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Measurable cones and stable, measurable functions: a model for probabilistic higher-order programming

Thomas Ehrhard, Michele Pagani, Christine Tasson
2017 Proceedings of the ACM on Programming Languages  
We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpo-enriched cartesian closed category.  ...  This category gives a denotational model of an extension of PCF supporting the main primitives of probabilistic functional programming, like continuous and discrete probabilistic distributions, sampling  ...  RELATED WORK AND CONCLUSION The first denotational models for higher-order probabilistic programming were based on probabilistic power domains [Jones and Plotkin 1989; Saheb-Djahromi 1980] .  ... 
doi:10.1145/3158147 dblp:journals/pacmpl/EhrhardPT18 fatcat:bmphkjj7kjf3roo6tihzkzg4jm

Probabilistic Stable Functions on Discrete Cones are Power Series (long version) [article]

Raphaëlle Crubillé
2018 arXiv   pre-print
We study the category Cstabm of measurable cones and measurable stable functions, which is a denotational model of an higher-order language with continuous probabilities and full recursion.  ...  We look at Cstabm as a model for discrete probabilities, by showing the existence of a cartesian closed, full and faithful functor which embeds probabilistic coherence spaces (a fully abstract denotational  ...  Cones and Stable Functions The category of measurable cones and measurable, stable functions (Cstab m ), was introduced by Ehrhard, Pagani, Tasson in [7] in the aim to give a model for PCF sample .  ... 
arXiv:1805.00512v1 fatcat:gtm57h2omfdj3psb3ltgldszje

Common Lyapunov Functions and Gradient Algorithms

D. Liberzon, R. Tempo
2004 IEEE Transactions on Automatic Control  
This note is concerned with the problem of finding a quadratic common Lyapunov function for a large family of stable linear systems.  ...  We present gradient iteration algorithms which give deterministic convergence for finite system families and probabilistic convergence for infinite families.  ...  Hadjicostis, and B. Polyak for helpful discussions. This research was performed in part while R.  ... 
doi:10.1109/tac.2004.829632 fatcat:njn6e7cbg5hkjotzfs7qfcabzm

Kähler-Einstein metrics and Archimedean zeta functions [article]

Robert J. Berman
2022 arXiv   pre-print
Some intriguing relations to the zero-free property of the local automorphic L-functions appearing in the Langlands program and arithmetic geometry are also pointed out.  ...  model.  ...  by the partition functions of the probabilistic model.  ... 
arXiv:2112.04791v2 fatcat:wdfkix2dqza5tovfzcpcivd5hy

Gradient algorithms for finding common Lyapunov functions [article]

Daniel Liberzon, Roberto Tempo
2002 arXiv   pre-print
This paper is concerned with the problem of finding a quadratic common Lyapunov function for a family of stable linear systems.  ...  We present gradient iteration algorithms which give deterministic convergence for finite system families and probabilistic convergence for infinite families.  ...  We are thankful to Chris Hadjicostis and Boris Polyak for helpful discussions.  ... 
arXiv:math/0206191v1 fatcat:lznpog6mdzf4jk4hmw3nqtr5he

Managing complexity: from visual perception to sustainable transitions—contributions of Brunswik's Theory of Probabilistic Functionalism

Roland W. Scholz
2017 Environment Systems and Decisions  
Special thanks to Markus Heindl who helped me to cope with the amazing imponderabilites of the EndNote program at a critical stage in the production of this paper.  ...  Thanks to Sandro Bösch and Georg Neubauer for editing the figures and to Elaine Ambrose who assisted in improving the English and the understandability of this manuscript.  ...  Lens Model for Formative Scenario Analysis (a highly simplified representation) Theory of Probabilistic Functionalism as a general theory of perceptual and cognitive complexity management in inextricably  ... 
doi:10.1007/s10669-017-9655-4 fatcat:sm2aq7rgojbl3ny2rlpmfymxum

Differentiable programming for functional connectomics [article]

Rastko Ciric
2022 arXiv   pre-print
Taken together, our results and software demonstrate the promise of differentiable programming for functional connectomics.  ...  However, existing workflows for functional connectomics are limited in their adaptability to new data, and principled workflow design is a challenging combinatorial problem.  ...  As described in the main text, the loss function (QC-FC) is a "second-order" correlation computed across the batch dimension between the correlation that represents each connectome edge and a measure of  ... 
arXiv:2206.00649v1 fatcat:4gvks7nn2rfnxe3meflyoue6ju

Geodesic Fiber Tracking in White Matter using Activation Function

Temesgen Bihonegn, Sumit Kaushik, Avinash Bansal, Lubomír Vojtíšek, Jan Slovák
2021 Computer Methods and Programs in Biomedicine  
and objective: The geodesic ray-tracing method has shown its effectiveness for the reconstruction of fibers in white matter structure.  ...  We also suggest to enhance the methods to be more robust to noise and to employ the fourth order tensor data in order to handle the fiber crossings properly.  ...  Acknowledgments The first three authors have been supported by the grant MUNI/A/0885/2019 of Masaryk University, Jan Slovák gratefully acknowledges support from the Grant Agency of the Czech Republic,  ... 
doi:10.1016/j.cmpb.2021.106283 fatcat:o3ogotphcnhmlm6xaqfumwidpu

Adaptive, Anisotropic and Hierarchical cones of Discrete Convex functions [article]

Jean-Marie Mirebeau
2014 arXiv   pre-print
We thus introduce a hierarchy of sub-cones of discrete convex functions, associated to stencils which can be adaptively, locally, and anisotropically refined.  ...  We address the discretization of optimization problems posed on the cone of convex functions, motivated in particular by the principal agent problem in economics, which models the impact of monopoly on  ...  The author thanks Pr Ekeland and Pr Rochet for introducing him to the monopolist problem, and the Mosek team for their free release policy for public research.  ... 
arXiv:1402.1561v2 fatcat:nwtagsoiq5fdfgqcmmctxrwfri

An objective function exploiting suboptimal solutions in metabolic networks

Edwin H Wintermute, Tami D Lieberman, Pamela A Silver
2013 BMC Systems Biology  
Metabolic mutants deviate minimally from this region, a function represented mathematically as a convex cone.  ...  We propose a novel objective function for cellular metabolism that accounts for and exploits degeneracy in the metabolic network to improve flux predictions.  ...  For a global view of the metabolic behavior predicted by the FBA, MOMA and PSEUDO objective functions, we aggregated and examined predictions for all 320 measured fluxes across 12 mutants ( Figure 4ABC  ... 
doi:10.1186/1752-0509-7-98 pmid:24088221 pmcid:PMC4016239 fatcat:micpal6vfndkvf6fo32nl6hulm

A Domain Theory for Statistical Probabilistic Programming [article]

Matthijs Vákár, Ohad Kammar, Sam Staton
2021 arXiv   pre-print
By contrast, quasi-Borel predomains do support both a commutative probabilistic powerdomain and higher-order functions.  ...  As we show, quasi-Borel predomains form both a model of Fiore's axiomatic domain theory and a model of Kock's synthetic measure theory.  ...  We are grateful to the reviewers for their suggestions.  ... 
arXiv:1811.04196v2 fatcat:45t52scam5hnbi2pglyrxqbfga

Fragility functions of blockwork wharves using artificial neural networks

Armando Calabrese, Carlo G. Lai
2013 Soil Dynamics and Earthquake Engineering  
The novel fragility functions herein proposed for blockwork wharves take into account different geometries, liquefaction occurrence and type of failure mechanism.  ...  A blockwork wharf-foundationbackfill complex is modeled with advanced nonlinear 2D finite difference software, wherein liquefaction occurrence is explicitly accounted for.  ...  Conclusions A methodology for a probabilistic seismic fragility assessment and its applications to blockwork wharf structures is proposed in this study.  ... 
doi:10.1016/j.soildyn.2013.05.002 fatcat:so4d2mnul5eotdgjiuyeig72s4

Rigidity and flexibility of biological networks

M. E. Gaspar, P. Csermely
2012 Briefings in Functional Genomics  
A detailed account on the combinatorial rigidity analysis of protein structures, as well as local flexibility measures of proteins and their applications in explaining allostery and thermostability is  ...  Finally, we show the importance of the balance between functional flexibility and rigidity in protein-protein interaction, metabolic, gene regulatory and neuronal networks.  ...  Acknowledgements The authors thank members of the LINK-group (www .linkgroup.hu), especially András Szilágyi for helpful comments.  ... 
doi:10.1093/bfgp/els023 pmid:23165349 fatcat:nwxdc3bhovbnhd6dpj43d66bae

Convoluted generalized white noise, Schwinger functions and their continuation to Wightman functions [article]

S. Albeverio, H. Gottschalk, J.-L. Wu
2004 arXiv   pre-print
Finally we give some remarks on scattering theory for these models.  ...  In particular, we give a general equivalent formulation of the cluster property in terms of truncated Schwinger functions which we then apply to the above fields.  ...  5.11 the obstructions to reflection positivity come fom the higher order truncated Schwinger functions.  ... 
arXiv:math-ph/0409056v1 fatcat:4oez4hbj6jerxmtctj2fwnsezi

Inverse Optimization of Convex Risk Functions [article]

Jonathan Yu-Meng Li
2022 arXiv   pre-print
We illustrate the imputed risk functions in a portfolio selection problem and demonstrate their practical value using real-life data.  ...  Specifically, given solution data from some (forward) risk-averse optimization problems we develop an inverse optimization framework that generates a risk function that renders the solutions optimal for  ...  The author thanks the associate editor and three reviewers for their detailed comments and suggestions that greatly improved the quality of the paper.  ... 
arXiv:1607.07099v2 fatcat:vvamak67xvdrtdemttyx4xjzrq
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