40 research outputs found
Application of dielectric resonators to surface impedance measurements of microwave susceptors
[EN] This paper describes the application of dielectric resonators (DR) to the measurements of
surface impedance of microwave susceptors. We demonstrate that the single-post (SiPDR)
configuration is applicable to plain susceptors before use, while the split-post (SPDR)
configuration - to crazed susceptors after use. Attention is given to the full characterisation
of active packaging, that is, the influence of paper support on the overall electric losses is
also investigated. The measurements can be preformed with various form-factor VNAs,
including benchtop VNAs and hand-held FieldFox, though the most economical setup is
constructed with a dedicated computer-controlled microwave signal oscillator system
available under the name of Q-Meter. Finally, an extension of dielectric resonator
measurements to surface imaging is presented, achieved by incorporating the resonator in a
2D automatic scanner.This project has received funding from the European Unionâs Horizon 2020 research and
innovation programme (H2020-NMBP-07-2017) under grant agreement MMAMA
No. 761036.Celuch, M.; Rudnicki, J.; Krupka, J.; Gwarek, W. (2019). Application of dielectric resonators to surface impedance measurements of microwave susceptors. En AMPERE 2019. 17th International Conference on Microwave and High Frequency Heating. Editorial Universitat PolitĂšcnica de ValĂšncia. 500-505. https://doi.org/10.4995/AMPERE2019.2019.9953OCS50050
Entropic trade-off relations for quantum operations
Spectral properties of an arbitrary matrix can be characterized by the
entropy of its rescaled singular values. Any quantum operation can be described
by the associated dynamical matrix or by the corresponding superoperator. The
entropy of the dynamical matrix describes the degree of decoherence introduced
by the map, while the entropy of the superoperator characterizes the a priori
knowledge of the receiver of the outcome of a quantum channel Phi. We prove
that for any map acting on a N--dimensional quantum system the sum of both
entropies is not smaller than ln N. For any bistochastic map this lower bound
reads 2 ln N. We investigate also the corresponding R\'enyi entropies,
providing an upper bound for their sum and analyze entanglement of the
bi-partite quantum state associated with the channel.Comment: 10 pages, 4 figure
Control of active B and L cathepsins in tissues of colorectal cancer using cystatins isolated from chicken egg proteins: in vitro studies
The activity of cysteine peptidases (cathepsins B and L) was estimated in homogenates of tissues sampled
during surgery from 60 patients operated due to colorectal tumors. The results were compared to those obtained
using tissues in which histopathology disclosed no tumorous cells, obtained from 20 patients of the same group,
treated as a control. Activity of the enzymes was inhibited using cysteine peptidase inhibitors isolated from chicken
egg proteins. Application of the inhibitors was found to inhibit activity of the enzymes which play a key role in
tumor development. It is suggested that in future the inhibitors may provide a component of new generation drugs
in the so-called inhibitor therapy. (Folia Histochemica et Cytobiologica 2011; Vol. 49, No. 4, pp. 670–676
Pascalâs Theorem in Real Projective Plane
SummaryIn this article we check, with the Mizar system [2], Pascalâs theorem in the real projective plane (in projective geometry Pascalâs theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappusâ theorem is a special case of a degenerate conic of two lines. For proving Pascalâs theorem, we use the techniques developed in the section âProjective Proofs of Pappusâ Theoremâ in the chapter âPappusâ Theorem: Nine proofs and three variationsâ [11]. We also follow some ideas from Harrisonâs work. With HOL Light, he has the proof of Pascalâs theorem2. For a lemma, we use PROVER93 and OTT2MIZ by Josef Urban4 [12, 6, 7]. We note, that we donât use Skolem/Herbrand functions (see âSkolemizationâ in [1]).Rue de la Brasserie 5, 7100 La LouviĂšre, BelgiumJesse Alama. Escape to Mizar for ATPs. arXiv preprint arXiv:1204.6615, 2012.Grzegorz Bancerek, CzesĆaw ByliĆski, Adam Grabowski, Artur KorniĆowicz, Roman Matuszewski, Adam Naumowicz, Karol PÄ
k, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261â279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi: 10.1007/978-3-319-20615-817.Roland Coghetto. Homography in â â2. Formalized Mathematics, 24(4):239â251, 2016. doi: 10.1515/forma-2016-0020.Roland Coghetto. Group of homography in real projective plane. Formalized Mathematics, 25(1):55â62, 2017. doi: 10.1515/forma-2017-0005.Agata DarmochwaĆ. The Euclidean space. Formalized Mathematics, 2(4):599â603, 1991.Adam Grabowski. Solving two problems in general topology via types. In Types for Proofs and Programs, International Workshop, TYPES 2004, Jouy-en-Josas, France, December 15-18, 2004, Revised Selected Papers, pages 138â153, 2004. doi: 10.1007/116179909.Adam Grabowski. Mechanizing complemented lattices within Mizar system. Journal of Automated Reasoning, 55:211â221, 2015. doi: 10.1007/s10817-015-9333-5.Kanchun, Hiroshi Yamazaki, and Yatsuka Nakamura. Cross products and tripple vector products in 3-dimensional Euclidean space. Formalized Mathematics, 11(4):381â383, 2003.Wojciech LeoĆczuk and Krzysztof PraĆŒmowski. A construction of analytical projective space. Formalized Mathematics, 1(4):761â766, 1990.Wojciech LeoĆczuk and Krzysztof PraĆŒmowski. Projective spaces â part I. Formalized Mathematics, 1(4):767â776, 1990.JĂŒrgen Richter-Gebert. Papposâs Theorem: Nine Proofs and Three Variations, pages 3â31. Springer Berlin Heidelberg, 2011. ISBN 978-3-642-17286-1. doi: 10.1007/978-3-642-17286-11.Piotr Rudnicki and Josef Urban. Escape to ATP for Mizar. In First International Workshop on Proof eXchange for Theorem Proving-PxTP 2011, 2011.Wojciech Skaba. The collinearity structure. Formalized Mathematics, 1(4):657â659, 1990.Nobuyuki Tamura and Yatsuka Nakamura. Determinant and inverse of matrices of real elements. Formalized Mathematics, 15(3):127â136, 2007. doi: 10.2478/v10037-007-0014-7.25210711
Fixpoint Theorem for Continuous Functions on Chain-Complete Posets
This text includes the definition of chain-complete poset, fix-point theorem on it, and the definition of the function space of continuous functions on chain-complete posets [10].Ishida Kazuhisa - Neyagawa-shi, Osaka, JapanShidama Yasunari - Shinshu University, Nagano, JapanGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. Bounds in posets and relational substructures. Formalized Mathematics, 6(1):81-91, 1997.Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996.CzesĆaw ByliĆski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.CzesĆaw ByliĆski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.CzesĆaw ByliĆski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Adam Grabowski. On the category of posets. Formalized Mathematics, 5(4):501-505, 1996. http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=000258624500003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=b7bc2757938ac7a7a821505f8243d9f3Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. Formalized Mathematics, 1(2):387-393, 1990.Glynn Winskel. The Formal Semantics of Programming Languages. The MIT Press, 1993.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 1990.Mariusz Ć»ynel and CzesĆaw ByliĆski. Properties of relational structures, posets, lattices and maps. Formalized Mathematics, 6(1):123-130, 1997
About Quotient Orders and Ordering Sequences
SummaryIn preparation for the formalization in Mizar [4] of lotteries as given in [14], this article closes some gaps in the Mizar Mathematical Library (MML) regarding relational structures. The quotient order is introduced by the equivalence relation identifying two elements x, y of a preorder as equivalent if x â©œ y and y â©œ x. This concept is known (see e.g. chapter 5 of [19]) and was first introduced into the MML in [13] and that work is incorporated here. Furthermore given a set A, partition D of A and a finite-support function f : A â â, a function ÎŁf : D â â, ÎŁf (X)= âxâX f(x) can be defined as some kind of natural ârestrictionâ from f to D. The first main result of this article can then be formulated as: âxâAf(x)=âXâDÎŁf(X)(=âXâDâxâXf(x)) After that (weakly) ascending/descending finite sequences (based on [3]) are introduced, in analogous notation to their infinite counterparts introduced in [18] and [13].The second main result is that any finite subset of any transitive connected relational structure can be sorted as a ascending or descending finite sequence, thus generalizing the results from [16], where finite sequence of real numbers were sorted.The third main result of the article is that any weakly ascending/weakly descending finite sequence on elements of a preorder induces a weakly ascending/weakly descending finite sequence on the projection of these elements into the quotient order. Furthermore, weakly ascending finite sequences can be interpreted as directed walks in a directed graph, when the set of edges is described by ordered pairs of vertices, which is quite common (see e.g. [10]).Additionally, some auxiliary theorems are provided, e.g. two schemes to find the smallest or the largest element in a finite subset of a connected transitive relational structure with a given property and a lemma I found rather useful: Given two finite one-to-one sequences s, t on a set X, such that rng t â rng s, and a function f : X â â such that f is zero for every x â rng s \ rng t, we have â f o s = â f o t.Johannes Gutenberg University, Mainz, GermanyGrzegorz Bancerek. Tarskiâs classes and ranks. Formalized Mathematics, 1(3):563â567, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41â46, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107â114, 1990.Grzegorz Bancerek, CzesĆaw ByliĆski, Adam Grabowski, Artur KorniĆowicz, Roman Matuszewski, Adam Naumowicz, Karol PÄ
k, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261â279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi: 10.1007/978-3-319-20615-817.CzesĆaw ByliĆski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529â536, 1990.CzesĆaw ByliĆski. Functions and their basic properties. Formalized Mathematics, 1(1): 55â65, 1990.CzesĆaw ByliĆski. Functions from a set to a set. Formalized Mathematics, 1(1):153â164, 1990.CzesĆaw ByliĆski. Partial functions. Formalized Mathematics, 1(2):357â367, 1990.CzesĆaw ByliĆski. Some basic properties of sets. Formalized Mathematics, 1(1):47â53, 1990.Thomas H. Cormen, Charles E. Leiserson, and Ronald L. Rivest. Introduction to algorithms. MIT Press, 3. ed. edition, 2009. ISBN 0-262-53305-7, 978-0-262-53305-8, 978-0-262-03384-8. http://scans.hebis.de/HEBCGI/show.pl?21502893_toc.pdf.Agata DarmochwaĆ. Finite sets. Formalized Mathematics, 1(1):165â167, 1990.JarosĆaw Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703â709, 1990.Gilbert Lee and Piotr Rudnicki. Dicksonâs lemma. Formalized Mathematics, 10(1):29â37, 2002.Michael Maschler, Eilon Solan, and Shmuel Zamir. Game theory. Cambridge Univ. Press, 2013. ISBN 978-1-107-00548-8. doi: 10.1017/CBO9780511794216.Takashi Mitsuishi, Katsumi Wasaki, and Yasunari Shidama. Property of complex functions. Formalized Mathematics, 9(1):179â184, 2001.Yatsuka Nakamura. Sorting operators for finite sequences. Formalized Mathematics, 12 (1):1â4, 2004.Konrad Raczkowski and PaweĆ Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441â444, 1990.Piotr Rudnicki and Andrzej Trybulec. On same equivalents of well-foundedness. Formalized Mathematics, 6(3):339â343, 1997.Bernd S. W. Schröder. Ordered Sets: An Introduction. BirkhĂ€user Boston, 2003. ISBN 978-1-4612-6591-7. https://books.google.de/books?id=hg8GCAAAQBAJ.Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569â573, 1990.Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575â579, 1990.Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski â Zorn lemma. Formalized Mathematics, 1(2):387â393, 1990.25212113
The Perfect Number Theorem and Wilson's Theorem
This article formalizes proofs of some elementary theorems of number theory (see [1, 26]): Wilson's theorem (that n is prime iff n > 1 and (n - 1)! â
-1 (mod n)), that all primes (1 mod 4) equal the sum of two squares, and two basic theorems of Euclid and Euler about perfect numbers. The article also formally defines Euler's sum of divisors function Ί, proves that Ί is multiplicative and that ÎŁ k|n Ί(k) = n.Casella Postale 49, 54038 Montignoso, ItalyM. Aigner and G. M. Ziegler. Proofs from THE BOOK. Springer-Verlag, Berlin Heidelberg New York, 2004.Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.JĂłzef BiaĆas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.CzesĆaw ByliĆski. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990.CzesĆaw ByliĆski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.CzesĆaw ByliĆski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.CzesĆaw ByliĆski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.CzesĆaw ByliĆski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.CzesĆaw ByliĆski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.CzesĆaw ByliĆski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.CzesĆaw ByliĆski. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.Agata DarmochwaĆ. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Yoshinori Fujisawa and Yasushi Fuwa. The Euler's function. Formalized Mathematics, 6(4):549-551, 1997.Yoshinori Fujisawa, Yasushi Fuwa, and Hidetaka Shimizu. Public-key cryptography and Pepin's test for the primality of Fermat numbers. Formalized Mathematics, 7(2):317-321, 1998.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Krzysztof Hryniewiecki. Recursive definitions. Formalized Mathematics, 1(2):321-328, 1990.Magdalena Jastrzebska and Adam Grabowski. On the properties of the Möbius function. Formalized Mathematics, 14(1):29-36, 2006, doi:10.2478/v10037-006-0005-0.Artur KorniĆowicz and Piotr Rudnicki. Fundamental Theorem of Arithmetic. Formalized Mathematics, 12(2):179-186, 2004.JarosĆaw Kotowicz and Yuji Sakai. Properties of partial functions from a domain to the set of real numbers. Formalized Mathematics, 3(2):279-288, 1992.RafaĆ Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.RafaĆ Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes. Formalized Mathematics, 1(5):829-832, 1990.W. J. LeVeque. Fundamentals of Number Theory. Dover Publication, New York, 1996.Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.Piotr Rudnicki. Little Bezout theorem (factor theorem). Formalized Mathematics, 12(1):49-58, 2004.Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.Piotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Formalized Mathematics, 9(1):95-110, 2001.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.Andrzej Trybulec and CzesĆaw ByliĆski. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.MichaĆ J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Hiroshi Yamazaki, Yasunari Shidama, and Yatsuka Nakamura. Bessel's inequality. Formalized Mathematics, 11(2):169-173, 2003
Prediction of overall survival for patients with metastatic castration-resistant prostate cancer : development of a prognostic model through a crowdsourced challenge with open clinical trial data
Background Improvements to prognostic models in metastatic castration-resistant prostate cancer have the potential to augment clinical trial design and guide treatment strategies. In partnership with Project Data Sphere, a not-for-profit initiative allowing data from cancer clinical trials to be shared broadly with researchers, we designed an open-data, crowdsourced, DREAM (Dialogue for Reverse Engineering Assessments and Methods) challenge to not only identify a better prognostic model for prediction of survival in patients with metastatic castration-resistant prostate cancer but also engage a community of international data scientists to study this disease. Methods Data from the comparator arms of four phase 3 clinical trials in first-line metastatic castration-resistant prostate cancer were obtained from Project Data Sphere, comprising 476 patients treated with docetaxel and prednisone from the ASCENT2 trial, 526 patients treated with docetaxel, prednisone, and placebo in the MAINSAIL trial, 598 patients treated with docetaxel, prednisone or prednisolone, and placebo in the VENICE trial, and 470 patients treated with docetaxel and placebo in the ENTHUSE 33 trial. Datasets consisting of more than 150 clinical variables were curated centrally, including demographics, laboratory values, medical history, lesion sites, and previous treatments. Data from ASCENT2, MAINSAIL, and VENICE were released publicly to be used as training data to predict the outcome of interest-namely, overall survival. Clinical data were also released for ENTHUSE 33, but data for outcome variables (overall survival and event status) were hidden from the challenge participants so that ENTHUSE 33 could be used for independent validation. Methods were evaluated using the integrated time-dependent area under the curve (iAUC). The reference model, based on eight clinical variables and a penalised Cox proportional-hazards model, was used to compare method performance. Further validation was done using data from a fifth trial-ENTHUSE M1-in which 266 patients with metastatic castration-resistant prostate cancer were treated with placebo alone. Findings 50 independent methods were developed to predict overall survival and were evaluated through the DREAM challenge. The top performer was based on an ensemble of penalised Cox regression models (ePCR), which uniquely identified predictive interaction effects with immune biomarkers and markers of hepatic and renal function. Overall, ePCR outperformed all other methods (iAUC 0.791; Bayes factor >5) and surpassed the reference model (iAUC 0.743; Bayes factor >20). Both the ePCR model and reference models stratified patients in the ENTHUSE 33 trial into high-risk and low-risk groups with significantly different overall survival (ePCR: hazard ratio 3.32, 95% CI 2.39-4.62, p Interpretation Novel prognostic factors were delineated, and the assessment of 50 methods developed by independent international teams establishes a benchmark for development of methods in the future. The results of this effort show that data-sharing, when combined with a crowdsourced challenge, is a robust and powerful framework to develop new prognostic models in advanced prostate cancer.Peer reviewe