High Level Occupation Times for Gaussian Stochastic Processes with Sample Paths in Orlicz Spaces

1987 ◽  
Vol 39 (1) ◽  
pp. 239-256
Author(s):  
Anna T. Lawniczak
Keyword(s):  
Large Deviation ◽  
Lower Semicontinuous ◽  
Orlicz Spaces ◽  
Compact Set ◽  
List Type ◽  
Occupation Times ◽  
Closed Set ◽  
Sample Paths ◽  
Open Set ◽  
Image Position

Let X be a complete separable metric space, and a family of probability measures on the Borel subsets of X. We say that obeys the large deviation principle (LDP) with a rate function I(·) if there exists a function I(·) from X into [0, ∞] satisfying:(i)0 ≦ I(x) ≦ ∞ for all x ∊ X.(ii)I(·) is lower semicontinuous.(iii)For each l < ∞ the set {x:I(x) ≦ l} is a compact set in X.(iv)For each closed set C ⊂ X(v)For each open set C ⊂ X

Large Deviations for Gaussian Stochastic Processes with Sample Paths in Orlicz Spaces

1988 ◽  
Vol 40 (2) ◽  
pp. 487-501
Author(s):  
Anna T. Lawniczak
Keyword(s):  
Large Deviation ◽  
Lower Semicontinuous ◽  
Orlicz Spaces ◽  
Compact Set ◽  
List Type ◽  
Closed Set ◽  
Borel Set ◽  
Sample Paths ◽  
Open Set ◽  
Image Position

Let X be a complete, separable metric space, and a family of probability measures on the Borel subsets of X. We say that obeys the large deviation principle (LDP) with a rate function I( · ) if there exists a function I( · ) from X into [0, ∞] satisfying:(i) 0 ≦ I(x) ≦ ∞ for all x ∊ X,(ii) I( · ) is lower semicontinuous,(iii) for each 1 < ∞ the set {x:I(x) ≦ 1} is compact set in X,(iv) for each closed set C ⊂ X(v) for each open set U ⊂ XIt is easy to see that if A is a Borel set such thatthenwhere A0 and Ā are respectively the interior and the closure of the Borel set A.

scholarly journals UNIFORM APPROXIMATION BY POLYNOMIAL, RATIONAL AND ANALYTIC FUNCTIONS

2008 ◽  
Vol 77 (3) ◽  
pp. 387-399
Author(s):  
T. G. HONARY ◽  
S. MORADI
Keyword(s):  
Rational Functions ◽  
Function Algebra ◽  
Continuous Functions ◽  
Compact Set ◽  
List Type ◽  
Type Number ◽  
Open Disk ◽  
Closed Disk ◽  
Open Set ◽  
Image Position

AbstractLet K and X be compact plane sets such that $K\subseteq X$. Let P(K) be the uniform closure of polynomials on K, let R(K) be the uniform closure of rational functions on K with no poles in K and let A(K) be the space of continuous functions on K which are analytic on int(K). Define P(X,K),R(X,K) and A(X,K) to be the set of functions in C(X) whose restriction to K belongs to P(K),R(K) and A(K), respectively. Let S0(A) denote the set of peak points for the Banach function algebra A on X. Let S and T be compact subsets of X. We extend the Hartogs–Rosenthal theorem by showing that if the symmetric difference SΔT has planar measure zero, then R(X,S)=R(X,T) . Then we show that the following properties are equivalent: (i)R(X,S)=R(X,T) ;(ii)$S\setminus T\subseteq S_0(R(X,S))$ and $T\setminus S\subseteq S_0(R(X,T))$;(iii)R(K)=C(K) for every compact set $K \subseteq S\Delta T$;(iv)$R(X,S \cap \overline {U})=R(X,T \cap \overline {U})$ for every open set U in ℂ ;(v)for every p∈X there exists an open disk Dp with centre p such that We prove an extension of Vitushkin’s theorem by showing that the following properties are equivalent: (i)A(X,S)=R(X,T) ;(ii)$A(X,S \cap \overline {D})=R(X,T \cap \overline {D})$ for every closed disk $\overline {D}$ in ℂ ;(iii)for every p∈X there exists an open disk Dp with centre p such that

Property (BB) and holomorphic functions on Fréchet-Montel spaces

1994 ◽  
Vol 115 (2) ◽  
pp. 305-313 ◽  
Author(s):  
Andreas Defant ◽  
Manuel Maestre
Keyword(s):  
Holomorphic Functions ◽  
Compact Set ◽  
Fréchet Spaces ◽  
Compact Open Topology ◽  
Bounded Set ◽  
Open Set ◽  
Projective Tensor ◽  
Montel Space ◽  
Image Position ◽  
Locally Convex

Two of the most important topologies on the space ℋ(E) of all holomorphic functions f:E → ℂ on a complex locally convex space E are the compact-open topology τ0 and the Nachbin-ported topology τε. We recall that a seminorm p on ℋ(E) is said to be τω-continuous if there is a compact K such that for every open set V with K contained in V there is a constant c > 0 satisfyingClearly, the following natural question arises: when do the topologies τ0 and τω coincide? In the setting of Fréchet spaces equality of τ0 and τω forces E to be a Montel space; Mujica [21] proved τ0 = τω for Fréchet-Schwartz spaces and Ansemil-Ponte [1] showed that for Fréchet-Montel spaces this happens if and only if the space of all continuous n-homogeneous polynomials with the compact-open topology, (Pn(E), τ0), is barrelled. By duality, it turns out that the question τ0 = τω is intimately related to ‘Grothendieck's problème des topologies’ which asks whether or not for two Fréchet spaces E1 and E2 each bounded set B of the (completed) projective tensor product is contained in the closed absolutely convex hull of the set B1 ⊗ B2, where Bk is a bounded subset of Ek for k = 1, 2. If this is the case, then the pair (E1, E2) is said to have property (BB). Observe that every compact set B in can always be lifted by compact subsets Bk of Ek (see e.g. [20], 15·6·3). Hence, for Fréchet-Montel spaces E1 and E2, property (BB) of (El,E2) means that is Fréchet-Montel and vice versa. Taskinen[24] found the first counterexample to Grothendieck's problem. In [25] he constructed a Fréchet-Montel space E0 for which (E0,E0) does not have property (BB), and Ansemil-Taskinen [2] showed that τ0 ≠ τω on ℋ(E0).

The interaction between bulk energy and surface energy in multiple integrals

1994 ◽  
Vol 124 (4) ◽  
pp. 737-756 ◽  
Author(s):  
Andrea Braides ◽  
Alessandra Coscia
Keyword(s):  
Energy Density ◽  
Surface Energy ◽  
Special Functions ◽  
Lower Semicontinuous ◽  
Integral Functional ◽  
Open Set ◽  
Lower Semicontinuous Envelope ◽  
Bulk Energy ◽  
Image Position ◽  
Vector Valued

This paper is devoted to the study of integral functional denned on the spaceSBV(Ω ℝk) of vector-valued special functions with bounded variation on the open set Ω⊂ℝn, of the formWe suppose only thatfis finite at one point, and thatgis positively 1-homogeneous and locally bounded on the sets ℝk⊗vm, where {v1,…,vR} ⊂Sn−1is a basis of ℝn. We prove that the lower semicontinuous envelope ofFin theL1(Ω;ℝk)-topology is finite and with linear growth on the wholeBV(Ω;ℝk), and that it admits the integral representationA formula forϕis given, which takes into account the interaction between the bulk energy densityfand the surface energy densityg.

Minimizing non-convex multiple integrals: a density result

2000 ◽  
Vol 130 (4) ◽  
pp. 721-741 ◽  
Author(s):  
P. Celada ◽  
S. Perrotta
Keyword(s):  
Lower Semicontinuous ◽  
Convergent Sequence ◽  
Variational Problems ◽  
Continuous Functions ◽  
Lower Semicontinuous Function ◽  
Semicontinuous Function ◽  
Open Set ◽  
Multiple Integrals ◽  
Image Position ◽  
Convex Lower Semicontinuous Function

We consider variational problems of the form where Ω is a bounded open set in RN, f : RN → R is a possibly non-convex lower semicontinuous function with p-growth at infinity for some 1 < p < ∞, and the boundary datum u0 is any function in W1, p (Ω). Assuming that the convex envelope f** of f is affine on each connected component of the set {f** < f}, we prove the existence of solutions to ( P) for every continuous function g such that (i) g has no strict local minima and (ii) every convergent sequence of extremum points of g eventually belongs to an interval where g is constant, thus showing that the set of continuous functions g that yield existence to (P) is dense in the space of continuous functions on R.

The torsionfree part of the Ziegler spectrum of RG when R is a Dedekind domain and G is a finite group

2002 ◽  
Vol 67 (3) ◽  
pp. 1126-1140 ◽  
Author(s):  
A. Marcja ◽  
M. Prest ◽  
C. Toffalori
Keyword(s):  
Finite Group ◽  
Free Variable ◽  
Dedekind Domain ◽  
Closed Set ◽  
Isomorphism Classes ◽  
Open Set ◽  
Image Position ◽  
Ziegler Spectrum ◽  
A Finite Group ◽  
The Right

For every ring S with identity, the (right) Ziegler spectrum of S, Zgs, is the set of (isomorphism classes of) indecomposable pure injective (right) S-modules. The Ziegler topology equips Zgs with the structure of a topological space. A typical basic open set in this topology is of the formwhere φ and ψ are pp-formulas (with at most one free variable) in the first order language Ls for S-modules; let [φ/ψ] denote the closed set Zgs - (φ/ψ). There is an alternative way to introduce the Ziegler topology on Zgs. For every choice of two f.p. (finitely presented) S-modules A, B and an S-module homomorphism f: A → B, consider the set (f) of the points N in Zgs such that some S-homomorphism h: A → N does not factor through f. Take (f) as a basic open set. The resulting topology on Zgs is, again, the Ziegler topology.The algebraic and model-theoretic relevance of the Ziegler topology is discussed in [Z], [P] and in many subsequent papers, including [P1], [P2] and [P3], for instance. Here we are interested in the Ziegler spectrum ZgRG of a group ring RG, where R is a Dedekind domain of characteristic 0 (for example R could be the ring Z of integers) and G is a finite group. In particular we deal with the R-torsionfree points of ZgRG.The main motivation for this is the study of RG-lattices (i.e., finitely generated R-torsionfree RG-modules).

ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Open Set ◽  
Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

scholarly journals Synthetic speech detection through short-term and long-term prediction traces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Clara Borrelli ◽  
Paolo Bestagini ◽  
Fabio Antonacci ◽  
Augusto Sarti ◽  
Stefano Tubaro
Keyword(s):  
Deep Learning ◽  
Speech Processing ◽  
Synthetic Speech ◽  
Opinion Formation ◽  
Closed Set ◽  
Speech Detection ◽  
Open Set ◽  
Technological Advances ◽  
Speech Generation ◽  
Long Term Prediction

AbstractSeveral methods for synthetic audio speech generation have been developed in the literature through the years. With the great technological advances brought by deep learning, many novel synthetic speech techniques achieving incredible realistic results have been recently proposed. As these methods generate convincing fake human voices, they can be used in a malicious way to negatively impact on today’s society (e.g., people impersonation, fake news spreading, opinion formation). For this reason, the ability of detecting whether a speech recording is synthetic or pristine is becoming an urgent necessity. In this work, we develop a synthetic speech detector. This takes as input an audio recording, extracts a series of hand-crafted features motivated by the speech-processing literature, and classify them in either closed-set or open-set. The proposed detector is validated on a publicly available dataset consisting of 17 synthetic speech generation algorithms ranging from old fashioned vocoders to modern deep learning solutions. Results show that the proposed method outperforms recently proposed detectors in the forensics literature.

scholarly journals Mosquito species identification using convolutional neural networks with a multitiered ensemble model for novel species detection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Adam Goodwin ◽  
Sanket Padmanabhan ◽  
Sanchit Hira ◽  
Margaret Glancey ◽  
Monet Slinowsky ◽  
...  
Keyword(s):  
Neural Networks ◽  
Species Identification ◽  
Convolutional Neural Networks ◽  
Novel Species ◽  
Novelty Detection ◽  
Mosquito Species ◽  
Image Database ◽  
Closed Set ◽  
Open Set

AbstractWith over 3500 mosquito species described, accurate species identification of the few implicated in disease transmission is critical to mosquito borne disease mitigation. Yet this task is hindered by limited global taxonomic expertise and specimen damage consistent across common capture methods. Convolutional neural networks (CNNs) are promising with limited sets of species, but image database requirements restrict practical implementation. Using an image database of 2696 specimens from 67 mosquito species, we address the practical open-set problem with a detection algorithm for novel species. Closed-set classification of 16 known species achieved 97.04 ± 0.87% accuracy independently, and 89.07 ± 5.58% when cascaded with novelty detection. Closed-set classification of 39 species produces a macro F1-score of 86.07 ± 1.81%. This demonstrates an accurate, scalable, and practical computer vision solution to identify wild-caught mosquitoes for implementation in biosurveillance and targeted vector control programs, without the need for extensive image database development for each new target region.

scholarly journals EvidentialMix: Learning with Combined Open-set and Closed-set Noisy Labels

2021 ◽  
Author(s):  
Ragav Sachdeva ◽  
Filipe R. Cordeiro ◽  
Vasileios Belagiannis ◽  
Ian Reid ◽  
Gustavo Carneiro
Keyword(s):  
Closed Set ◽  
Open Set ◽  
Noisy Labels
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