposed by Kelly and Wall, and a large class of related procedures. Also, any
coarse-graining that fixes the geometry of the bulk 'causal wedge' bounded by
C, fails to reproduce CHI. This is in sharp contrast to the holographic
entanglement entropy, where the area of the extremal surface X measures the
same information that is found in the 'entanglement wedge' bounded by X.Comment: 21 pages, 5 figure
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