5,653 research outputs found
Black Holes as Quantum Gravity Condensates
We model spherically symmetric black holes within the group field theory
formalism for quantum gravity via generalised condensate states, involving sums
over arbitrarily refined graphs (dual to 3d triangulations). The construction
relies heavily on both the combinatorial tools of random tensor models and the
quantum geometric data of loop quantum gravity, both part of the group field
theory formalism. Armed with the detailed microscopic structure, we compute the
entropy associated with the black hole horizon, which turns out to be
equivalently the Boltzmann entropy of its microscopic degrees of freedom and
the entanglement entropy between the inside and outside regions. We recover the
area law under very general conditions, as well as the Bekenstein-Hawking
formula. The result is also shown to be generically independent of any specific
value of the Immirzi parameter.Comment: 22 page
Galois descent of semi-affinoid spaces
We study the Galois descent of semi-affinoid non-archimedean analytic spaces.
These are the non-archimedean analytic spaces which admit an affine special
formal scheme as model over a complete discrete valuation ring, such as for
example open or closed polydiscs or polyannuli. Using Weil restrictions and
Galois fixed loci for semi-affinoid spaces and their formal models, we describe
a formal model of a -analytic space , provided that is
semi-affinoid for some finite tamely ramified extension of . As an
application, we study the forms of analytic annuli that are trivialized by a
wide class of Galois extensions that includes totally tamely ramified
extensions. In order to do so, we first establish a Weierstrass preparation
result for analytic functions on annuli, and use it to linearize finite order
automorphisms of annuli. Finally, we explain how from these results one can
deduce a non-archimedean analytic proof of the existence of resolutions of
singularities of surfaces in characteristic zero.Comment: Exposition improved and minor modifications. 37 pages. To appear in
Math.
Anomaly and Change Detection in Graph Streams through Constant-Curvature Manifold Embeddings
Mapping complex input data into suitable lower dimensional manifolds is a
common procedure in machine learning. This step is beneficial mainly for two
reasons: (1) it reduces the data dimensionality and (2) it provides a new data
representation possibly characterised by convenient geometric properties.
Euclidean spaces are by far the most widely used embedding spaces, thanks to
their well-understood structure and large availability of consolidated
inference methods. However, recent research demonstrated that many types of
complex data (e.g., those represented as graphs) are actually better described
by non-Euclidean geometries. Here, we investigate how embedding graphs on
constant-curvature manifolds (hyper-spherical and hyperbolic manifolds) impacts
on the ability to detect changes in sequences of attributed graphs. The
proposed methodology consists in embedding graphs into a geometric space and
perform change detection there by means of conventional methods for numerical
streams. The curvature of the space is a parameter that we learn to reproduce
the geometry of the original application-dependent graph space. Preliminary
experimental results show the potential capability of representing graphs by
means of curved manifold, in particular for change and anomaly detection
problems.Comment: To be published in IEEE IJCNN 201
Coherent states in quantum gravity: a construction based on the flux representation of LQG
As part of a wider study of coherent states in (loop) quantum gravity, we
introduce a modification to the standard construction, based on the recently
introduced (non-commutative) flux representation. The resulting quantum states
have some welcomed features, in particular concerning peakedness properties,
when compared to other coherent states in the literature.Comment: 24 pages, 2 figures; Revised version to match the published one. Some
references added. Discussion of the resolution of the identity include
Change Point Methods on a Sequence of Graphs
Given a finite sequence of graphs, e.g., coming from technological,
biological, and social networks, the paper proposes a methodology to identify
possible changes in stationarity in the stochastic process generating the
graphs. In order to cover a large class of applications, we consider the
general family of attributed graphs where both topology (number of vertexes and
edge configuration) and related attributes are allowed to change also in the
stationary case. Novel Change Point Methods (CPMs) are proposed, that (i) map
graphs into a vector domain; (ii) apply a suitable statistical test in the
vector space; (iii) detect the change --if any-- according to a confidence
level and provide an estimate for its time occurrence. Two specific
multivariate CPMs have been designed: one that detects shifts in the
distribution mean, the other addressing generic changes affecting the
distribution. We ground our proposal with theoretical results showing how to
relate the inference attained in the numerical vector space to the graph
domain, and vice versa. We also show how to extend the methodology for handling
multiple change points in the same sequence. Finally, the proposed CPMs have
been validated on real data sets coming from epileptic-seizure detection
problems and on labeled data sets for graph classification. Results show the
effectiveness of what proposed in relevant application scenarios
Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine
Lumped volume dynamic equations are derived using an energy state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data
The Preliminary Ruling Procedure, Today: Revisiting Article 267 TFEUâs Constitutional Backbone
As the title of the Special Issue suggests, its main purpose is to shed new light on the content, scope, extent, and limits of Article 267 TFEU in todayâs Union and, in turn, on the nature of this procedure and the European Court of Justice (ECJ)âs role as a sui generis supranational court. Such role has been played first and foremost through the rulings rendered in the context of the preliminary ruling procedure, which has been defined as the âkeystoneâ of the EU judicial system,2 the âmost important aspect of the work of the Courtâ,3 the âjewel in the Crownâ of the Courtâs jurisdiction,4 and the âgeniusâ without which core principles, such as direct effect and primacy, could have not been conceived.5 Indeed, the procedure enshrined in Article 267 TFEU has shaped and continues to shape profoundly the EU legal order and the relationship between the EU and the Member States.Moreover, this procedure shall not be seen simply as a tool used by the Court of Luxembourg to strengthen the evolution of EU law. In fact, the way Article 267 TFEU has been constantly interpreted, redesigned, and materially reformed over the decades is also a symptom of the dynamics underpinning such evolution. This transformative and mimetic nature of Article 267 TFEU explains the evergreen interest in the procedure despite the absence of any amendment to the Treaties since the 1950s, confirmed by the large number of studies published on the subject over the last few years
A four-cylinder Stirling engine controls model
A four working space, double acting piston, Stirling engine simulation was developed for controls studies. Two simulations, one for detailed fluid behavior, and a second model with simple fluid behavior but containing the four working space aspects and engine inertias, validate these models separately, then upgrade the four working space model by incorporating the detailed fluid behavior model for all four working spaces. The single working space model contains the detailed fluid dynamics. The four working space (FWS) model was built to observe the behavior of the whole engine. The drive dynamics and vehicle inertia effects are simulated. The capabilities of the model are exercised to look at working fluid supply transients, short circuit transients, and piston ring leakage effects
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