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On the Compact-regular Coreflection of a Stably Compact Locale

Martín Hötzel Escardó
1999 Electronical Notes in Theoretical Computer Science  
A nucleus on a frame is a finite-meet preserving closure operator. The nuclei on a frame form themselves a frame, with the Scott continuous nuclei as a subframe.  ...  We refer to this subframe as the patch frame.  ...  The proof given in [6] observes that the join of a set J of perfect nuclei is given by the pointwise join of the finite compositions of members of J (which are not necessarily nuclei).  ... 
doi:10.1016/s1571-0661(04)80076-8 fatcat:pa5t644gf5bhbm7ujadyzllc2y

The regular-locally compact coreflection of a stably locally compact locale

Martı́n Hötzel Escardó
2001 Journal of Pure and Applied Algebra  
The Scott continuous nuclei form a subframe of the frame of all nuclei. We refer to this subframe as the patch frame.  ...  maps, (ii) the category of compact regular locales and continuous maps as a core ective subcategory of the category of stably compact locales and perfect maps, and (iii) the category of Stone locales  ...  This adjunction can be interpreted as saying that the patch frame of the frame of opens of a stably compact locale is the universal solution to the problem of transforming the way-below relation into the  ... 
doi:10.1016/s0022-4049(99)00172-3 fatcat:25idvecmc5hqtmdlth4dhmohuu

Funayama's theorem revisited

Guram Bezhanishvili, David Gabelaia, Mamuka Jibladze
2013 Algebra Universalis  
Let N (L) ¬¬ be the Booleanization of N (L); that is, the Boolean frame of regular nuclei on L.  ...  Therefore, the poset N (L) of all nuclei on L is also a frame, and the embedding L → N (L) is a frame homomorphism.  ... 
doi:10.1007/s00012-013-0247-y fatcat:6lqexp7okje6tisyxct6i6h4nu

Free meets and atomic assemblies of frames

J. Martínez, W. Wm. McGovern
2009 Algebra Universalis  
Wilson proves that all subsets of L have free meets if and only if the dual frame law holds in L and the assembly NL is a boolean frame.  ...  Wilson's doctoral dissertation, the author takes up the subject of free meets, that is, subsets S of a frame L whose meet V S is preserved by a designated class of frame homomorphisms out of L.  ...  The map p →p is itself a prenucleus on PL. Therefore, the set NL of all nuclei is a frame. However, joins in the frame of nuclei cannot generally be computed by taking pointwise joins of functions.  ... 
doi:10.1007/s00012-010-0048-5 fatcat:6nbouox42bh2dnlsp5avkrlctq

Closure operators on dcpos [article]

France Dacar
2021 arXiv   pre-print
in the special case of the frame of all nuclei on a frame.  ...  We go on to construct the joins in the complete lattice of Scott-continuous closure operators on a dcpo, and to prove that the complete lattice of nuclei on a preframe is a frame, giving some constructions  ...  We denote by ClTheor(E) the poset of all closure theories on E ordered by inclusion. 3 We say that a subset X of E obeys a closure rule B | → c on E, or that the closure rule B | → c is obeyed by the  ... 
arXiv:1709.06170v2 fatcat:oixg3fk6fbbc3dxkgzknmsxj6q

Automated stromal nerve rejection in corneal confocal images in vivo

Eric N. Brown, Jon J. Camp, Sanjay V. Patel, Jay W. McLaren, William M. Bourne, Richard A. Robb, Kenneth M. Hanson
2000 Medical Imaging 2000: Image Processing  
However, in the 57 normal corneas, use of the nerve-removal algorithm reduced estimates of density by 57.0 ± 164.6cells/mm 3 (mean ± SD, p<0.038) in the anterior two-thirds of the stroma.  ...  With the advent of corneal confocal microscopy, investigators can determine keratocyte density in the corneal stroma in vivo.  ...  Brian Welch, Elson Liu, and David Holmes III (Biomedical Imaging Resource, Mayo Clinic and Mayo Foundation, Rochester, MN) for their help with the design of the nerve rejection algorithm.  ... 
doi:10.1117/12.387625 dblp:conf/miip/BrownCPMBR00 fatcat:2kbztfsigrc5tjghgw7epdsjpe

Methods for improving the quality of syllable based speech synthesis

Y.R. Venugopalakrishna, M.V. Vinodh, Hema A. Murthy, C.S. Ramalingam
2008 2008 IEEE Spoken Language Technology Workshop  
Nevertheless, audible artifacts are present due to discontinuities in pitch, energy, and formant trajectories at the joining point of the units.  ...  In this paper, we present some minimal signal modification techniques for reducing these artifacts.  ...  These new speech frames are inserted at the joining point. This was carried out by varying the number of new frames to be inserted. Two frame insertions showed good results.  ... 
doi:10.1109/slt.2008.4777832 dblp:conf/slt/VenugopalakrishnaVMR08 fatcat:moir6tku7bca7fckhsp32kc3de

More on a Curious Nucleus [article]

Levon Haykazyan
2019 arXiv   pre-print
Harold Simmons introduced a pre-nucleus and its associated nucleus that measure the subfitness of a frame in Simmons [2010]. In this paper we continue the study if this pre-nucleus.  ...  We answer the questions posed in Simmons [2010].  ...  In section 2 we study the pre-nucleus on a general frame. We show that ξ is equal to the join of all (pre-)nuclei that only admit the top element ⊤ (Theorem 2.2).  ... 
arXiv:1807.08020v2 fatcat:ggxb37sprjhbtjnld4dws4hy6u

Compactly generated Hausdorff locales

Martín H. Escardó
2006 Annals of Pure and Applied Logic  
More generally, for any Hausdorff locale, the second dual of the frame of opens gives the frame of opens of the colimit.  ...  We show that this is the case if and only if the natural map of its frame of opens into the second Lawson dual is an isomorphism.  ...  In terms of frames and nuclei, the HMJ theorem says that, for any frame L, the assignment j → j −1 (1) is an order isomorphism from compact fitted nuclei on L to the preframe L ∧ .  ... 
doi:10.1016/j.apal.2005.05.020 fatcat:drrgbds5wrhc5g5oddjtoljuqy

Book Review: Derivatives, nuclei and dimensions on the frame of torsion theories

P. T. Johnstone
1990 Bulletin of the American Mathematical Society  
Nuclei on a frame correspond to localizations of the frame itself, considered as a category (that is, to its quotients in the category of frames); they are unary operators ( j, say) on the frame which  ...  For example, the composite of two different nuclei is in general only a prenucleus.  ... 
doi:10.1090/s0273-0979-1990-15927-0 fatcat:z2d67ik23rbzph5h5chwbv5wda

Genetic Instability Due to Spindle Anomalies Visualized in Mutants of Dictyostelium

Mary Ecke, Jana Prassler, Günther Gerisch
2021 Cells  
Aberrant centrosome activities in mutants of Dictyostelium discoideum result in anomalies of mitotic spindles that affect the reliability of chromosome segregation.  ...  Dual-color fluorescence labeling of the microtubule system and the chromosomes in live cells revealed the variability of spindle arrangements, of centrosome-nuclear interactions, and of chromosome segregation  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/cells10092240 pmid:34571889 pmcid:PMC8469108 fatcat:4phs7xgpo5huvnkpmfkvmybr24

A special class of congruences on $${\kappa}$$ κ -frames

Graham Manuell
2017 Algebra Universalis  
Madden has shown that in contrast to the situation with frames, the smallest dense quotient of a κ-frame need not be Boolean.  ...  In particular, we show that d-reduced κ-frames are precisely the quotients of κ-frames by clear congruences and that every κ-frame congruence is the meet of clear congruences.  ...  Acknowledgements I would like to thank John Frith and Christopher Gilmour for discussions about the content and presentation of this paper.  ... 
doi:10.1007/s00012-017-0439-y fatcat:4hwfs4pmpfdcdncietc4buy2xy

Page 6061 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
In this paper concepts of equivalent frames are introduced and studied by using dense nuclei. Strong compactness on frames is studied by utilizing the concept of equivalent frames.  ...  Summary: “In the theory of frames (or ‘pointless topologies’), several authors have tried to find a suitable form of nearly open nuclei which are generalizations of near open sets in general topol- ogy  ... 

A Note on Frame Distributions

Anders Kock, Gonzalo E. Reyes
1997 BRICS Report Series  
In the context of constructive locale or frame theory (locale<br />theory over a fixed base locale), we study some aspects of 'frame distributions', meaning sup preserving maps from a frame to the base  ...  We derive a relationship between results of Jibladze-Johnstone and Bunge-Funk, and also descriptions in distribution terms, as well as in double negation terms, of the 'interior of closure' operator on  ...  It follows that for x ≤ z, o(z) • c(x) is a nucleus and is the join o(z) ∨ c(x) in the frame of nuclei.  ... 
doi:10.7146/brics.v4i33.18959 fatcat:6wjgpkyptrdm7ixldmws3vbpma

Movement in a confluent 3T3 monolayer and the causes of contact inhibition of overlapping

E Martz, M S Steinberg
1974 Journal of Cell Science  
However, during a 22-day period, more than one third of originally adjacent pairs of nuclei became separated by 1-5 intervening nuclei, and their average distance of separation increased more than 2-fold  ...  Data presented in the present report reveal that similar movements occur in confluent monolayers of mouse 3T3 fibroblasts, previously shown to display contact inhibition of speed, contact inhibition of  ...  This work was supported by Grants GB-2315 and GB-5759X from the National Science Foundation, and by a special grant for research (P-532) from the New Jersey Division of the American Cancer Society.  ... 
pmid:4407161 fatcat:uc2tgfwgnjh3tgqtz7laoz7mue
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