197,774 research outputs found
On Asplund functions
No full textsummary:A class of convex functions where the sets of subdifferentials behave like the unit ball of the dual space of an Asplund space is found. These functions, which we called Asplund functions also possess some stability properties. We also give a sufficient condition for a function to be an Asplund function in terms of the upper-semicontinuity of the subdifferential map
Replication Data for: "Contrasting responses of plant and lichen carbon based secondary compounds across an elevational gradient"
No full textThis dataset contains concentrations of phenolic compounds in individual species of lichens and vascular plants sampled across an elevational gradient from 1120 to 1600 m above sea level near Finse in southern Norway
Mazur intersection property for Asplund spaces
No full textAbstractThe main result of the present note states that it is consistent with the ZFC axioms of set theory (relying on Martin's Maximum MM axiom), that every Asplund space of density character ω1 has a renorming with the Mazur intersection property. Combined with the previous result of Jiménez and Moreno (based upon the work of Kunen under the continuum hypothesis) we obtain that the MIP renormability of Asplund spaces of density ω1 is undecidable in ZFC
Asplund spaces and the finest locally convex topology
No full textIn our previous paper we systematized several known equivalent definitions of Fréchet (G\^ ateaux) Differentiability Spaces and Asplund (weak Asplund) Spaces. As an application, we extended the classical Mazur\u27s theorem, and also proved that the product of any family of Banach spaces is an Asplund lcs if and only if each is Asplund. The actual work continues this line of research in the frame of locally convex spaces, including the classes of Fréchet spaces (i.e. metrizable and complete locally convex spaces) and projective limits, quojections, -spaces and -spaces, as well as, the class of free locally convex spaces over Tychonoff spaces .
First we prove some negative results: We show that for every infinite Tychonoff space the space is not even a G\^ ateaux Differentiability Space (GDS in short) and contains no infinite-dimensional Baire vector subspaces.
On the other hand, we show that all barrelled GDS spaces are quasi-Baire spaces, what implies that strict -spaces are not GDS. This fact refers, for example, to concrete important spaces
, , .
A special role of the space , i.e. an -dimensional vector space equipped with the finest locally convex topology, in this line of research has been distinguished and analysed. It seems that little is known about the Asplund property for Fréchet spaces. We show however that a quojection , i.e. a Fréchet space which is a strict projective limit of the corresponding Banach spaces , is an Asplund (weak Asplund) space if and only if each
Banach space is Asplund (weak Asplund). In particular, every reflexive quojection is Asplund.
Some applications and several illustrating examples are provided
Towards privacy-preserving anomaly-based intrusion detection in energy communities
No full textEnergy communities consist of decentralized energy production, storage, consumption, and distribution and are gaining traction in modern power systems. However, these communities may increase the vulnerability of the grid to cyber threats. We propose an anomaly-based intrusion detection system to enhance the security of energy communities. The system leverages LSTM autoencoders to detect deviations from normal operational patterns in order to identify anomalies induced by attacks or faults. Operational data for training and evaluation are derived from a Simulink-based model of an energy community. The results show that the autoencoder-based intrusion detection system achieves good detection performance across multiple attack scenarios, up to 0.9270 and 0.9735 in precision and recall respectively. We also demonstrate potential for real-world application of the system by training a federated model that enables distributed intrusion detection while preserving data privacy
On the Asplund property of locally convex spaces
No full texthe aim of this paper is to investigate the Frechet differentiability of continuous convex functions on locally convex spaces, to give the characterization of the Asplund property of locally convex spaces in geometrical terms, and to generalize the Asplund theorem of Mazur Theorem to locally convex spaces. (C) 1996 Academic Press, Inc
A note on polynomial characterizations of asplund spaces
No full textIn this note we obtain several characterizations of Asplund spaces by means of ideals of Pietsch integral and nuclear polynomials, extending previous results of R. Alencar and R. Cilia-J. Gutiérrez
φ-regular functions in Asplund spaces
No full textWe introduce in the context of Asplund spaces, a new class of (φ-regular functions. This new concept generalizes the one of prox-regularity introduced by Poliquin & Rockafellar (2000) in Rn and extended to Banach spaces by Bernard & Thibault (2004). In particular, the class of φ-regular functions includes all lower semi-continuous convex functions, all lower-C2 functions, and convexly C1,0-composite functions as well. Geometrical and subdifferential characterizations for this new class of functions are investigated
Tutorial: guidelines for standardized performance tests for electrodes intended for neural interfaces and bioelectronics
No full textImplantable neural interfaces advance the possibilities for neuroscientists to study the brain. They are also promising for use in a multitude of bioelectronic therapies. Electrode technology plays a central role in these developments, as the electrode surfaces form the physical interfaces between technology and the biological targets. Despite this, a common understanding of how electrodes should best be evaluated and compared with respect to their efficiency in recording and stimulation is currently lacking. Without broadly accepted performance tests, it is difficult to rank the many suggestions for electrode materials available in the literature, or to identify where efforts should be focused to advance the field most efficiently. This tutorial critically discusses the most relevant performance tests for characterization of neural interface electrodes and explains their implementation, interpretation and respective limitations. We propose a unified standard to facilitate transparent reporting on electrode performance, promote efficient scientific process and ultimately accelerate translation into clinical practice
Dr. Duane M. Jackson, Morehouse College, July 2011
No full textThis video is a conversation with Dr. Duane M. Jackson. Dr. Jackson talks about his paper, "Recall and the Serial Position Effect: The Role of Primacy and Recency on Accounting Students' Performance." Jackie Daniel, AUC Woodruff Library, is the interviewer
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