On the riesz charge of the lower envelope of δ-subharmonic functions

1992 ◽  
Vol 1 (2) ◽  
pp. 191-204 ◽  
Author(s):  
Alexandre Eremenko ◽  
Bent Fuglede ◽  
Mikhail Sodin
Keyword(s):  
Lower Envelope ◽  
Subharmonic Functions ◽  
Riesz Charge

scholarly journals On the mean value property of superharmonic and subharmonic functions

2006 ◽  
Vol 2006 ◽  
pp. 1-3
Author(s):  
Robert Dalmasso
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Subharmonic Functions ◽  
Mean Value Property ◽  
The Mean

We prove a converse of the mean value property for superharmonic and subharmonic functions. The case of harmonic functions was treated by Epstein and Schiffer.

Linking sensory neurons to visually guided behavior: Relating MST activity to steering in a virtual environment

2013 ◽  
Vol 30 (5-6) ◽  
pp. 315-330 ◽  
Author(s):  
SETH W. EGGER ◽  
KENNETH H. BRITTEN
Keyword(s):  
Cortical Neurons ◽  
Traditional Approach ◽  
Sensory System ◽  
Sensory Information ◽  
Neuronal Population ◽  
Difficult Problem ◽  
Lower Envelope ◽  
Visually Guided ◽  
Medial Superior Temporal ◽  
Visual Cortical

AbstractMany complex behaviors rely on guidance from sensations. To perform these behaviors, the motor system must decode information relevant to the task from the sensory system. However, identifying the neurons responsible for encoding the appropriate sensory information remains a difficult problem for neurophysiologists. A key step toward identifying candidate systems is finding neurons or groups of neurons capable of representing the stimuli adequately to support behavior. A traditional approach involves quantitatively measuring the performance of single neurons and comparing this to the performance of the animal. One of the strongest pieces of evidence in support of a neuronal population being involved in a behavioral task comes from the signals being sufficient to support behavior. Numerous experiments using perceptual decision tasks show that visual cortical neurons in many areas have this property. However, most visually guided behaviors are not categorical but continuous and dynamic. In this article, we review the concept of sufficiency and the tools used to measure neural and behavioral performance. We show how concepts from information theory can be used to measure the ongoing performance of both neurons and animal behavior. Finally, we apply these tools to dorsal medial superior temporal (MSTd) neurons and demonstrate that these neurons can represent stimuli important to navigation to a distant goal. We find that MSTd neurons represent ongoing steering error in a virtual-reality steering task. Although most individual neurons were insufficient to support the behavior, some very nearly matched the animal’s estimation performance. These results are consistent with many results from perceptual experiments and in line with the predictions of Mountcastle’s “lower envelope principle.”

scholarly journals Terrain classification of ladar data over Haitian urban environments using a lower envelope follower and adaptive gradient operator

2010 ◽  
Author(s):  
Amy L. Neuenschwander ◽  
Melba M. Crawford ◽  
Lori A. Magruder ◽  
Christopher A. Weed ◽  
Richard Cannata ◽  
...  
Keyword(s):  
Urban Environments ◽  
Lower Envelope ◽  
Terrain Classification ◽  
Gradient Operator

Optimization of the Robust Stability Limit for Multi-Cutter Turning Processes

2015 ◽  
Author(s):  
Marta J. Reith ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Robust Stability ◽  
Optimal Parameter ◽  
Stability Limit ◽  
Boundary Function ◽  
Lower Envelope ◽  
Computation Method ◽  
Parameter Region ◽  
Dynamical Parameters ◽  
The Stability ◽  
Machining Parameter

Multi-cutter turning systems bear huge potential in increasing cutting performance. In this study we show that the stable parameter region can be extended by the optimal tuning of system parameters. The optimal parameter regions can be identified by means of stability charts. Since the stability boundaries are highly sensitive to the dynamical parameters of the machine tool, the reliable exploitation of the so-called stability pockets is limited. Still, the lower envelope of the stability lobes is an appropriate upper boundary function for optimization purposes with an objective function taken for maximal material removal rates. This lower envelope is computed by the Robust Stability Computation method presented in the paper. It is shown in this study, that according to theoretical results obtained for optimally tuned cutters, the safe stable machining parameter region can significantly be extended, which has also been validated by machining tests.

Universal (pluri)subharmonic functions

Analysis ◽  
2007 ◽  
Vol 27 (2-3) ◽  
Author(s):  
Paul M. Gauthier ◽  
Mohamad R. Pouryayevali
Keyword(s):  
Subharmonic Functions

In this note, we establish the existence of universal subharmonic functions on ℝ

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