201 research outputs found
DALSA: Domain Adaptation for Supervised Learning From Sparsely Annotated MR Images
We propose a new method that employs transfer learning techniques to
effectively correct sampling selection errors introduced by sparse annotations
during supervised learning for automated tumor segmentation. The practicality
of current learning-based automated tissue classification approaches is
severely impeded by their dependency on manually segmented training databases
that need to be recreated for each scenario of application, site, or
acquisition setup. The comprehensive annotation of reference datasets can be
highly labor-intensive, complex, and error-prone. The proposed method derives
high-quality classifiers for the different tissue classes from sparse and
unambiguous annotations and employs domain adaptation techniques for
effectively correcting sampling selection errors introduced by the sparse
sampling. The new approach is validated on labeled, multi-modal MR images of 19
patients with malignant gliomas and by comparative analysis on the BraTS 2013
challenge data sets. Compared to training on fully labeled data, we reduced the
time for labeling and training by a factor greater than 70 and 180 respectively
without sacrificing accuracy. This dramatically eases the establishment and
constant extension of large annotated databases in various scenarios and
imaging setups and thus represents an important step towards practical
applicability of learning-based approaches in tissue classification
Normal Cones and Thompson Metric
The aim of this paper is to study the basic properties of the Thompson metric
in the general case of a real linear space ordered by a cone . We
show that has monotonicity properties which make it compatible with the
linear structure. We also prove several convexity properties of and some
results concerning the topology of , including a brief study of the
-convergence of monotone sequences. It is shown most of the results are
true without any assumption of an Archimedean-type property for . One
considers various completeness properties and one studies the relations between
them. Since is defined in the context of a generic ordered linear space,
with no need of an underlying topological structure, one expects to express its
completeness in terms of properties of the ordering, with respect to the linear
structure. This is done in this paper and, to the best of our knowledge, this
has not been done yet. The Thompson metric and order-unit (semi)norms
are strongly related and share important properties, as both are
defined in terms of the ordered linear structure. Although and
are only topological (and not metrical) equivalent on , we
prove that the completeness is a common feature. One proves the completeness of
the Thompson metric on a sequentially complete normal cone in a locally convex
space. At the end of the paper, it is shown that, in the case of a Banach
space, the normality of the cone is also necessary for the completeness of the
Thompson metric.Comment: 36 page
Twisted convolution and Moyal star product of generalized functions
We consider nuclear function spaces on which the Weyl-Heisenberg group acts
continuously and study the basic properties of the twisted convolution product
of the functions with the dual space elements. The final theorem characterizes
the corresponding algebra of convolution multipliers and shows that it contains
all sufficiently rapidly decreasing functionals in the dual space.
Consequently, we obtain a general description of the Moyal multiplier algebra
of the Fourier-transformed space. The results extend the Weyl symbol calculus
beyond the traditional framework of tempered distributions.Comment: LaTeX, 16 pages, no figure
Weighted composition operators on Korenblum type spaces of analytic functions
[EN] We investigate the continuity, compactness and invertibility of weighted composition operators W-psi,W-phi: f -> psi(f circle phi) when they act on the classical Korenblum space A(-infinity) and other related Frechet or (LB)-spaces of analytic functions on the open unit disc which are defined as intersections or unions of weighted Banach spaces with sup-norms. Some results about the spectrum of these operators are presented in case the self-map phi has a fixed point in the unit disc. A precise description of the spectrum is obtained in this case when the operator acts on the Korenblum space.This research was partially supported by the research project MTM2016-76647-P and the grant BES-2017-081200.Gomez-Orts, E. (2020). Weighted composition operators on Korenblum type spaces of analytic functions. Revista de la Real Academia de Ciencias Exactas FĂsicas y Naturales Serie A MatemĂĄticas. 114(4):1-15. https://doi.org/10.1007/s13398-020-00924-1S1151144Abramovich, Y.A., Aliprantis, C.D.: An invitation to operator theory. Graduate Studies in Mathematics. Amer. Math. Soc., 50 (2002)Albanese, A.A., Bonet, J., Ricker, W.J.: The CesĂ ro operator in the FrĂ©chet spaces and . Glasgow Math. J. 59, 273â287 (2017)Albanese, A.A., Bonet, J., Ricker, W.J.: The CesĂ ro operator on Korenblum type spaces of analytic functions. Collect. Math. 69(2), 263â281 (2018)Albanese, A.A., Bonet, J., Ricker, W.J.: Operators on the FrĂ©chet sequence spaces . Rev. R. Acad. Cienc. Exactas FĂs. Nat. Ser. A Mat. RACSAM 113(2), 1533â1556 (2019)Albanese, A.A., Bonet, J., Ricker, W.J.: Linear operators on the (LB)-sequence spaces . Descriptive topology and functional analysis. II, 43â67, Springer Proc. Math. Stat., 286, Springer, Cham (2019)Arendt, W., Chalendar, I., Kumar, M., Srivastava, S.: Powers of composition operators: asymptotic behaviour on Bergman, Dirichlet and Bloch spaces. J. Austral. Math. Soc. 1â32. https://doi.org/10.1017/S1446788719000235Aron, R., Lindström, M.: Spectra of weighted composition operators on weighted Banach spaces of analytic funcions. Israel J. Math. 141, 263â276 (2004)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 54(1), 70â79 (1993)Bonet, J.: A note about the spectrum of composition operators induced by a rotation. RACSAM 114, 63 (2020). https://doi.org/10.1007/s13398-020-00788-5Bonet, J., DomaĆski, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 64(1), 101â118 (1998)Bourdon, P.S.: Essential angular derivatives and maximum growth of Königs eigenfunctions. J. Func. Anal. 160, 561â580 (1998)Bourdon, P.S.: Invertible weighted composition operators. Proc. Am. Math. Soc. 142(1), 289â299 (2014)Carleson, L., Gamelin, T.: Complex Dynamics. Springer, Berlin (1991)Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton, FL (1995)Contreras, M., HernĂĄndez-DĂaz, A.G.: Weighted composition operators in weighted Banach spacs of analytic functions. J. Austral. Math. Soc., Ser. A 69, 41â60 (2000)Eklund, T., Galindo, P., Lindström, M.: Königs eigenfunction for composition operators on Bloch and spaces. J. Math. Anal. Appl. 445, 1300â1309 (2017)Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Grad. Texts in Math. 199. Springer, New York (2000)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Kamowitz, H.: Compact operators of the form . Pac. J. Math. 80(1) (1979)Korenblum, B.: An extension of the Nevanlinna theory. Acta Math. 135, 187â219 (1975)Köthe, G.: Topological Vector Spaces II. Springer, New York Inc (1979)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomophic functions. Stud. Math. 75, 19â45 (2006)Meise, R., Vogt, D.: Introduction to functional analysis. Oxford Grad. Texts in Math. 2, New York, (1997)Montes-RodrĂguez, A.: Weighted composition operators on weighted Banach spaces of analytic functions. J. Lond. Math. Soc. 61(3), 872â884 (2000)QueffĂ©lec, H., QueffĂ©lec, M.: Diophantine Approximation and Dirichlet series. Hindustain Book Agency, New Delhi (2013)Shapiro, J.H.: Composition Operators and Classical Function Theory. Springer, New York (1993)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Amer. Math. Soc. 162, 287â302 (1971)Zhu, K.: Operator Theory on Function Spaces, Math. Surveys and Monographs, Amer. Math. Soc. 138 (2007
Duals of variable exponent Hörmander spaces () and some applications
In this paper we characterize the dual \bigl(\B^c_{p(\cdot)} (\Omega)
\bigr)' of the variable exponent H\"or\-man\-der space \B^c_{p(\cdot)}
(\Omega) when the exponent satisfies the conditions , the Hardy-Littlewood maximal operator is
bounded on for some and is
an open set in . It is shown that the dual
\bigl(\B^c_{p(\cdot)} (\Omega) \bigr)' is isomorphic to the
H\"ormander space \B^{\mathrm{loc}}_\infty (\Omega) (this is the
counterpart of the isomorphism \bigl(\B^c_{p(\cdot)} (\Omega) \bigr)'
\simeq \B^{\mathrm{loc}}_{\widetilde{p'(\cdot)}} (\Omega), , recently proved by the authors) and hence the
representation theorem
\bigl( \B^c_{p(\cdot)} (\Omega) \bigr)' \simeq
l^{\N}_\infty is obtained. Our proof
relies heavily on the properties of
the Banach envelopes of the steps of \B^c_{p(\cdot)} (\Omega) and on the
extrapolation theorems in the variable Lebesgue spaces of entire
analytic functions obtained in a precedent paper. Other results for
, , are also given (e.g. \B^c_p
(\Omega) does not contain any infinite-dimensional -Banach
subspace with or the quasi-Banach space \B_p \cap
\E'(Q) contains a copy of when is a cube in ).
Finally, a question on complex interpolation (in the sense of Kalton)
of variable exponent H\"ormander spaces is proposed.J. Motos is partially supported by grant MTM2011-23164 from the Spanish Ministry of Science and Innovation. The authors wish to thank the referees for the careful reading of the manuscript and for many helpful suggestions and remarks that improved the exposition. In particular, the remark immediately following Theorem 2.1 and the Question 2 were motivated by the comments of one of them.Motos Izquierdo, J.; Planells Gilabert, MJ.; Talavera Usano, CF. (2015). Duals of variable exponent Hörmander spaces () and some applications. Revista- Real Academia de Ciencias Exactas Fisicas Y Naturales Serie a Matematicas. 109(2):657-668. https://doi.org/10.1007/s13398-014-0209-zS6576681092Aboulaich, R., Meskine, D., Souissi, A.: New diffussion models in image processing. Comput. Math. Appl. 56(4), 874â882 (2008)Acerbi, E., Mingione, G.: Regularity results for stationary electro-rheological fluids. Arch. Ration. Mech. Anal. 164(3), 213â259 (2002)Bastero, J.: l q -subspaces of stable p -Banach spaces, 0 < p †1 . Arch. Math. (Basel) 40, 538â544 (1983)Boas, R.P.: Entire functions. Academic Press, London (1954)Boza, S.: Espacios de Hardy discretos y acotaciĂłn de operadores. Dissertation, Universitat de Barcelona (1998)Cruz-Uribe, D., Fiorenza, A.: Variable Lebesgue spaces, foundations and harmonic analysis. BirkhĂ€user, Basel (2013)Cruz-Uribe, D.: SFO, A. Fiorenza, J. M. Martell, C. PĂ©rez: The boundedness of classical operators on variable L p spaces. Ann. Acad. Sci. Fenn. Math. 31, 239â264 (2006)Diening, L., Harjulehto, P., HĂ€stö, P., RĆŻĆŸiÄka, M.: Lebesgue and sobolev spaces with variable exponents. lecture notes in mathematics, vol. 2007. Springer, Berlin, Heidelberg (2011)Hörmander, L.: The analysis of linear partial operators II, Grundlehren 257. Springer, Berlin, Heidelberg (1983)Hörmander, L.: The analysis of linear partial operators I, Grundlehren 256. Springer, Berlin, Heidelberg (1983)Kalton, N.J., Peck, N.T., Roberts, J.W.: An F -space sampler, London Mathematical Society Lecture Notes, vol. 89. Cambridge University Press, Cambridge (1985)Kalton, N.J.: Banach envelopes of non-locally convex spaces. Canad. J. Math. 38(1), 65â86 (1986)Kalton, N.J., Mitrea, M.: Stability results on interpolation scales of quasi-Banach spaces and applications. Trans. Am. Math. Soc. 350(10), 3903â3922 (1998)Kalton, N.J.: Quasi-Banach spaces, Handbook of the Geometry of Banach Spaces, vol. 2. In: Johnson, W.B., Lindenstrauss, J. (eds.), pp. 1099â1130. Elsevier, Amsterdam (2003)Köthe, G.: Topological vector spaces I. Springer, Berlin, Heidelberg (1969)Motos, J., Planells, M.J., Talavera, C.F.: On variable exponent Lebesgue spaces of entire analytic functions. J. Math. Anal. Appl. 388, 775â787 (2012)Motos, J., Planells, M.J., Talavera, C.F.: A note on variable exponent Hörmander spaces. Mediterr. J. Math. 10, 1419â1434 (2013)Stiles, W.J.: Some properties of l p , 0 < p < 1 . Studia Math. 42, 109â119 (1972)Triebel, H.: Theory of function spaces. BirkhĂ€user, Basel (1983)Vogt, D.: Sequence space representations of spaces of test functions and distributions. In: Zapata, G.I. (ed.) Functional analysis, holomorphy and approximation theory, Lecture Notes in Pure and Applied Mathematics, vol. 83, pp. 405â443 (1983
Properties of field functionals and characterization of local functionals
Functionals (i.e. functions of functions) are widely used in quantum field
theory and solid-state physics. In this paper, functionals are given a rigorous
mathematical framework and their main properties are described. The choice of
the proper space of test functions (smooth functions) and of the relevant
concept of differential (Bastiani differential) are discussed.
The relation between the multiple derivatives of a functional and the
corresponding distributions is described in detail. It is proved that, in a
neighborhood of every test function, the support of a smooth functional is
uniformly compactly supported and the order of the corresponding distribution
is uniformly bounded. Relying on a recent work by Yoann Dabrowski, several
spaces of functionals are furnished with a complete and nuclear topology. In
view of physical applications, it is shown that most formal manipulations can
be given a rigorous meaning.
A new concept of local functionals is proposed and two characterizations of
them are given: the first one uses the additivity (or Hammerstein) property,
the second one is a variant of Peetre's theorem. Finally, the first step of a
cohomological approach to quantum field theory is carried out by proving a
global Poincar\'e lemma and defining multi-vector fields and graded functionals
within our framework.Comment: 32 pages, no figur
New Protocetid Whale from the Middle Eocene of Pakistan: Birth on Land, Precocial Development, and Sexual Dimorphism
BACKGROUND: Protocetidae are middle Eocene (49-37 Ma) archaeocete predators ancestral to later whales. They are found in marine sedimentary rocks, but retain four legs and were not yet fully aquatic. Protocetids have been interpreted as amphibious, feeding in the sea but returning to land to rest. METHODOLOGY/PRINCIPAL FINDINGS: Two adult skeletons of a new 2.6 meter long protocetid, Maiacetus inuus, are described from the early middle Eocene Habib Rahi Formation of Pakistan. M. inuus differs from contemporary archaic whales in having a fused mandibular symphysis, distinctive astragalus bones in the ankle, and a less hind-limb dominated postcranial skeleton. One adult skeleton is female and bears the skull and partial skeleton of a single large near-term fetus. The fetal skeleton is positioned for head-first delivery, which typifies land mammals but not extant whales, evidence that birth took place on land. The fetal skeleton has permanent first molars well mineralized, which indicates precocial development at birth. Precocial development, with attendant size and mobility, were as critical for survival of a neonate at the land-sea interface in the Eocene as they are today. The second adult skeleton is the most complete known for a protocetid. The vertebral column, preserved in articulation, has 7 cervicals, 13 thoracics, 6 lumbars, 4 sacrals, and 21 caudals. All four limbs are preserved with hands and feet. This adult is 12% larger in linear dimensions than the female skeleton, on average, has canine teeth that are 20% larger, and is interpreted as male. Moderate sexual dimorphism indicates limited male-male competition during breeding, which in turn suggests little aggregation of food or shelter in the environment inhabited by protocetids. CONCLUSIONS/SIGNIFICANCE: Discovery of a near-term fetus positioned for head-first delivery provides important evidence that early protocetid whales gave birth on land. This is consistent with skeletal morphology enabling Maiacetus to support its weight on land and corroborates previous ideas that protocetids were amphibious. Specimens this complete are virtual 'Rosetta stones' providing insight into functional capabilities and life history of extinct animals that cannot be gained any other way
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