237 research outputs found
On the linearization of Regge calculus
We study the linearization of three dimensional Regge calculus around
Euclidean metric. We provide an explicit formula for the corresponding
quadratic form and relate it to the curlTcurl operator which appears in the
quadratic part of the Einstein-Hilbert action and also in the linear elasticity
complex. We insert Regge metrics in a discrete version of this complex,
equipped with densely defined and commuting interpolators. We show that the
eigenpairs of the curlTcurl operator, approximated using the quadratic part of
the Regge action on Regge metrics, converge to their continuous counterparts,
interpreting the computation as a non-conforming finite element method.Comment: 26 page
Perturbation-Assisted Sample Synthesis: A Novel Approach for Uncertainty Quantification
This paper introduces a novel generator called Perturbation-Assisted Sample
Synthesis (PASS), designed for drawing reliable conclusions from complex data,
especially when using advanced modeling techniques like deep neural networks.
PASS utilizes perturbation to generate synthetic data that closely mirrors the
distribution of raw data, encompassing numerical and unstructured data types
such as gene expression, images, and text. By estimating the data-generating
distribution and leveraging large pre-trained generative models, PASS enhances
estimation accuracy, providing an estimated distribution of any statistic
through Monte Carlo experiments. Building on PASS, we propose a generative
inference framework called Perturbation-Assisted Inference (PAI), which offers
a statistical guarantee of validity. In pivotal inference, PAI enables accurate
conclusions without knowing a pivotal's distribution as in simulations, even
with limited data. In non-pivotal situations, we train PASS using an
independent holdout sample, resulting in credible conclusions. To showcase
PAI's capability in tackling complex problems, we highlight its applications in
three domains: image synthesis inference, sentiment word inference, and
multimodal inference via stable diffusion
Non-cooperative Equilibria of Fermi Systems With Long Range Interactions
We define a Banach space of models for fermions or quantum spins in the lattice with long range interactions and explicit the structure of (generalized) equilibrium states for any . In particular, we give a first answer to an old open problem in mathematical physics - first addressed by Ginibre in 1968 within a different context - about the validity of the so--called Bogoliubov approximation on the level of states. Depending on the model , our method provides a systematic way to study all its correlation functions and can thus be used to analyze the physics of long range interactions. Furthermore, we show that the thermodynamics of long range models is governed by the non--cooperative equilibria of a zero-sum game, called here the thermodynamic game
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more
n-Harmonic mappings between annuli
The central theme of this paper is the variational analysis of homeomorphisms
h\colon \mathbb X \onto \mathbb Y between two given domains . We look for the extremal mappings in the
Sobolev space which minimize the energy
integral Because of the
natural connections with quasiconformal mappings this -harmonic alternative
to the classical Dirichlet integral (for planar domains) has drawn the
attention of researchers in Geometric Function Theory. Explicit analysis is
made here for a pair of concentric spherical annuli where many unexpected
phenomena about minimal -harmonic mappings are observed. The underlying
integration of nonlinear differential forms, called free Lagrangians, becomes
truly a work of art.Comment: 120 pages, 22 figure
Continuity of quantum entropic quantities via almost convexity
Based on the proofs of the continuity of the conditional entropy by Alicki,
Fannes, and Winter, we introduce in this work the almost locally affine (ALAFF)
method. This method allows us to prove a great variety of continuity bounds for
the derived entropic quantities. First, we apply the ALAFF method to the
Umegaki relative entropy. This way, we recover known almost tight bounds, but
also some new continuity bounds for the relative entropy. Subsequently, we
apply our method to the Belavkin-Staszewski relative entropy (BS-entropy). This
yields novel explicit bounds in particular for the BS-conditional entropy, the
BS-mutual and BS-conditional mutual information. On the way, we prove almost
concavity for the Umegaki relative entropy and the BS-entropy, which might be
of independent interest. We conclude by showing some applications of these
continuity bounds in various contexts within quantum information theory.Comment: 68 pages, 6 figure
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