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Perfect matchings in pruned grid graphs
2008
Discrete Mathematics
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Now define φ(R j ) = R j+1 if R j is left justified, S r j = 0, and j < m − 1, and φ(R j ) = R j−1 if R j is right justified and S r j = 0. φ is an injection from the set of rows with zero surplus (except ...
If S r j = 0 and R j is not complete, then S r j+1 > 0 and S r j−1 > 0, provided of course that j + 1 < m and j − 1 ≥ 0, respectively. ...
doi:10.1016/j.disc.2007.11.032
fatcat:7jftff2j3nabpgod3pc7okwf2q
A note on r-maximal subspaces of V∞
1984
Annals of Pure and Applied Logic
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Then there is a recursive space R such that W + R = V. Proof. We will construct R, and R, in stages so that R,+ RI = V, and W+ R0 = V. ...
Let p(s+ 1) be the least p >p(s) such that either (1) U,E WP+R& or (2) 3x E Wp [x$(u,)T R;+ R;]. In case (2) let IA+:'= IhU{x + u,}, otherwise let I&+"' = 16. Then note that R;+' n R;+' = (0). ...
doi:10.1016/0168-0072(84)90037-x
fatcat:nrujwtiqunftxawcr6q72z6cvm
No-hole k-tuple (r + 1)-distant colorings of odd cycles
1996
Discrete Applied Mathematics
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(k -1) + a(2k + 2r + 1) + (1-a)(2k + 2r)
. . . 2k + r -a(m -1) -1 k+r-a(m-1)-m . . . 2k + r -a(m -1) -m -1 k+r-a(m-1)-2m . . . 2k + r -a(m -1) -2m -
2r + 1 -(a -l)(m -1) -m . .
2k + 2r + 1 -(a -l ...
Note that the gaps between color sets alternately contain r and r + 1 colors up to u 1 + za, after which all gaps contain r colors. ...
doi:10.1016/0166-218x(95)00108-4
fatcat:xwd3ebse5rdqbajzlqdhqt62aq
Two theorems on the addition of residue classes
1990
Discrete Mathematics
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. , 0, r, r, n -r, n -r) where r < n/2. ...
The number of subsequences r such that C r = k is then If q = r < n -r then f(u) = 3 * 2"-3. If q = r = n -r =n/2 then f(u) = 2"-l, so this is impossible. 6. (0, . . . , 0, q, n -q, r, n -r) . ...
doi:10.1016/0012-365x(90)90174-g
fatcat:lbwyduhs7fdnfcm37x6jpoo24y
When Is U(n) Cyclic? An Algebraic Approach
1999
Mathematics Magazine
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Thus t = r and c = b, and the order of hag ...
Thus the order of h'ag must be qtc, where t < r and cib. If t < r, then 1= =(g7 (hI)'(g -= ( `l ) so lhi divides q'r-Iab, a contradiction. ...
doi:10.1080/0025570x.1999.11996716
fatcat:2hc465fjlfhzbikvjlag4bfe4q
Competition Graphs of Hamiltonian Digraphs
1998
SIAM Journal on Discrete Mathematics
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Suppose the circuit contains exactly n r ≥ 1 red vertices and n b ≥ 1 sequences of q consecutive blue vertices. Then n r + n b ≤ m − q + 1. ...
doi:10.1137/s089548019629735x
fatcat:ku62v23eznhpnjwo3rpmk6acqy
The number of maximal independent sets in a connected graph
1988
Discrete Mathematics
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On the other hand, suppose that u $ r(f); G:). ...
= I(G* -x) + I(G*r(x; G*)) Sg(n -1) + m(n -d(x) -1).
Fig. 3 3 Fig. 3 ...
doi:10.1016/0012-365x(88)90114-8
fatcat:hpikg2xwwbdmzarztflhz3m47m
A Many-Sorted Interpolation Theorem for L(Q)
1980
Proceedings of the American Mathematical Society
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EXT be the collection of the following sentences of LA : of EXT will be of the form (M, M', c¡, c'¡, R¡, q) and moreover (M, c¡, R¡ f M, q ¡ {0} X M) cA (M', c'¡, R¡ \ M', q \ {1} X M). ...
Definition. (3JÎ, q) cend (3c, r) iff 3J? cend 3c and for all j £ J and a £ Af, whenever X c aE then X £ q(j, a) iff X £ r(j, a). Definition. The 2 formulas are those </> such that Un*(<f>) = 0. ...
doi:10.2307/2043742
fatcat:otjjous27ngntfxbnv6rndlie4
A many-sorted interpolation theorem for $L(Q)$
1980
Proceedings of the American Mathematical Society
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EXT be the collection of the following sentences of LA : of EXT will be of the form (M, M', c¡, c'¡, R¡, q) and moreover (M, c¡, R¡ f M, q ¡ {0} X M) cA (M', c'¡, R¡ \ M', q \ {1} X M). ...
Definition. (3JÎ, q) cend (3c, r) iff 3J? cend 3c and for all j £ J and a £ Af, whenever X c aE then X £ q(j, a) iff X £ r(j, a). Definition. The 2 formulas are those </> such that Un*(<f>) = 0. ...
doi:10.1090/s0002-9939-1980-0581007-8
fatcat:fmb2jgpvbrewfcwmx5kom6lftm
φ meson production in NA60
2006
European Physical Journal C: Particles and Fields
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First measurement of the ρ spectral function in nuclear collisions
2006
Nuclear Physics A
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The NA60 experiment has studied low-mass muon pairs in 158 AGeV Indium-Indium collisions at the CERN SPS. A strong excess of pairs is observed above the expectation from neutral meson decays. The unprecedented sample size of 360 000 events and the good mass resolution of about 2% allow to isolate the excess by subtraction of the known sources. The shape of the resulting mass spectrum is consistent with a dominant contribution from π + π − → ρ → µ + µ − annihilation. The associated ρ spectral
doi:10.1016/j.nuclphysa.2006.06.121
fatcat:2htheiywg5ek5neohnd6mvtqwq
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... ction shows a strong broadening, but essentially no shift in mass. Thermal dilepton production in the mass region <1 GeV is largely mediated by the light vector mesons ρ, ω and φ. Among these, the ρ is the most important, due to its strong coupling to the ππ channel and its short lifetime of only 1.3 fm/c. These properties have given it a key role as the test particle for "in-medium modifications" of hadron properties close to the QCD phase boundary. Changes both in width and in position were originally advocated as precursor signatures of the chiral transition [1]. There seems to be some consensus now that the width of the ρ should increase towards the transition region, based on a number of quite different theoretical approaches [1] [2] [3] [4] [5] . On the other hand, no consensus exists on how the mass of the ρ should change in approaching the transition: predictions exist for a decrease [1,6], a constant behavior [4, 5] , and even an increase [3] . The CERES/NA45 experiment at the CERN SPS studied the production of low-mass electron pairs in p-Be/Au [7], S-Au [8] and Pb-Au [9] . The common feature of all results from nuclear collisions was an excess of the observed dilepton yield above the known electromagnetic decays of the produced neutral mesons, by a factor of 2-3, for masses above 1
ϕ production in p-A and In-In collisions
2006
Nuclear Physics A
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Low Mass Dimuon Production in Indium-Indium Collisions at the CERN SPS
[article]
2006
arXiv
pre-print
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NA60 is a fixed-target experiment at the CERN SPS which measured dimuon production in nucleus-nucleus and proton-nucleus collisions. In this paper we report on a precision measurement of low-mass muon pairs in 158 AGeV indium-indium collisions. A significant excess of pairs is observed above the yield expected from neutral meson decays. The excess can be isolated by subtraction of expected sources, thanks to the excellent mass resolution and large sample size.
arXiv:nucl-ex/0606023v1
fatcat:w2grnmqx6ffxlg2xnetd5j622e
Integrated multi-modality image-guided navigation for neurosurgery: open-source software platform using state-of-the-art clinical hardware
2021
International Journal of Computer Assisted Radiology and Surgery
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Image-guided surgery (IGS) is an integral part of modern neuro-oncology surgery. Navigated ultrasound provides the surgeon with reconstructed views of ultrasound data, but no commercial system presently permits its integration with other essential non-imaging-based intraoperative monitoring modalities such as intraoperative neuromonitoring. Such a system would be particularly useful in skull base neurosurgery. We established functional and technical requirements of an integrated multi-modality
doi:10.1007/s11548-021-02374-5
pmid:33937966
pmcid:PMC8295168
fatcat:j7374fngqfcl3ok75yxloexb3u
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... GS system tailored for skull base surgery with the ability to incorporate: (1) preoperative MRI data and associated 3D volume reconstructions, (2) real-time intraoperative neurophysiological data and (3) live reconstructed 3D ultrasound. We created an open-source software platform to integrate with readily available commercial hardware. We tested the accuracy of the system's ultrasound navigation and reconstruction using a polyvinyl alcohol phantom model and simulated the use of the complete navigation system in a clinical operating room using a patient-specific phantom model. Experimental validation of the system's navigated ultrasound component demonstrated accuracy of [Formula: see text] and a frame rate of 25 frames per second. Clinical simulation confirmed that system assembly was straightforward, could be achieved in a clinically acceptable time of [Formula: see text] and performed with a clinically acceptable level of accuracy. We present an integrated open-source research platform for multi-modality IGS. The present prototype system was tailored for neurosurgery and met all minimum design requirements focused on skull base surgery. Future work aims to optimise the system further by addressing the remaining target requirements.
LINE-1 retrotransposition impacts the genome of human pre implantation embryos and extraembryonic tissues
[article]
2019
bioRxiv
pre-print
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Long Interspersed Element 1 (LINE-1/L1) is an abundant retrotransposon that has greatly impacted human genome evolution. LINE-1s are responsible for the generation of millions of insertions in the current human population. The characterization of sporadic cases of mosaic individuals carrying pathogenic L1-insertions, suggest that heritable insertions occurs during early embryogenesis. However, the timing and potential genomic impact of LINE-1 mobilization during early embryogenesis is unknown.
doi:10.1101/522623
fatcat:fu2kuw5zgrdafph5jjifqxylwe
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... ere, we demonstrate that inner cell mass of human pre-implantation embryos support the expression and retrotransposition of LINE-1s. Additionally, we show that LINE-1s are expressed in trophectoderm cells of embryos, and identify placenta-restricted endogenous LINE-1 insertions in newborns. Using human embryonic stem cells as a model of postimplantation epiblast cells, we demonstrate ongoing LINE-1 retrotransposition, which can impact expression of targeted genes. Our data demonstrate that LINE-1 retrotransposition starts very shortly after fertilization and may represent a previously underappreciated factor in human biology and disease.
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