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Donut Domains: Efficient Non-convex Domains for Abstract Interpretation [chapter]

Khalil Ghorbal, Franjo Ivančić, Gogul Balakrishnan, Naoto Maeda, Aarti Gupta
2012 Lecture Notes in Computer Science  
Most abstract domains that are used widely rely on convexity for their scalability.  ...  This work combines already known abstract domains in a novel way in order to design new abstract domains that tackle some non-convex invariants.  ...  The authors would like to thank Sriram Sankaranarayanan, Enea Zaffanella and anonymous reviewers for their valuable comments on an earlier draft of this work.  ... 
doi:10.1007/978-3-642-27940-9_16 fatcat:xdnwvbxrmzejhox5arjoknwxsa

Abstract Interpretation over Non-lattice Abstract Domains [chapter]

Graeme Gange, Jorge A. Navas, Peter Schachte, Harald Søndergaard, Peter J. Stuckey
2013 Lecture Notes in Computer Science  
Nonetheless, and for good reason, the literature on program analysis provides many examples of non-lattice domains, including non-convex numeric domains.  ...  The classical theoretical framework for static analysis of programs is abstract interpretation.  ...  Acknowledgments We wish to thank the anonymous reviewers for many insightful suggestions. This work was supported through ARC grant DP110102579.  ... 
doi:10.1007/978-3-642-38856-9_3 fatcat:czcjdjiuajc53o5ofg6l63v35q

An Abstract Domain to Infer Octagonal Constraints with Absolute Value [chapter]

Liqian Chen, Jiangchao Liu, Antoine Miné, Deepak Kapur, Ji Wang
2014 Lecture Notes in Computer Science  
However, the octagon domain itself is restricted to express convex sets and has limitations in handling non-convex properties which are sometimes required for proving some numerical properties in a program  ...  In this paper, we intend to extend the octagon abstract domain with absolute value, to infer certain non-convex properties by exploiting the absolute value function.  ...  Introduction The precision and efficiency of program analysis based on abstract interpretation [9, 10] rely a lot on the chosen abstract domains.  ... 
doi:10.1007/978-3-319-10936-7_7 fatcat:ozvzgtekrbhoniyhkranp6m3au

Total Variation Isoperimetric Profiles [article]

Daryl DeFord, Hugo Lavenant, Zachary Schutzman, Justin Solomon
2019 arXiv   pre-print
Efficient algorithms for computing this profile, however, are not known in practice. Hence, in this paper, we propose a convex Eulerian relaxation of the isoperimetric profile using total variation.  ...  We prove theoretical properties of our relaxation, showing that it still satisfies an isoperimetric inequality and yields a convex function of the prescribed area.  ...  We also thank Will Adler for providing areal interpolation code. J. Solomon acknowledges the generous support of the Prof. Amar G.  ... 
arXiv:1809.07943v2 fatcat:ja46p2atgjborj5yryl6pgyyoy

Dichroic coherent diffractive imaging

A. Tripathi, J. Mohanty, S. H. Dietze, O. G. Shpyrko, E. Shipton, E. E. Fullerton, S. S. Kim, I. McNulty
2011 Proceedings of the National Academy of Sciences of the United States of America  
A series of dichroic coherent diffraction patterns, ptychographically recorded, are numerically inverted using non-convex and non-linear optimization theory, and we follow the magnetic domain configuration  ...  We demonstrate this approach by imaging ferrimagnetic "maze" domains in a Gd/Fe multilayer with perpendicular anisotropy.  ...  The top frame shows behavior when the non-convexity is not too severe, while the bottom frame shows behavior when the constraint sets are highly non-convex.  ... 
doi:10.1073/pnas.1104304108 pmid:21825152 pmcid:PMC3158233 fatcat:njwikf644zcb3nr4bqiz56jh5e

Towards a parameterless 3D mesh segmentation

Sara Farag, Wael Abdelrahman, Saeid Nahavandi, Douglas Creighton, Zeng Zhu
2013 International Conference on Graphic and Image Processing (ICGIP 2012)  
This target is essential for the evolution of the 3D mesh segmentation domain from theory to be practically used by experts and non-experts of 3D computer graphics.  ...  Algorithm weakness is in the case of concave 3D mesh such as a a ball or a donut.  ... 
doi:10.1117/12.2010891 fatcat:twkjvy3afrcv3pz2ivr65yhfiy

Linking covariant and canonical LQG II: spin foam projector

Thomas Thiemann, Antonia Zipfel
2014 Classical and quantum gravity  
In a seminal paper, Kaminski, Kisielowski an Lewandowski for the first time extended the definition of spin foam models to arbitrary boundary graphs.  ...  This makes it finally possible to investigate the question whether any of the presently considered spin foam models yields a rigging map for any of the presently defined Hamiltonian constraint operators  ...  Let now ψ ′ q = E([−q, q])ψ ′ ∈ H q be in the domain of the averaging map and ψ, ψ ′ in the domain ofĤ(N ) for any lapse function 33 .  ... 
doi:10.1088/0264-9381/31/12/125008 fatcat:ow7yxbtmdnaytmeotc5gfjv4ge

Simultaneous Denoising, Deconvolution, and Demixing of Calcium Imaging Data

Eftychios A. Pnevmatikakis, Daniel Soudry, Yuanjun Gao, Timothy A. Machado, Josh Merel, David Pfau, Thomas Reardon, Yu Mu, Clay Lacefield, Weijian Yang, Misha Ahrens, Randy Bruno (+4 others)
2016 Neuron  
We present a modular approach for analyzing calcium imaging recordings of large neuronal ensembles.  ...  Modeling the fluorescence trace with an AR process allows for a flexible and interpretable modeling framework that still retains computational tractability.  ...  The resulting optimization problem is convex, i.e., it has no local minima, and can be solved efficiently, with complexity that scales just linearly with the number of observed timesteps, and quadratically  ... 
doi:10.1016/j.neuron.2015.11.037 pmid:26774160 pmcid:PMC4881387 fatcat:io72cxhfnvgsxavc4mc5cvxfti

A survey of Euler diagrams

Peter Rodgers
2014 Journal of Visual Languages and Computing  
This work lead to the requirement to automatically generate Euler diagrams from an abstract description.  ...  Euler diagram research surveyed in this paper includes theoretical results, generation techniques, transformation methods and the development of automated reasoning systems for Euler diagrams.  ...  While many of the zones have simple, rectangular shapes, the last three zones to be added may be non-convex.  ... 
doi:10.1016/j.jvlc.2013.08.006 fatcat:nbvjcu5ttvftdgys7e4z3m44xa

Discovery of Latent Factors in High-dimensional Data Using Tensor Methods [article]

Furong Huang
2016 arXiv   pre-print
This is the first work that gives global convergence guarantees for the stochastic gradient descent on non-convex functions with exponentially many local minima and saddle points.  ...  It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have applications in almost every domain.  ...  We identify strict saddle property for non-convex problem that allows for efficient optimization.  ... 
arXiv:1606.03212v1 fatcat:j2nlv4fpyvbfjidutiofteuu4u

Nonstandard Finite Difference Schemes

Ronald E. Mickens
2018 Notices of the American Mathematical Society  
For example, I developed a non-smooth convex optimization algorithm that has been used in a number of application areas from air traffic management to multi-sensor multi-source data fusion.  ...  Some options for coffee include: • Buckeye Donuts, corner of 18th and High St, Columbus;; old school donut shop open 24 hours and serving breakfast sandwiches and gyros,  ...  Abstracts: Speakers should submit abstracts on the easy-to-use interactive Web form.  ... 
doi:10.1090/noti1617 fatcat:nzhfdj7fsncndnhfiaegkizvue

Shape-changing interfaces

Marcelo Coelho, Jamie Zigelbaum
2010 Personal and Ubiquitous Computing  
We conclude by providing application themes for shape-changing materials in HCI and directions for future work.  ...  In this paper, we present a foundation for the design of shape-changing surfaces in human-computer interaction.  ...  , and Steve Helsing for all of their initial suggestions, collaborations, and providing some of the original sources of inspiration for this work.  ... 
doi:10.1007/s00779-010-0311-y fatcat:fg5bpmzwszdwdgs4igzvhmg54m

Free Choice in Deontic Inquisitive Semantics (DIS) [chapter]

Martin Aher
2012 Lecture Notes in Computer Science  
We define for every sentence ϕ in our language, the proposition ϕ expressed by ϕ, and the counter-proposition ϕ for ϕ. Both ϕ and ϕ will be sets of possibilities.  ...  We will refer to the elements of ϕ as the possibilities for ϕ and to the elements of ϕ as the counter-possibilites for ϕ. Definition 4. Possibilities and counter-possibilities.  ...  We thank the audience there as well as the reviewers for Amsterdam Colloquium for their comments.  ... 
doi:10.1007/978-3-642-31482-7_3 fatcat:vqnczv27vrbh5bekucsnhlocxm

Local image statistics: maximum-entropy constructions and perceptual salience

Jonathan D. Victor, Mary M. Conte
2012 Optical Society of America. Journal A: Optics, Image Science, and Vision  
While many studies suggest that only a limited number of image statistics are used for perceptual judgments, a full understanding of visual function requires analysis not only of the impact of individual  ...  Thus, there is a need for construction of stimuli in which one or more statistical elements are introduced in a controlled fashion, so that their individual and joint contributions can be analyzed.  ...  Chubb for many very helpful discussions, insights, and comments on the text, Jason Mintz for programming assistance, and Daniel J. Thengone for technical assistance and comments on the text.  ... 
doi:10.1364/josaa.29.001313 pmid:22751397 pmcid:PMC3396046 fatcat:bj53w2oazvectmahvkj6ztj354

Towards a fourth spatial dimension of brain activity

Arturo Tozzi, James F. Peters
2016 Cognitive Neurodynamics  
ACKNOWLEDGEMENTS The Authors would like to thank Norbert Jausovec for his precious comments. and let f : S d ®R d be a continuous map.  ...  Balanced Excitatory and Inhibitory Synaptic Currents Promote Efficient Coding and Metabolic Efficiency.  ...  Mmight stand for manifolds with any kind of curvature, either concave, convex or flat.  ... 
doi:10.1007/s11571-016-9379-z pmid:27275375 pmcid:PMC4870410 fatcat:kgfvl25o6fcpfdiitcmvaumska
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