Bai, Tongdong; Stachel, John
In his response to EPR, Bohr introduces several ideal experimental arrangements that often are not understood correctly, and his discussion about them is given a positivist reading. Our analysis demonstrates the difference between such areading and Bohr's actual position, and also clarifies the meaning of several of Bohr's key physical and philosophical ideas: * The role of the quantum of action in the distinction between classical and quantum systems; * The criterion of measurability for theoretically defined concepts; * The freedom in placement of the "cut" between measuring instrument and measured system; * The non-visualizability of the quantum formalism; and Bohr's concepts of phenomenon and complementarity.
The Bohr Correspondence Principle
Indian Academy of Sciences (India)
IAS Admin
corresponding to the two values of the electron spin), if it is known to have the mini- mum energy. But in Bohr's theory, the orientation of the plane of orbit is arbitrary, and hence the number of distinct states is infinite. In fact,“Bohr theory of hydrogen ...
Willden, Jeff
2001-01-01
"Bohr's Atomic Model" is a small interactive multimedia program that introduces the viewer to a simplified model of the atom. This interactive simulation lets students build an atom using an atomic construction set. The underlying design methodology for "Bohr's Atomic Model" is model-centered instruction, which means the central model of the…
Indian Academy of Sciences (India)
IAS Admin
We present an account of the work of Niels Bohr and Paul Dirac, their interactions and personal- ities. 1. Introduction. In this essay I would like to convey to my readers some- thing about the personalities and work of Niels Bohr and Paul Dirac, juxtaposed against one another. Let me hope that the portraits I will paint of these ...
Reading Bohr physics and philosophy
Plotnitsky, Arkady
2006-01-01
Reading Bohr: Physics and Philosophy offers a new perspective on Niels Bohr's interpretation of quantum mechanics as complementarity, and on the relationships between physics and philosophy in Bohr's work, which has had momentous significance for our understanding of quantum theory and of the nature of knowledge in general. Philosophically, the book reassesses Bohr's place in the Western philosophical tradition, from Kant and Hegel on. Physically, it reconsiders the main issues at stake in the Bohr-Einstein confrontation and in the ongoing debates concerning quantum physics. It also devotes greater attention than in most commentaries on Bohr to the key developments and transformations of his thinking concerning complementarity. Most significant among them were those that occurred, first, under the impact of Bohr's exchanges with Einstein and, second, under the impact of developments in quantum theory itself, both quantum mechanics and quantum field theory. The importance of quantum field theory for Bohr's thi...
International Nuclear Information System (INIS)
Latimer, C.J.
1983-01-01
It is shown that the old quantum theory in its simplest (Bohr) form can still make an important contribution to understanding atomic phenomena in the fields of hydrogenic spectra, non-hydrogenic spectra, and atoms in strong electric or magnetic fields. (U.K.)
Indian Academy of Sciences (India)
IAS Admin
of Bohr's birth, while Dirac passed away in October of the previous year. There was a gap of almost a gener- ation between them. ... the one hand, in order to produce in this model a length scale of the order of the atomic size, and also to en- sure stability of the electron orbits, it was essential to bring in Planck's constant.
The Bohr Correspondence Principle
Indian Academy of Sciences (India)
IAS Admin
quite straightforward, and easily understood even with. XII grade algebra. To recall, Bohr assumed that an elec- tron describes a circular orbit about the nucleus, and the angular momentum is quantized to be an integer multiple of h. Of course, in general, the orbit can be elliptical, but let us restrict ourselves to circular orbits.
Indian Academy of Sciences (India)
IAS Admin
This difficulty reinforced a suspicion developed earlier in his studies of electrons in metals, where he showed .... Bohr still sent his papers for Rutherford to communicate to the journals, and often to deal with, .... of those twenty years in which you and your family have shown us so much friendship, my wife and I send you and ...
International Nuclear Information System (INIS)
1985-01-01
This report is organized around the contribution of A. Pais, 'Niels Bohr and the development of physics', presented at CERN on the occasion of a special colloquium in the honour of Niels Bohr. It gives a broad survey of Bohr's life, the revolution in physics created by his quantum theory and his attempts to influence the peaceful development of nuclear energy. (orig.)
Bellac, Michel Le
2014-11-01
The final form of quantum physics, in the particular case of wave mechanics, was established in the years 1925-1927 by Heisenberg, Schrödinger, Born and others, but the synthesis was the work of Bohr who gave an epistemological interpretation of all the technicalities built up over those years; this interpretation will be examined briefly in Chapter 10. Although Einstein acknowledged the success of quantum mechanics in atomic, molecular and solid state physics, he disagreed deeply with Bohr's interpretation. For many years, he tried to find flaws in the formulation of quantum theory as it had been more or less accepted by a large majority of physicists, but his objections were brushed away by Bohr. However, in an article published in 1935 with Podolsky and Rosen, universally known under the acronym EPR, Einstein thought he had identified a difficulty in the by then standard interpretation. Bohr's obscure, and in part beyond the point, answer showed that Einstein had hit a sensitive target. Nevertheless, until 1964, the so-called Bohr-Einstein debate stayed uniquely on a philosophical level, and it was actually forgotten by most physicists, as the few of them aware of it thought it had no practical implication. In 1964, the Northern Irish physicist John Bell realized that the assumptions contained in the EPR article could be tested experimentally. These assumptions led to inequalities, the Bell inequalities, which were in contradiction with quantum mechanical predictions: as we shall see later on, it is extremely likely that the assumptions of the EPR article are not consistent with experiment, which, on the contrary, vindicates the predictions of quantum physics. In Section 3.2, the origin of Bell's inequalities will be explained with an intuitive example, then they will be compared with the predictions of quantum theory in Section 3.3, and finally their experimental status will be reviewed in Section 3.4. The debate between Bohr and Einstein goes much beyond a
Niels Bohr and quantum physics
International Nuclear Information System (INIS)
Migdal, A.B.
1985-01-01
The way of thinking and scientific style of Niels Bohr are discussed in connection with developments of his emotional and spiritual life. As shows the analysis of the works by N. Bohr, by his predecessors in contemporaries, he has produced an incomparable influence upon the development of quantum mechanics as a philosopher of physics. His struggle against nuclear weapons is dwelt upon
Genetics Home Reference: Bohring-Opitz syndrome
... Hopkins Medicine: Failure to Thrive KidsHealth from Nemours: Failure to Thrive MalaCards: bohring-opitz syndrome Oregon Health Sciences University: Metopic Synostosis Orphanet: Bohring-Opitz syndrome Patient Support ...
Brunori, Maurizio
2012-01-01
Before the outbreak of World War II, Jeffries Wyman postulated that the "Bohr effect" in hemoglobin demanded the oxygen linked dissociation of the imidazole of two histidines of the polypeptide. This proposal emerged from a rigorous analysis of the acid-base titration curves of oxy- and deoxy-hemoglobin, at a time when the information on the…
One Hundred Years of Bohr Model
Indian Academy of Sciences (India)
IAS Admin
In this article I shall present a brief review of the hundred-year young Bohr model of the atom. In particular, I will first introduce the Thomson and the Rutherford models of atoms, their shortcom- ings and then discuss in some detail the develop- ment of the atomic model by Niels Bohr. Fur- ther, I will mention its refinements at ...
Bohr vs. Einstein: Fortolkning af kvantemekanikken
DEFF Research Database (Denmark)
Andersen, Christian Kraglund; Wade, Andrew Christopher James
2013-01-01
Siden 1913, da Bohr fremlagde sin kvantemekaniske model for atomet, har fysikere diskuteret, hvordan kvan- temekanikken skal fortolkes. Specielt aktive i denne diskussion var Bohr og Einstein, som havde modstridende opfattelser af, hvordan kvantemekanikken skulle forstås. Kan katte være både...... levende og døde på samme tid? Kan vi teleportere partikler mellem Månen og Jorden? Disse spørgsmål, og mange flere, forsøgte Bohr og Einstein at besvare, og det vil vi ligeledes i denne artikel....
Camilleri, Kristian; Schlosshauer, Maximilian
2015-02-01
Niels Bohr's doctrine of the primacy of "classical concepts" is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr's doctrine was primarily an epistemological thesis, derived from his understanding of the functional role of experiment. A hitherto largely overlooked disagreement between Bohr and Heisenberg about the movability of the "cut" between measuring apparatus and observed quantum system supports the view that, for Bohr, such a cut did not originate in dynamical (ontological) considerations, but rather in functional (epistemological) considerations. As such, both the motivation and the target of Bohr's doctrine of classical concepts are of a fundamentally different nature than what is understood as the dynamical problem of the quantum-to-classical transition. Our analysis suggests that, contrary to claims often found in the literature, Bohr's doctrine is not, and cannot be, at odds with proposed solutions to the dynamical problem of the quantum-classical transition that were pursued by several of Bohr's followers and culminated in the development of decoherence theory.
Bohr's Philosophy of Wave–Particle Complementarity
Indian Academy of Sciences (India)
IAS Admin
We begin by noting that as early as 1914, only a year after his celebrated work on the atomic model, Bohr wrote to his friend C W Oseen, “.... the possibility for an embracing picture should not be sought in the generality of viewpoints but perhaps rather in the strictest possible limitation of viewpoints” [1]. It is indeed striking ...
One Hundred Years of Bohr Model
Indian Academy of Sciences (India)
IAS Admin
science at school and college level. In this article I shall present a brief review of the hundred-year young Bohr model of the atom. In particular, I will first introduce the Thomson and .... This model, despite being successful, had one major problem. ... This tempted several people to look for an empirical formula which would ...
Bohr's Philosophy of Wave–Particle Complementarity
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 18; Issue 10. Bohr's Philosophy of Wave–Particle Complementarity. Dipankar Home. General Article Volume 18 Issue 10 October 2013 pp 905-916. Fulltext. Click here to view fulltext PDF. Permanent link:
Bohr's Philosophy of Wave–Particle Complementarity
Indian Academy of Sciences (India)
IAS Admin
Einstein's theory fixes the magnitude of the light-quantum” [2]. At that time, in view of his reluctance to accept the light-quantum or photon hypothesis, Bohr had even contemplated a formulation of quantum theory that would be able to describe the interaction between radiation and atomic systems without requiring the.
Niels Bohr and the Atomic Structure
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 18; Issue 10. Niels Bohr and the Atomic Structure. M Durga Prasad. General Article Volume 18 Issue 10 October 2013 pp 897-904. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/018/10/0897-0904 ...
Complementarity beyond physics Niels Bohr's parallels
Bala, Arun
2017-01-01
In this study Arun Bala examines the implications that Niels Bohr’s principle of complementarity holds for fields beyond physics. Bohr, one of the founding figures of modern quantum physics, argued that the principle of complementarity he proposed for understanding atomic processes has parallels in psychology, biology, and social science, as well as in Buddhist and Taoist thought. But Bohr failed to offer any explanation for why complementarity might extend beyond physics, and his claims have been widely rejected by scientists as empty speculation. Scientific scepticism has only been reinforced by the naïve enthusiasm of postmodern relativists and New Age intuitionists, who seize upon Bohr’s ideas to justify anti-realist and mystical positions. Arun Bala offers a detailed defence of Bohr’s claim that complementarity has far-reaching implications for the biological and social sciences, as well as for comparative philosophies of science, by explaining Bohr’s parallels as responses to the omnipresence...
Address at the opening session of the Niels Bohr Symposium
International Nuclear Information System (INIS)
Mayor, F.
1998-01-01
In his address at the opening session of the Niels Bohr Symposium organized jointly by UNESCO and the Niels Bohr Institute in Copenhagen in May 1998 in order to examine the latest developments in key fields of physics, the Director General of UNESCO presented the scientific work and the spirit of Niels Bohr, emphasizing the impact of his discoveries for new openings in science and in society in general
Realization of Bohr-like circular wavepackets
Mestayer, Jeff; Wyker, B.; Dunning, F. B.; Reinhold, C.; Yoshida, S.; Burgdörfer, J.
2008-05-01
We demonstrate a protocol to create localized wavepackets in very-high n Rydberg states that travel in near-circular orbits around the nucleus. Although these wavepackets slowly dephase and eventually lose their localization, their motion can be followed for several orbital periods. These wavepackets represent the closest analog yet achieved to the original Bohr model of the atom, i.e., an electron in circular classical orbit around the nucleus. The time evolution of the momentum and position of the wavepackets is monitored using, respectively, short half-cycle pulses and sudden field steps, which are applied after a variable time delay and along different directions. The present technique is explained with the aid of CTMC simulations, and possible extension to creation of elusive ``planetary atoms'' in highly correlated stable multiply-excited states is discussed. Research supported by the NSF, the Robert A. Welch Foundation, the OBES, U.S. DoE to ORNL, and by the FWF (Austria).
Paul Ehrenfest, Niels Bohr, and Albert Einstein: Colleagues and Friends
Klein, Martin J.
2010-09-01
In May 1918 Paul Ehrenfest received a monograph from Niels Bohr in which Bohr had used Ehrenfest's adiabatic principle as an essential assumption for understanding atomic structure. Ehrenfest responded by inviting Bohr, whom he had never met, to give a talk at a meeting in Leiden in late April 1919, which Bohr accepted; he lived with Ehrenfest, his mathematician wife Tatyana, and their young family for two weeks. Albert Einstein was unable to attend this meeting, but in October 1919 he visited his old friend Ehrenfest and his family in Leiden, where Ehrenfest told him how much he had enjoyed and profited from Bohr's visit. Einstein first met Bohr when Bohr gave a lecture in Berlin at the end of April 1920, and the two immediately proclaimed unbounded admiration for each other as physicists and as human beings. Ehrenfest hoped that he and they would meet at the Third Solvay Conference in Brussels in early April 1921, but his hope was unfulfilled. Einstein, the only physicist from Germany who was invited to it in this bitter postwar atmosphere, decided instead to accompany Chaim Weizmann on a trip to the United States to help raise money for the new Hebrew University in Jerusalem. Bohr became so overworked with the planning and construction of his new Institute for Theoretical Physics in Copenhagen that he could only draft the first part of his Solvay report and ask Ehrenfest to present it, which Ehrenfest agreed to do following the presentation of his own report. After recovering his strength, Bohr invited Ehrenfest to give a lecture in Copenhagen that fall, and Ehrenfest, battling his deep-seated self-doubts, spent three weeks in Copenhagen in December 1921 accompanied by his daughter Tanya and her future husband, the two Ehrenfests staying with the Bohrs in their apartment in Bohr's new Institute for Theoretical Physics. Immediately after leaving Copenhagen, Ehrenfest wrote to Einstein, telling him once again that Bohr was a prodigious physicist, and again
Bohr Hamiltonian with different mass parameters applied to band ...
Indian Academy of Sciences (India)
, is investigated within the framework of a recently developed extended Bohr Hamiltonian model. The relative distance between spherical orbitals is taken into account by considering single-particle energies as a parameter which changes with ...
Bohr's discussion of the fourth uncertainty relation revisited
Costa de Beauregard, O.
1986-09-01
Bohr's 1930 derivation of the uncertainty relation c 2 δm δt≥h bears a close relationship to Einstein's 1913 derivation of the “gravitational redshift” via the “equivalence principle.” A rewording of Bohr's argument is presented here, not taking the last step of acceleration as “equivalent” to a uniform gravity field, thus yielding a derivation of the formula c 2 δm δt≥h, avoiding Treder's 1971 objection.
Creation and development of Bohr's theory (on the 90th anniversary of the Bohr theory of the atom)
International Nuclear Information System (INIS)
Milant'ev, Vladimir P
2004-01-01
The history of the creation and development of Bohr's atomic theory is discussed. Even now, with a consistent quantum theory available, Bohr's theory is not simply the property of history, of methodological interest only. To this day, the ideas of the theory not only provide an excellent introduction to atomic physics, but are also used successfully in treating atomic Rydberg states, exotic atoms, etc. (from the history of physics)
Reconstructing Bohr's Reply to EPR in Algebraic Quantum Theory
Ozawa, Masanao; Kitajima, Yuichiro
2012-04-01
Halvorson and Clifton have given a mathematical reconstruction of Bohr's reply to Einstein, Podolsky and Rosen (EPR), and argued that this reply is dictated by the two requirements of classicality and objectivity for the description of experimental data, by proving consistency between their objectivity requirement and a contextualized version of the EPR reality criterion which had been introduced by Howard in his earlier analysis of Bohr's reply. In the present paper, we generalize the above consistency theorem, with a rather elementary proof, to a general formulation of EPR states applicable to both non-relativistic quantum mechanics and algebraic quantum field theory; and we clarify the elements of reality in EPR states in terms of Bohr's requirements of classicality and objectivity, in a general formulation of algebraic quantum theory.
Jocular Physics: A Tribute to Bohr in Humor
Halpern, Paul
2011-04-01
Copenhagen, starting in the 1920s and 1930s and continuing after the Second World War, was not just a center for extraordinary developments in quantum and nuclear physics; it also provided a perfect stage for physicists' abundant humor. We will examine the Journal of Jocular Physics, a humorou tribute to Bohr published on the occasions of his 50th , 60th and 70th birthdays. We will discuss how the articles in the journal reflected attempts by the contributors, such as Léon Rosenfeld, Victor Weisskopf and others, to interpret and explain aspects of Bohr's philosophy, such as complementarity and the abandonment of pure Laplacian determinism.
The Bohr-Heisenberg correspondence principle viewed from phase space
DEFF Research Database (Denmark)
Dahl, Jens Peder
2002-01-01
Phase-space representations play an increasingly important role in several branches of physics. Here, we review the author's studies of the Bohr-Heisenberg correspondence principle within the Weyl-Wigner phase-space representation. The analysis leads to refined correspondence rules that can...
The coupling one quasi-particle to a Bohr core
International Nuclear Information System (INIS)
Lewenkopf, C.H.
1988-01-01
Odd nuclei are studied coupling one quasi-particle to a Bohr's core, solved by Kumar Baranger's method. Calculations are performed for energies and transition rates for the following isotopes: 133 Xe, 183 W, 99 Tc and 101 Rh. Limitations of the model are discussed. (author) [pt
Bohr--Sommerfeld Lagrangians of moduli spaces of Higgs bundles
DEFF Research Database (Denmark)
Biswas, Indranil; Gammelgaard, Niels Leth; Logares, Marina
Let $X$ be a compact connected Riemann surface of genus at least two. Let $M_H(r,d)$ denote the moduli space of semistable Higgs bundles on $X$ of rank $r$ and degree $d$. We prove that the compact complex Bohr-Sommerfeld Lagrangians of $M_H(r,d)$ are precisely the irreducible components of the n...
The many relationships between the IBM and the Bohr model
International Nuclear Information System (INIS)
Rowe, D.J.; Thiamova, G.
2005-01-01
Relationships between the IBM-1 and the Bohr collective model are explored in which the states of the IBM in its various dynamical symmetry limits are identified with subsets of Bohr model states of corresponding dynamical symmetries. The maps of interest are ones which give the contractions of the IBM in the limit of large boson number. The known map from the IBM into the Bohr model gives a contraction appropriate for the U(5) dynamical symmetry limit. A new map is given consistent with a contraction of the O(6) dynamical symmetry of the IBM. This map gives an explicit identification of IBM states in an O(6)-bar O(5) basis with states of the Wilets-Jean model and makes it possible to benefit from the different but complementary perspectives of the two models. For example, it leads to explicit expressions for the matrix elements of an IBM O(6) irrep in terms of the known matrix elements of the corresponding Wilets-Jean model. The relationship also shows how to obtain the familiar rotor plus beta- and gamma-vibrational bands of the Bohr-Mottelson model, in the IBM, by the addition to an O(6) Hamiltonian of a scalar cubic in the quadrupole moment operators of the type considered recently by Van Isacker. The establishment of close relationships between the two models enables one to benefit from the different and complementary perspectives they afford. For example, recent developments of an algebraic version of the collective model has shown that the Bohr model has an SU(1,1)xO(5) dynamical group with representations ranging from those of a spherical vibrator to a beta-vibrational soft-gamma rotor of the Wilets-Jean limit and, with the addition of an interaction, to a rotor of the standard Bohr-Mottelson type with beta- and gamma-vibrational bands. A parallel range of results can now be obtained in the IBM, albeit with some differences, within the framework of an SU(1,1)xO(5) dynamical group
Creation of non-dispersive Bohr-like wave packets
Mestayer, Jeff; Wyker, B.; Dunning, F. B.; Reinhold, C. O.; Yoshida, S.; Burgdörfer, J.
2009-05-01
We demonstrate the use of a periodic train of half-cycle pulses to create strongly-localized non-dispersive wave packets in very-high-n (n ˜ 300) Rydberg atoms that travel in near-circular orbits about the nucleus. This motion can be maintained for hundreds of orbital periods mimicking the original Bohr model of the hydrogen atom which envisioned an electron in circular classical orbit about the nucleus. The conditions for formation of non-dispersive Bohr-like wave packets are discussed with the aid of Classical Trajectory Monte Carlo (CTMC) simulations and demonstrated through experiment. Research supported by the NSF, the Robert A. Welch Foundation, the OBES, U.S. DoE to ORNL, and by the FWF (Austria).
Popper and Bohr on Realism in Quantum Mechanics
Directory of Open Access Journals (Sweden)
Don Howard
2012-11-01
Full Text Available Popper's program in the foundations of quantum mechanics defending objectivity and realism developed out of a profound dissatisfaction with the point of view associated with Bohr, which is usually designated the Copenhagen interpretation. Here I will argue that while Popper's aim is a noble one, his program does not succeed on two counts: he does not succeed in showing that Bohr's philosophy must be rejected as a variety of subjectivism, and his alternative interpretation of indeterminacy rests on a highly questionable assumption according to which simultaneously precise conjugate parameters are possible. Nevertheless I like Popper's propensity interpretation of probability and think that the propensity idea deserves further research. Quanta 2012; 1: 33–57.
Creation of nondispersive Bohr-like wave packets
Mestayer, J. J.; Wyker, B.; Dunning, F. B.; Yoshida, S.; Reinhold, C. O.; Burgdörfer, J.
2009-03-01
We demonstrate the use of a periodic train of half-cycle pulses to maintain strongly-localized wave packets in very-high- n (ñ300) Rydberg atoms that travel in near-circular orbits about the nucleus. This motion can be followed for hundreds of orbital periods and mimics the original Bohr model of the hydrogen atom which envisioned an electron in circular classical orbit about the nucleus.
Niels Bohr. Physicist and philospher of the atomic era
International Nuclear Information System (INIS)
Fischer, Ernst Peter
2012-01-01
The physicist and Nobel-prize carrier Niels Bohr (1885-1962) changed by his research our view to the world. By his atomic model for the first time the stability of matter could be explained, but simultaneously the atomic physics and nuclear technique based on this made our world so dangerous as never before. In an impressive portrait Ernst Peter Fischer describes the life and action of this fascinating man, his great physical finding, as well as his political engagement.
Niels Bohr and the philosophy of physics twenty-first century perspectives
Folse, Henry
2017-01-01
Niels Bohr and Philosophy of Physics: Twenty-First Century Perspectives examines the philosophical views, influences and legacy of the Nobel Prize physicist and philosophical spokesman of the quantum revolution, Niels Bohr. The sixteen contributions in this collection by some of the best contemporary philosophers and physicists writing on Bohr's philosophy today all carefully distinguish his subtle and unique interpretation of quantum mechanics from views often imputed to him under the banner of the “Copenhagen Interpretation.” With respect to philosophical influences on Bohr's outlook, the contributors analyse prominent similarities between his viewpoint and Kantian ways of thinking, the views of the Danish philosopher Harald Høffding, and themes characteristic of American pragmatism. In recognizing the importance of Bohr's epistemological naturalism they examine his defence of the indispensability of classical concepts from a variety of different perspectives. This collection shows us that Bohr's int...
De novo nonsense mutations in ASXL1 cause Bohring-Opitz syndrome
DEFF Research Database (Denmark)
Hoischen, Alexander; van Bon, Bregje W M; Rodríguez-Santiago, Benjamín
2011-01-01
Bohring-Opitz syndrome is characterized by severe intellectual disability, distinctive facial features and multiple congenital malformations. We sequenced the exomes of three individuals with Bohring-Opitz syndrome and in each identified heterozygous de novo nonsense mutations in ASXL1, which...... is required for maintenance of both activation and silencing of Hox genes. In total, 7 out of 13 subjects with a Bohring-Opitz phenotype had de novo ASXL1 mutations, suggesting that the syndrome is genetically heterogeneous....
Traffic restrictions on Routes Bloch, Maxwell and Bohr
IT Department
2008-01-01
Excavation and pipework is being carried out in the framework of the transfer of the waste water treatment plant for the effluents from the surface treatment workshops from Building 254 to Building 676, currently under construction. This work may encroach onto Routes Bloch, Maxwell and Bohr and disrupt the flow of traffic. Users are requested to comply with the road signs that will be erected. The work is expected to last until the beginning of December 2008. Thank you for your understanding. TS/CE and TS/FM Groups Tel.7 4188 or 16 4314
The Niels Bohr Archive is Placing Collections on its Website
DEFF Research Database (Denmark)
Aaserud, Finn
2010-01-01
-quality digital copies in TIFF format to be kept as a security backup of the collection itself. From these, we then made black-and-white PDF-files of significantly lower resolution with the intention of making them available to researchers as digital documents. The sound recordings and films were digitized out...... this supplement, the documents of which we hope to make available on our website by 2013, the centennial for Bohr's model of the nuclear atom. We have found the task of digitizing our collections generally complex, sometimes frustrating, and in the end satisfying. At this stage it is particularly important...
Realization of Localized Bohr-Like Wave Packets
Mestayer, J. J.; Wyker, B.; Lancaster, J. C.; Dunning, F. B.; Reinhold, C. O.; Yoshida, S.; Burgdörfer, J.
2008-06-01
We demonstrate a protocol to create localized wave packets in very-high-n Rydberg states which travel in nearly circular orbits around the nucleus. Although these wave packets slowly dephase and eventually lose their localization, their motion can be monitored over several orbital periods. These wave packets represent the closest analog yet achieved to the original Bohr model of the hydrogen atom, i.e., an electron in a circular classical orbit around the nucleus. The possible extension of the approach to create “planetary atoms” in highly correlated stable multiply excited states is discussed.
El modelo semicuántico de Bohr en los libros de texto The Bohr's quantum model in the textbook
Directory of Open Access Journals (Sweden)
Jorge Eliécer Moreno Ramírez
2010-01-01
Full Text Available La didáctica de las ciencias naturales está cuestionando la transposición de los modelos científicos en modelos didácticos. Otras investigaciones muestran que el conocimiento científico convertido en conocimiento escolar produce deformaciones de la actividad científica y la simplificación de modelos, contribuyendo con la actitud negativa de los estudiantes hacia las ciencias y al fracaso escolar reportado por algunos estudios. Se pregunta si el modelo atómico de Bohr que se muestra en los textos se corresponde histórica y epistemológicamente con las actividades científicas y cuáles son las posibles deformaciones que de ésta se hace cuando se muestra el modelo en los libros. Los resultados de la investigación muestran una clara diferencia entre la propuesta de Bohr (1913 y la transposición del modelo, lo que invita a una reflexión profunda acerca de la confiabilidad que pueden tener los textos utilizados para la enseñanza de la ciencia químicaNatural science teaching is questioning the transposition that is made of scientific models into didactic models, because research has shown that when scientific knowledge is transformed into scholarly knowledge in order to be taught it causes the deformation of the scientific activity and the simplification of the models. This contributes to the negative attitude of students towards science, and student failure shown in some studies. This research inquired if the transposition of Bohr's atomic model that is shown in textbooks corresponds historically and epistemologically to scientific activity and what the possible deformations are that, coming from this model, are made to the scientific activity that comes from the transposition. The research results show differences between what Bohr (1913 proposed and the transposition of the model in textbooks. This information will contribute to the analysis that is being done regarding the dependability of textbooks.
De novo nonsense mutations in ASXL1 cause Bohring-Opitz syndrome
DEFF Research Database (Denmark)
Hoischen, Alexander; van Bon, Bregje W M; Rodríguez-Santiago, Benjamín
2011-01-01
Bohring-Opitz syndrome is characterized by severe intellectual disability, distinctive facial features and multiple congenital malformations. We sequenced the exomes of three individuals with Bohring-Opitz syndrome and in each identified heterozygous de novo nonsense mutations in ASXL1, which...
Okonjo, Kehinde Onwochei
2017-09-01
As a prelude to separating tertiary from quaternary structure contributions to the Bohr effect, we employed the Wyman equation to analyze Bohr data for human hemoglobin to which 2,3-bisphosphoglycerate, 2,3-BPG, is bound. Changes in the pK a s of the histidine Bohr groups result in a net reduction of their contributions to the Bohr effect at pH 7.4 compared to their contributions in stripped hemoglobin. The non-histidine 2,3-BPG binding groups - the β-chain terminal amino group and Lys82β - make negative and positive contributions, respectively, to the Bohr effect. The final result is that the Bohr effect at physiological pH is higher for 2,3-BPG bound compared to stripped hemoglobin. Contributions linked to His2β, His77β and His143β enable us to separate tertiary from quaternary Bohr contributions in stripped and in 2,3-BPG bound hemoglobin. Both contributions serve to make the Bohr effect for 2,3-BPG bound hemoglobin higher than for stripped hemoglobin at physiological pH. Copyright © 2017 Elsevier B.V. All rights reserved.
DEFF Research Database (Denmark)
Gjedde, Albert
2004-01-01
The author explores novel lessons emerging from the oxygen diffusion controversy between Christian Bohr on one side and August and Marie Krogh on the other. THe controversy found its emphatic expression in August and Marie Krogh's "Seven Little Devils", a series of papers published back-to-back i......The author explores novel lessons emerging from the oxygen diffusion controversy between Christian Bohr on one side and August and Marie Krogh on the other. THe controversy found its emphatic expression in August and Marie Krogh's "Seven Little Devils", a series of papers published back......-to-back in the 1910 volume of Skandinavisches Archiv für Physiologie. The Devils unjustifiably sealed the fate of Christian Bohr's theory of active cellular participation in the transport of oxygen from the lungs to the pulmonary circulation. The author's renewed examination of the original papers of Bohr...... and the Kroghs reveals that Bohr's concept of active cellular participation in diffusion is entirely compatible with the mechanism of capillary recruitment, for the discovery of which Krogh was later awarded Nobel's Prize, years after Bohr's untimely and unexpected death in 1911. Udgivelsesdato: 2004-null...
The quest for reality Bohr and Wittgenstein : two complementary views
Stenholm, Stig
2015-01-01
In both science and philosophy, the twentieth century saw a radical breakdown of certainty in the human worldview, as quantum uncertainty and linguistic ambiguity destroyed the comfortable certitudes of the past. As these disciplines form the foundation for a human position in the world, a major epistemological reorganization had to take place. In this book, quantum theorist Stig Stenholm presents Bohr and Wittgenstein, in physics and in philosophy, as central figures representing this revision. Each of them took up the challenge of replacing apparent order and certainty with a provisional understanding based on limited concepts in constant flux. Stenholm concludes that the modern synthesis created by their heirs is far from satisfactory, and the story is so far an unfinished one. The book will appeal to any researcher in either discipline curious about the foundation of modern science, and works to provoke a renewal of discussion, and the eventual emergence of a reformed clarity and understanding.
Systematic measurements of the Bohr-Weisskopf effect at ISOLDE
Nojiri, Y; Matsuki, S; Ragnarsson, I; Neugart, R; Redi, O; Stroke, H H; Duong, H T; Marescaux, D; Pinard, J; Juncar, P; Ekstrom, C; Pellarin, M; Vialle, J-L; Inamura, T
2002-01-01
The " Bohr-Weisskopf " effect, or " hyperfine structure (hfs) anomaly ", which results from the effect of the distribution of nuclear magnetization on the electro-nuclear interaction, will be measured systematically at the PS Booster ISOLDE, first for a long chain of radioactive cesium isotopes, analogously to previous isotope shift and hfs studies. In addition to the direct measurement of magnetic moment values, the results are expected to provide independent data for testing nuclear wavefunctions, these will be of importance for interpreting systematic parity non-conservation experiments, complementary to the single isotope study which requires a high precision knowledge of the electron wavefunction. Substantial progress in these calculations has been achieved recently. Precision measurements of the hfs splittings and nuclear magnetic moments are required, with sensitivity adequate for the radioactive isotopes produced. A triple resonance atomic beam magnetic resonance apparatus with optical pumping state s...
The Niels Bohr Archive is Placing Collections on its Website
DEFF Research Database (Denmark)
Aaserud, Finn
2010-01-01
Papers, which is of a manageable size, which had just been released by the family for research use, and which we deemed of special interest. In addition, we applied to make a good part of our film and sound collections similarly available, both because some of this material was in a deteriorating...... physical state and because we wanted to try out several kinds of collections. The scanning of the documents could begin at once as an in-house project, which at the same time made it possible to continue paying salaries to our permanent staff. The scanning had two purposes. First, we made high...... our small staff was also occupied with other matters, such as completing the Niels Bohr Collected Works. In early 2007 my old friend Joe Anderson at the AIP Center for History of Physics alerted us to the existence of the archives software Archon, freely available from the University of Illinois...
Systematic Measurements of the Bohr-Weisskopf Effect at ISOLDE
2002-01-01
Nuclear electric and magnetic structure properties are measurable by high-resolution atomic spectroscopy through isotope shifts and the Bohr-Weisskopf effect (hyperfine structure anomalies). \\\\ \\\\ The greatest value of these measurements is when made systematically over a large number of isotopes. This has been done in the case of isotopes shifts most extensively by the experiment at ISOLDE. To date the magnetic distribution studies are few and isolated. Here we propose to intitiate a program at ISOLDE to measure hfs anomalies systematically. The experiments, requiring high-precision data on magnetic dipole constants as well as on nuclear g-factors, will be done by atomic-beam magnetic resonance with the use of laser excitation for polarization of the beam and a sixpole magnet acting as an analyser. \\\\ \\\\ The heavy alkali elements are the most promising candidates for hfs anomaly studies because of the large effect expected, the high production yields at ISOLDE and most importantly, the interesting variations...
Il danese tranquillo Niels Bohr, un fisico e il suo tempo, 1885-1962
Pais, Abraham
1993-01-01
Niels Bohr è una figura centrale nella fisica del Novecento, padre fondatore della teoria atomica e della meccanica quantistica. La storia della sua vita, ricca e piena anche sul piano affettivo e personale, non può dunque ridursi a un resoconto dei suoi successi scientifici e Pais, allievo e poi amico di Bohr, ne è perfettamente consapevole. Il libro si sviluppa su vari piani: capitoli strettamente biografici o storico-scientifici si alternano a discussioni sulle idee di Bohr in campo politico e filosofico, sui suoi rapporti con Einstein, sul suo ruolo nei drammatici anni della guerra e su molti altri aspetti della vicenda umana.
Diophantine approximation and Dirichlet series
Queffélec, Hervé
2013-01-01
This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...
Atoms, metaphors and paradoxes Niels Bohr and the construction of a new physics
Petruccioli, Sandro
2006-01-01
This book gives a detailed study of the development and the interpretation given to Niels Bohr's Principle of Correspondence. It also describes the role that this principle played in guiding Bohr's research over the critical period from 1920 to 1927. Quantum mechanics, developed in the 1920s and 1930s by Bohr, Heisenberg, Born, Schrödinger and Dirac, represents one of the most profound turning points in science. This theory required a wholly new kind of physics in which many of the principles, concepts and models representing reality, that had formed the basis of classical physics since Galileo and Newton, had to be abandoned. This book re-examines the birth of quantum mechanics, in particular examining the development of crucial and original insights of Niels Bohr.
Katsumori, Makoto
2011-01-01
Through detailed textual and conceptual analysis, and with special attention to the potentially conflicting elements of Bohr's thought, this volume's fresh approach analyzes the relations between realism and antirealism through the prism of complementarity.
Bohr quantum theory of the magnetic monopoles and classical electron electromagnetic mass problem
Pankovic, Vladan
2010-01-01
In the first part of this work we apply Bohr (old or naive quantum atomic) theory for analysis of the remarkable electro-dynamical problem of magnetic monopoles. We reproduce formally exactly some basic elements of the Dirac magnetic monopoles theory, especially Dirac electric/magnetic charge quantization condition. It follows after application of Bohr theory at the system, simply called magnetic monopole "atom", consisting of the practically standing, massive magnetic monopole as the "nucleu...
Memories of Crisis: Bohr, Kuhn, and the Quantum Mechanical ``Revolution''
Seth, Suman
2013-04-01
``The history of science, to my knowledge,'' wrote Thomas Kuhn, describing the years just prior to the development of matrix and wave mechanics, ``offers no equally clear, detailed, and cogent example of the creative functions of normal science and crisis.'' By 1924, most quantum theorists shared a sense that there was much wrong with all extant atomic models. Yet not all shared equally in the sense that the failure was either terribly surprising or particularly demoralizing. Not all agreed, that is, that a crisis for Bohr-like models was a crisis for quantum theory. This paper attempts to answer four questions: two about history, two about memory. First, which sub-groups of the quantum theoretical community saw themselves and their field in a state of crisis in the early 1920s? Second, why did they do so, and how was a sense of crisis related to their theoretical practices in physics? Third, do we regard the years before 1925 as a crisis because they were followed by the quantum mechanical revolution? And fourth, to reverse the last question, were we to call into the question the existence of a crisis (for some at least) does that make a subsequent revolution less revolutionary?
Can we close the Bohr-Einstein quantum debate?
Kupczynski, Marian
2017-11-13
Recent experiments allow one to conclude that Bell-type inequalities are indeed violated; thus, it is important to understand what this means and how we can explain the existence of strong correlations between outcomes of distant measurements. Do we have to announce that Einstein was wrong, Nature is non-local and non-local correlations are produced due to quantum magic and emerge, somehow, from outside space-time? Fortunately, such conclusions are unfounded because, if supplementary parameters describing measuring instruments are correctly incorporated in a theoretical model, then Bell-type inequalities may not be proved. We construct a simple probabilistic model allowing these correlations to be explained in a locally causal way. In our model, measurement outcomes are neither predetermined nor produced in an irreducibly random way. We explain why, contrary to the general belief, the introduction of setting-dependent parameters does not restrict experimenters' freedom of choice. Since the violation of Bell-type inequalities does not allow the conclusion that Nature is non-local and that quantum theory is complete, the Bohr-Einstein quantum debate may not be closed. The continuation of this debate is important not only for a better understanding of Nature but also for various practical applications of quantum phenomena.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).
Niels Bohr on the wave function and the classical/quantum divide
Zinkernagel, Henrik
2016-02-01
It is well known that Niels Bohr insisted on the necessity of classical concepts in the account of quantum phenomena. But there is little consensus concerning his reasons, and what he exactly meant by this. In this paper, I re-examine Bohr's interpretation of quantum mechanics, and argue that the necessity of the classical can be seen as part of his response to the measurement problem. More generally, I attempt to clarify Bohr's view on the classical/quantum divide, arguing that the relation between the two theories is that of mutual dependence. An important element in this clarification consists in distinguishing Bohr's idea of the wave function as symbolic from both a purely epistemic and an ontological interpretation. Together with new evidence concerning Bohr's conception of the wave function collapse, this sets his interpretation apart from both standard versions of the Copenhagen interpretation, and from some of the reconstructions of his view found in the literature. I conclude with a few remarks on how Bohr's ideas make much sense also when modern developments in quantum gravity and early universe cosmology are taken into account.
Bohr's Electron was Problematic for Einstein: String Theory Solved the Problem
Webb, William
2013-04-01
Neils Bohr's 1913 model of the hydrogen electron was problematic for Albert Einstein. Bohr's electron rotates with positive kinetic energies +K but has addition negative potential energies - 2K. The total net energy is thus always negative with value - K. Einstein's special relativity requires energies to be positive. There's a Bohr negative energy conflict with Einstein's positive energy requirement. The two men debated the problem. Both would have preferred a different electron model having only positive energies. Bohr and Einstein couldn't find such a model. But Murray Gell-Mann did! In the 1960's, Gell-Mann introduced his loop-shaped string-like electron. Now, analysis with string theory shows that the hydrogen electron is a loop of string-like material with a length equal to the circumference of the circular orbit it occupies. It rotates like a lariat around its centered proton. This loop-shape has no negative potential energies: only positive +K relativistic kinetic energies. Waves induced on loop-shaped electrons propagate their energy at a speed matching the tangential speed of rotation. With matching wave speed and only positive kinetic energies, this loop-shaped electron model is uniquely suited to be governed by the Einstein relativistic equation for total mass-energy. Its calculated photon emissions are all in excellent agreement with experimental data and, of course, in agreement with those -K calculations by Neils Bohr 100 years ago. Problem solved!
Why has the bohr-sommerfeld model of the atom been ignoredby general chemistry textbooks?
Niaz, Mansoor; Cardellini, Liberato
2011-12-01
Bohr's model of the atom is considered to be important by general chemistry textbooks. A major shortcoming of this model was that it could not explain the spectra of atoms containing more than one electron. In order to increase the explanatory power of the model, Sommerfeld hypothesized the existence of elliptical orbits. This study has the following objectives: 1) Formulation of criteria based on a history and philosophy of science framework; and 2) Evaluation of university-level general chemistry textbooks based on the criteria, published in Italy and U.S.A. Presentation of a textbook was considered to be "satisfactory" if it included a description of the Bohr-Sommerfeld model along with diagrams of the elliptical orbits. Of the 28 textbooks published in Italy that were analyzed, only five were classified as "satisfactory". Of the 46 textbooks published in U.S.A., only three were classified as "satisfactory". This study has the following educational implications: a) Sommerfeld's innovation (auxiliary hypothesis) by introducing elliptical orbits, helped to restore the viability of Bohr's model; b) Bohr-Sommerfeld's model went no further than the alkali metals, which led scientists to look for other models; c) This clearly shows that scientific models are tentative in nature; d) Textbook authors and chemistry teachers do not consider the tentative nature of scientific knowledge to be important; e) Inclusion of the Bohr-Sommerfeld model in textbooks can help our students to understand how science progresses.
Love, literature and the quantum atom Niels Bohr's 1913 trilogy revisited
Aaserud, Finn
2013-01-01
Niels Bohr ranks with Einstein among the physicists of the 20th century. He rose to this status through his invention of the quantum theory of the atom and his leadership in its defense and development. He also ranks with Einstein in his humanism and his sense of responsibility to his science and the society that enabled him to create it. Our book presents unpublished excerpts from extensive correspondence between Bohr and his immediate family, and uses it to describe and analyze the psychological and cultural background to his invention. The book also contains a reprinting of the three papers of 1913 - the "Trilogy" - in which Bohr worked out the provisional basis of a quantum theory of the atom.
The Bohr--Einstein ''weighing-of-energy'' debate and the principle of equivalence
International Nuclear Information System (INIS)
Hughes, R.J.
1990-01-01
The Bohr--Einstein debate over the ''weighing of energy'' and the validity of the time--energy uncertainty relation is reexamined in the context of gravitation theories that do not respect the equivalence principle. Bohr's use of the equivalence principle is shown to be sufficient, but not necessary, to establish the validity of this uncertainty relation in Einstein's ''weighing-of-energy'' gedanken experiment. The uncertainty relation is shown to hold in any energy-conserving theory of gravity, and so a failure of the equivalence principle does not engender a failure of quantum mechanics. The relationship between the gravitational redshift and the equivalence principle is reviewed
Probing the (empirical quantum structure embedded in the periodic table with an effective Bohr model
Directory of Open Access Journals (Sweden)
Wellington Nardin Favaro
2013-01-01
Full Text Available The atomic shell structure can be observed by inspecting the experimental periodic properties of the Periodic Table. The (quantum shell structure emerges from these properties and in this way quantum mechanics can be explicitly shown considering the (semi-quantitative periodic properties. These periodic properties can be obtained with a simple effective Bohr model. An effective Bohr model with an effective quantum defect (u was considered as a probe in order to show the quantum structure embedded in the Periodic Table. u(Z shows a quasi-smoothed dependence of Z, i.e., u(Z ≈ Z2/5 - 1.
EPR before EPR: A 1930 Einstein-Bohr thought Experiment Revisited
Nikolic, Hrvoje
2012-01-01
In 1930, Einstein argued against the consistency of the time-energy uncertainty relation by discussing a thought experiment involving a measurement of the mass of the box which emitted a photon. Bohr seemingly prevailed over Einstein by arguing that Einstein's own general theory of relativity saves the consistency of quantum mechanics. We revisit…
The language of Orthodox theology & quantum mechanics: St Gregory Palamas and Niels Bohr
DEFF Research Database (Denmark)
Tanev, Stoyan
2013-01-01
The objective of this chapter is to provide an analytical framework that would enable the comparison of the ways of using words and language in the cases of St. Gregory Palamas and Niels Bohr. The main motivation will be to explore Christos Yannaras’ point about the opportunity of using quantum m...
Quantum Explorers: Bohr, Jordan, and Delbrück Venturing into Biology
Joaquim, Leyla; Freire, Olival; El-Hani, Charbel N.
2015-09-01
This paper disentangles selected intertwined aspects of two great scientific developments: quantum mechanics and molecular biology. We look at the contributions of three physicists who in the 1930s were protagonists of the quantum revolution and explorers of the field of biology: Niels Bohr, Pascual Jordan, and Max Delbrück. Their common platform was the defense of the Copenhagen interpretation in physics and the adoption of the principle of complementarity as a way of looking at biology. Bohr addressed the problem of how far the results reached in physics might influence our views about life. Jordan and Delbrück were followers of Bohr's ideas in the context of quantum mechanics and also of his tendency to expand the implications of the Copenhagen interpretation to biology. We propose that Bohr's perspective on biology was related to his epistemological views, as Jordan's was to his political positions. Delbrück's propensity to migrate was related to his transformation into a key figure in the history of twentieth-century molecular biology.
Hundrede år efter Bohr: Nobelprisen for fysik under gennemsnittet
DEFF Research Database (Denmark)
Julsgaard, Brian; Mølmer, Klaus
2013-01-01
I 2012 blev nobelprisen i fysik givet for eksperimenter på enkelte atomer og fotoner. Eksperimenterne har bekræftet kvantemekanikkens helt basale forudsigelser om, hvad der sker, når man f.eks. måler på et kvantesystem. I denne artikel beskriver vi nogle af disse eksperimenter, som Niels Bohr og...
The Life and Work of Niels Bohr – A Brief Sketch
Indian Academy of Sciences (India)
IAS Admin
his family life, background, and education; the importance of his stay in England after PhD, and the crucial contact with. Rutherford; the period of the Old Quantum .... During the second World War, as Denmark was occupied by Nazi. Germany, Bohr had to be “smuggled out” to the USA under a false name – Nicholas Baker!
The Life and Work of Niels Bohr – A Brief Sketch
Indian Academy of Sciences (India)
IAS Admin
1962 at the University of Cologne. There are many statements of Bohr which are at the same time both profound and often subtly humorous. Here are a few: •. Strictly speaking, the conscious analysis of any concept stands in a relation of exclusion to its immediate application. •. Every sentence I say must be understood not ...
Darwinism in disguise? A comparison between Bohr's view on quantum mechanics and QBism.
Faye, Jan
2016-05-28
The Copenhagen interpretation is first and foremost associated with Niels Bohr's philosophy of quantum mechanics. In this paper, I attempt to lay out what I see as Bohr's pragmatic approach to science in general and to quantum physics in particular. A part of this approach is his claim that the classical concepts are indispensable for our understanding of all physical phenomena, and it seems as if the claim is grounded in his reflection upon how the evolution of language is adapted to experience. Another, recent interpretation, QBism, has also found support in Darwin's theory. It may therefore not be surprising that sometimes QBism is said to be of the same breed as the Copenhagen interpretation. By comparing the two interpretations, I conclude, nevertheless, that there are important differences. © 2016 The Author(s).
A new relation of parameters of Bohr-Mottelson rotational spectra formula
International Nuclear Information System (INIS)
Li Mingliang; Xu Fuxin
2003-01-01
With the first three terms of Harris formula included and Mottelson's method followed, a new relation of the parameters of Bohr-Mottelson rotational spectra formula is brought forward. Superdeformed bands of even-even nuclei and normal deformed bands of nuclei in actinide and rare-earth are fitted with four-parameter Bohr-Mottelson rotational spectra formula. The relations of the parameters A, B, C, D are studied. The result show, for normal deformed bands, the new relation approach the experiment value in the same degree as the relation deduced from ab formula, but for superdeformed bands, the new relation is closer to the experiment than the relation deduced from ab formula. Three-parameter Harris formula may have better convergence than two-parameter Harris formula
Quantum Humor: The Playful Side of Physics at Bohr's Institute for Theoretical Physics
Halpern, Paul
2012-09-01
From the 1930s to the 1950s, a period of pivotal developments in quantum, nuclear, and particle physics, physicists at Niels Bohr's Institute for Theoretical Physics in Copenhagen took time off from their research to write humorous articles, letters, and other works. Best known is the Blegdamsvej Faust, performed in April 1932 at the close of one of the Institute's annual conferences. I also focus on the Journal of Jocular Physics, a humorous tribute to Bohr published on the occasions of his 50th, 60th, and 70th birthdays in 1935, 1945, and 1955. Contributors included Léon Rosenfeld, Victor Weisskopf, George Gamow, Oskar Klein, and Hendrik Casimir. I examine their contributions along with letters and other writings to show that they offer a window into some issues in physics at the time, such as the interpretation of complementarity and the nature of the neutrino, as well as the politics of the period.
On the Bohr radius relationship to spin-orbit interaction, spin magnitude, and Thomas precession
Lush, David C.
2007-01-01
The dynamics of the spin-orbit interaction in atomic hydrogen are studied in a classical electrodynamics-like setting. A Rutherfordian atomic model is used assuming a circular electron orbit, without the quantum principle as imposed arbitrarily in the Bohr model, but with an ad hoc incorporation in the electron of intrinsic spin and associated magnetic dipole moment. Analyzing the motions of the electron spin and orbital angular momenta, it is found that in the presence of Thomas precession, ...
Multilevel fitting of 235U resonance data sensitive to Bohr-and Brosa-fission channels
International Nuclear Information System (INIS)
Moore, M.S.
1995-01-01
The recent determination of the K, J dependence of the neutron induced fission cross section of 235 U by the Dubna group has led to a renewed interest in the mechanism of fission from saddle to scission. The K quantum numbers designate the so-called Bohr fission channels, which describe the fission properties at the saddle point. Certain other fission properties, e.g., the fragment mass and kinetic-energy distribution, are related to the properties of the scission point. The neutron energy dependence of the fragment kinetic energies has been measured by Hambsch et al., who analyzed their data according to a channel description of Brosa et al. How these two channel descriptions, the saddle-point Bohr channels and the scission-point Brosa channels, relate to one another is an open question, and is the subject matter of the present paper. We use the correlation coefficient between various data sets, in which variations are reported from resonance to resonance, as a measure of both-the statistical reliability of the data and of the degree to which different scission variables relate to different Bohr channels. We have carried out an adjustment of the ENDF/B-VI multilevel evaluation of the fission cross section of 235 U, one that provides a reasonably good fit to the energy dependence of the fission, capture, and total cross sections below 100 eV, and to the Bohr-channel structure deduced from an earlier measurement by Pattenden and Postma. We have also further explored the possibility of describing the data of Hambsch et al. in the Brosa-channel framework with the same set of fission-width vectors, only in a different reference system. While this approach shows promise, it is clear that better data are also needed for the neutron energy variation of the scission-point variables
Des images et des paraboles : Niels Bohr et le discours descriptif en physique quantique
Directory of Open Access Journals (Sweden)
Ilias Yocaris
2011-01-01
Full Text Available Cette étude porte sur l’importance accordée aux images verbales dans le discours descriptif utilisé en mécanique quantique, et plus précisément sur la conception de la langue scientifique qui est celle de Niels Bohr (1885-1962 : en raison d’une série de considérations techniques, méthodologiques et épistémologiques que nous nous proposons d’analyser in extenso, Bohr considère effectivement que les phénomènes subatomiques ne peuvent être évoqués directement (sans référence au contexte observationnel, par le biais d’un langage dénotatif non figural, mais uniquement de manière métaphorique, détournée, ce qui réduit à ses yeux le discours descriptif des physiciens à « des images et des paraboles ». En examinant les textes de Bohr à la lumière d’un certain nombre de travaux épistémologiques, de commentaires et d’expérimentations auxquels ils ont donné lieu ultérieurement, nous nous proposons de décrire les implications conceptuelles d’une telle prise de position, qui constitue une vraie révolution sur le plan philosophique.
Indian Academy of Sciences (India)
IAS Admin
V S Borkar is the Institute. Chair Professor of. Electrical Engineering at. IIT Bombay. His research interests are stochastic optimization, theory, algorithms and applica- tions. 1 'Markov Chain Monte Carlo' is another one (see [1]), not to mention schemes that combine both. Stochastic approximation is one of the unsung.
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
El modelo atómico de Bohr: una aplicación
Directory of Open Access Journals (Sweden)
Raul Garcia Llamas
2013-06-01
Full Text Available Se aplica la teoría atómica de Bohr cuyo centenario se celebra este 2013, utilizando la aproximación electrostática y un algoritmo numérico para resolver las ecuaciones clásicas de movimiento del núcleo y de los electrones en átomos complejos, con el fin de estudiar su dinámica. Se presentan resultados numéricos para el caso del átomo de Hidrogeno y el átomo de Helio.
Wave-particle duality and Bohr's complementarity principle in quantum mechanics
International Nuclear Information System (INIS)
Sen, D.; Basu, A.N.; Sengupta, S.
1995-01-01
Interest on Bohr's complementarity principle has recently been revived particularly because of several thought experiments and some actually performed experiments to test the validity of mutual exclusiveness of wave and particle properties. A critical review of the situation is undertaken and it is pointed out that the problem with mutual exclusiveness arises because of some vagueness in the conventional formulation. An attempt is made to remove this vagueness by connecting the origin of mutual exclusiveness to some principles of quantum mechanics. Accordingly, it becomes obvious that to contradict complementarity principle without contradicting quantum mechanics would be impossible. Some of the recent experiments are critically analysed. (author). 31 refs., 3 ills
International Nuclear Information System (INIS)
Sastry, M.D.
2013-01-01
This contribution reviews developments in the atomic spectroscopy subsequent to Bohr's model. This follows a brief description of Bohr's model of hydrogen atom that accounts for sharp line spectra of hydrogen atom. The developments include the effects of electron and nuclear spins, spectroscopy of multi electron atom which involve electron-electron repulsion and different angular momentum coupling schemes. More recently, Bohr's atom model has found application to processes at nano dimensions of semiconducting materials. It has now become possible to create a hydrogen-like atom, an exciton, with its size comparable or even more than that of the particle it self. This brings in extra quantization and has profound effects on the motion of the particles involved viz electron and hole. (author)
Gjedde, Albert
2010-01-01
The year 2010 is the centennial of the publication of the "Seven Little Devils" in the predecessor of "Acta Physiologica". In these seven papers, August and Marie Krogh sought to refute Christian Bohr's theory that oxygen diffusion from the lungs to the circulation is not entirely passive but rather facilitated by a specific cellular activity…
Energy Technology Data Exchange (ETDEWEB)
Fewster, Christopher J [Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom); Sahlmann, Hanno [Spinoza Institute, Universiteit Utrecht (Netherlands)
2008-11-21
We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new quantization of an important building block of the Hamiltonian constraint.
Farina, William J., Jr.; Bodzin, Alec M.
2018-01-01
Web-based learning is a growing field in education, yet empirical research into the design of high quality Web-based university science instruction is scarce. A one-week asynchronous online module on the Bohr Model of the atom was developed and implemented guided by the knowledge integration framework. The unit design aligned with three identified…
DEFF Research Database (Denmark)
Hastings, Rob; Cobben, Jan-Maarten; Gillessen-Kaesbach, Gabriele
2011-01-01
Bohring-Opitz syndrome (BOS) is a rare congenital disorder of unknown etiology diagnosed on the basis of distinctive clinical features. We suggest diagnostic criteria for this condition, describe ten previously unreported patients, and update the natural history of four previously reported patients...
Excited collective states of nuclei within Bohr Hamiltonian with Tietz-Hua potential
Chabab, M.; El Batoul, A.; Hamzavi, M.; Lahbas, A.; Oulne, M.
2017-07-01
In this paper, we present new analytical solutions of the Bohr Hamiltonian problem that we derived with the Tietz-Hua potential, here used for describing the β -part of the nuclear collective potential plus that of the harmonic oscillator for the γ -part. Also, we proceed to a systematic comparison of the numerical results obtained with this kind of β -potential with others which are widely used in such a framework as well as with the experiment. The calculations are carried out for energy spectra and electromagnetic transition probabilities for γ -unstable and axially symmetric deformed nuclei. In the same frame, we show the effect of the shape flatness of the β -potential beyond its minimum on transition rates calculations.
Bohr model description of the critical point for the first order shape phase transition
Budaca, R.; Buganu, P.; Budaca, A. I.
2018-01-01
The critical point of the shape phase transition between spherical and axially deformed nuclei is described by a collective Bohr Hamiltonian with a sextic potential having simultaneous spherical and deformed minima of the same depth. The particular choice of the potential as well as the scaled and decoupled nature of the total Hamiltonian leads to a model with a single free parameter connected to the height of the barrier which separates the two minima. The solutions are found through the diagonalization in a basis of Bessel functions. The basis is optimized for each value of the free parameter by means of a boundary deformation which assures the convergence of the solutions for a fixed basis dimension. Analyzing the spectral properties of the model, as a function of the barrier height, revealed instances with shape coexisting features which are considered for detailed numerical applications.
Bohr model description of the critical point for the first order shape phase transition
Directory of Open Access Journals (Sweden)
R. Budaca
2018-01-01
Full Text Available The critical point of the shape phase transition between spherical and axially deformed nuclei is described by a collective Bohr Hamiltonian with a sextic potential having simultaneous spherical and deformed minima of the same depth. The particular choice of the potential as well as the scaled and decoupled nature of the total Hamiltonian leads to a model with a single free parameter connected to the height of the barrier which separates the two minima. The solutions are found through the diagonalization in a basis of Bessel functions. The basis is optimized for each value of the free parameter by means of a boundary deformation which assures the convergence of the solutions for a fixed basis dimension. Analyzing the spectral properties of the model, as a function of the barrier height, revealed instances with shape coexisting features which are considered for detailed numerical applications.
Excited collective states of nuclei within Bohr Hamiltonian with Tietz-Hua potential
Energy Technology Data Exchange (ETDEWEB)
Chabab, M.; El Batoul, A.; Lahbas, A.; Oulne, M. [Cadi Ayyad University, High Energy Physics and Astrophysics Laboratory, Faculty of Sciences Semlalia, Marrakesh (Morocco); Hamzavi, M. [University of Zanjan, Department of Physics, Zanjan (Iran, Islamic Republic of)
2017-07-15
In this paper, we present new analytical solutions of the Bohr Hamiltonian problem that we derived with the Tietz-Hua potential, here used for describing the β-part of the nuclear collective potential plus that of the harmonic oscillator for the γ-part. Also, we proceed to a systematic comparison of the numerical results obtained with this kind of β-potential with others which are widely used in such a framework as well as with the experiment. The calculations are carried out for energy spectra and electromagnetic transition probabilities for γ-unstable and axially symmetric deformed nuclei. In the same frame, we show the effect of the shape flatness of the β-potential beyond its minimum on transition rates calculations. (orig.)
Niels Bohr, Max Delbruck and the paradox of light and life
International Nuclear Information System (INIS)
Scott, G.P.
1983-01-01
This paper features a concise, interdisciplinary history of philosophical issues which were the basis of Delbruck's scientific career. The paradox in living behavior of freedom-to-adapt versus deterministic atomism required complete reassessment with the advent of quantum mechanics. Apparent contradictions implied, for example, by the wave-particle model led Bohr to a belief in the ''complementarity of nature,'' which in 1932 he applied to biology. His claim was that purely physicochemical explanations of purposeful life functions such as ''self-generation and freedom of the will'' were impossible since mutually exclusive situations were involved. Thus Delbruck was challenged to spend his career investigating these vital functions. Beginning with ''fruit-fly photochemistry'' he established the molecular nature of the gene and then collected a world-wide group for a research effort on phage virus, which culminated in discovery of the DNA double helix by Watson and Crick. The second phase of his career featured a study of the total stimulus-response system of the fungus Phycomuces, which is still in progress. The extreme light-sensitivity observed, approaching one-quantum response, has raised the question of the survival value of amplified quantum noise. In critical comments to the author, Delbruck opposed the ''Compton-switch model'' for mind-body interaction; and in his lecture, ''Mind from Matter?'' he revealed his ''a priori concept of truth,'' which embraces a neutral monism and rejects the language of emergent evolution. His views are contrasted with those expressed in Popper's First Darwin Lecture
Bohr-Weisskopf effect influence of the distributed nuclear magnetization on hfs
Stroke, Hinko Henry; Pinard, J
2000-01-01
Nuclear magnetic moments provide a sensitive test of nuclear wave functions, in particular those of neutrons, which are not readily obtainable from other nuclear data. These are taking added importance by recent proposals to study parity non-conservation (PNC) effects in alkali atoms in isotopic series. By taking ratios of the PNC effects in pairs of isotopes, uncertainties in the atomic wave functions are largely cancelled out at the cost of knowledge of the change in the neutron wave function, the Bohr-Weisskopf effect (1950) in the hyperfine structure interaction of atoms measures the influence of the spatial distribution of the nuclear magnetization, and thereby provides an additional constraint on the determination of the neutron wave function. The added great importance of B-W in the determination of QED effects from the hfs in hydrogen-like ions of heavy elements, as measured recently at GSI, is noted, the B-W experiments require precision measurements of the hfs interactions and, independently, of the...
What is complementarity?: Niels Bohr and the architecture of quantum theory
International Nuclear Information System (INIS)
Plotnitsky, Arkady
2014-01-01
This article explores Bohr’s argument, advanced under the heading of ‘complementarity,’ concerning quantum phenomena and quantum mechanics, and its physical and philosophical implications. In Bohr, the term complementarity designates both a particular concept and an overall interpretation of quantum phenomena and quantum mechanics, in part grounded in this concept. While the argument of this article is primarily philosophical, it will also address, historically, the development and transformations of Bohr’s thinking, under the impact of the development of quantum theory and Bohr’s confrontation with Einstein, especially their exchange concerning the EPR experiment, proposed by Einstein, Podolsky and Rosen in 1935. Bohr’s interpretation was progressively characterized by a more radical epistemology, in its ultimate form, which was developed in the 1930s and with which I shall be especially concerned here, defined by his new concepts of phenomenon and atomicity. According to this epistemology, quantum objects are seen as indescribable and possibly even as inconceivable, and as manifesting their existence only in the effects of their interactions with measuring instruments upon those instruments, effects that define phenomena in Bohr’s sense. The absence of causality is an automatic consequence of this epistemology. I shall also consider how probability and statistics work under these epistemological conditions. (paper)
Complementarity and the Nature of Uncertainty Relations in Einstein–Bohr Recoiling Slit Experiment
Directory of Open Access Journals (Sweden)
Shogo Tanimura
2015-07-01
Full Text Available A model of the Einstein–Bohr recoiling slit experiment is formulated in a fully quantum theoretical setting. In this model, the state and dynamics of a movable wall that has two slits in it, as well as the state of a particle incoming to the two slits, are described by quantum mechanics. Using this model, we analyzed complementarity between exhibiting an interference pattern and distinguishing the particle path. Comparing the Kennard–Robertson type and the Ozawa-type uncertainty relations, we conclude that the uncertainty relation involved in the double-slit experiment is not the Ozawa-type uncertainty relation but the Kennard-type uncertainty relation of the position and the momentum of the double-slit wall. A possible experiment to test the complementarity relation is suggested. It is also argued that various phenomena which occur at the interface of a quantum system and a classical system, including distinguishability, interference, decoherence, quantum eraser, and weak value, can be understood as aspects of entanglement. Quanta 2015; 4: 1–9.
El pabellón Niels Bohr. Tradición Danesa y Modernidad
Directory of Open Access Journals (Sweden)
Carmen García Sánchez
2015-12-01
Full Text Available La casa de invitados de Niels Bohr fue el primer edificio del arquitecto danés Vilhelm Wohlert (1920-2007. Arraigado a la tradición danesa, representa una renovación basada en la absorción de influencias extranjeras: la arquitectura americana y la tradición japonesa. La caja de madera tiene el carácter sensible de un organismo vivo, siempre cambiante según las variaciones de luz del día o temperatura. Puertas plegables y contraventanas generan extensiones de las habitaciones. Cuando se abren, crean una prolongación del espacio interior, que se extiende a la naturaleza circundante, y se expande hacia el espacio exterior, permitiendo su movilización. Se establece una arquitectura de flujos. Protagoniza un ejemplo de la modernidad como refinamiento en la técnica de los límites y la idea de que la arquitectura no es un objeto material, sino el espacio generado en su interior. Podría ser visto como un ikebana; “el arte del espacio”, donde se produce una circulación de aire entre sus componentes; algo vivo que expresa la tercera dimensión, el equilibrio asimétrico, un interés por la materia, su textura y efecto emocional que emana. Hay armonía y equilibrio, que transmiten serenidad y belleza; un encuentro con la naturaleza; un mundo de relaciones amable al ser humano.
Directory of Open Access Journals (Sweden)
Yoshitada Sakai
Full Text Available BACKGROUND: Carbon dioxide (CO(2 therapy refers to the transcutaneous administration of CO(2 for therapeutic purposes. This effect has been explained by an increase in the pressure of O(2 in tissues known as the Bohr effect. However, there have been no reports investigating the oxygen dissociation of haemoglobin (Hb during transcutaneous application of CO(2in vivo. In this study, we investigate whether the Bohr effect is caused by transcutaneous application of CO2 in human living body. METHODS: We used a novel system for transcutaneous application of CO(2 using pure CO(2 gas, hydrogel, and a plastic adaptor. The validity of the CO(2 hydrogel was confirmed in vitro using a measuring device for transcutaneous CO(2 absorption using rat skin. Next, we measured the pH change in the human triceps surae muscle during transcutaneous application of CO(2 using phosphorus-31 magnetic resonance spectroscopy ((31P-MRS in vivo. In addition, oxy- and deoxy-Hb concentrations were measured with near-infrared spectroscopy in the human arm with occulted blood flow to investigate O2 dissociation from Hb caused by transcutaneous application of CO(2. RESULTS: The rat skin experiment showed that CO(2 hydrogel enhanced CO(2 gas permeation through the rat skin. The intracellular pH of the triceps surae muscle decreased significantly 10 min. after transcutaneous application of CO(2. The NIRS data show the oxy-Hb concentration decreased significantly 4 min. after CO(2 application, and deoxy-Hb concentration increased significantly 2 min. after CO(2 application in the CO(2-applied group compared to the control group. Oxy-Hb concentration significantly decreased while deoxy-Hb concentration significantly increased after transcutaneous CO(2 application. CONCLUSIONS: Our novel transcutaneous CO(2 application facilitated an O(2 dissociation from Hb in the human body, thus providing evidence of the Bohr effect in vivo.
Vayenas, Constantinos G
2012-01-01
This book shows that the strong interaction forces, which keep hadrons and nuclei together, are relativistic gravitational forces exerted between very small particles in the mass range of neutrinos. First, this book considers the problematic motion of two charged particles under the influence of electrostatic and gravitational forces only, which shows that bound states are formed by following the same semi-classical methodology used by Bohr to describe the H atom. This approach is also coupled with Newton's gravitational law and with Einstein's special relativity. The results agree with experi
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X. The clas......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X....... The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
International Nuclear Information System (INIS)
Ginsburg, C.A.
1980-01-01
In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
Farina, William J.; Bodzin, Alec M.
2017-12-01
Web-based learning is a growing field in education, yet empirical research into the design of high quality Web-based university science instruction is scarce. A one-week asynchronous online module on the Bohr Model of the atom was developed and implemented guided by the knowledge integration framework. The unit design aligned with three identified metaprinciples of science learning: making science accessible, making thinking visible, and promoting autonomy. Students in an introductory chemistry course at a large east coast university completed either an online module or traditional classroom instruction. Data from 99 students were analyzed and results showed significant knowledge growth in both online and traditional formats. For the online learning group, findings revealed positive student perceptions of their learning experiences, highly positive feedback for online science learning, and an interest amongst students to learn chemistry within an online environment.
Topological approximations of multisets
Directory of Open Access Journals (Sweden)
El-Sayed A. Abo-Tabl
2013-07-01
Full Text Available Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we define and investigate three types of lower and upper multiset approximations of any multiset. These types based on the multiset base of multiset topology induced by a multiset relation. Moreover, the relationships between generalized rough msets and mset topologies are given. In addition, an illustrative example is given to illustrate the relationships between different types of generalized definitions of rough multiset approximations.
Expectation Consistent Approximate Inference
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability...
Approximations of Fuzzy Systems
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Vinai K. Singh
2013-03-01
Full Text Available A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems, with product inference, centroid defuzzification and Gaussian functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. Loose-cluster approximation. Continuous curve Our Theory. Dashed curve Our Simulation. Loose cluster approx. not only. captures -the anomalous. qualitative features but is also,. quantitatively, quite accurate. Notes:
Bosma, Wieb
1990-01-01
The distribution is determined of some sequences that measure how well a number is approximated by its mediants (or intermediate continued fraction convergents). The connection with a theorem of Fatou, as well as a new proof of this, is given.
International Nuclear Information System (INIS)
Knobloch, A.F.
1980-01-01
A simplified cost approximation for INTOR parameter sets in a narrow parameter range is shown. Plausible constraints permit the evaluation of the consequences of parameter variations on overall cost. (orig.) [de
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
Approximation Behooves Calibration
DEFF Research Database (Denmark)
da Silva Ribeiro, André Manuel; Poulsen, Rolf
2013-01-01
Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009.......Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009....
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Improved Approximation Algorithm for
Byrka, Jaroslaw; Li, S.; Rybicki, Bartosz
2014-01-01
We study the k-level uncapacitated facility location problem (k-level UFL) in which clients need to be connected with paths crossing open facilities of k types (levels). In this paper we first propose an approximation algorithm that for any constant k, in polynomial time, delivers solutions of
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
Generalized Approximate Message Passing
DEFF Research Database (Denmark)
Oxvig, Christian Schou; Arildsen, Thomas; Larsen, Torben
2017-01-01
This tech report details a collection of results related to the Generalised Approximate Message Passing (GAMP) algorithm. It is a summary of the results that the authors have found critical in understanding the GAMP algorithm. In particular, emphasis is on the details that are crucial in implemen...
Wolff, Hans
This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested by Robbins and Monro. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic…
DEFF Research Database (Denmark)
Madsen, Rasmus Elsborg
2005-01-01
The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM...
Directory of Open Access Journals (Sweden)
Christian Corda
2018-01-01
Full Text Available In this paper we consider the metric entropies of the maps of an iterated function system deduced from a black hole which are known the Bekenstein–Hawking entropies and its subleading corrections. More precisely, we consider the recent model of a Bohr-like black hole that has been recently analysed in some papers in the literature, obtaining the intriguing result that the metric entropies of a black hole are created by the metric entropies of the functions, created by the black hole principal quantum numbers, i.e., by the black hole quantum levels. We present a new type of topological entropy for general iterated function systems based on a new kind of the inverse of covers. Then the notion of metric entropy for an Iterated Function System ( I F S is considered, and we prove that these definitions for topological entropy of IFS’s are equivalent. It is shown that this kind of topological entropy keeps some properties which are hold by the classic definition of topological entropy for a continuous map. We also consider average entropy as another type of topological entropy for an I F S which is based on the topological entropies of its elements and it is also an invariant object under topological conjugacy. The relation between Axiom A and the average entropy is investigated.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2011-01-01
Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
Fragments of approximate counting
Czech Academy of Sciences Publication Activity Database
Buss, S.R.; Kolodziejczyk, L. A.; Thapen, Neil
2014-01-01
Roč. 79, č. 2 (2014), s. 496-525 ISSN 0022-4812 R&D Projects: GA AV ČR IAA100190902 Institutional support: RVO:67985840 Keywords : approximate counting * bounded arithmetic * ordering principle Subject RIV: BA - General Mathematics Impact factor: 0.541, year: 2014 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9287274&fileId=S0022481213000376
Optimization and approximation
Pedregal, Pablo
2017-01-01
This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.
Approximate Bayesian recursive estimation
Czech Academy of Sciences Publication Activity Database
Kárný, Miroslav
2014-01-01
Roč. 285, č. 1 (2014), s. 100-111 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf
Topics in Metric Approximation
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
International Nuclear Information System (INIS)
El Sawi, M.
1983-07-01
A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution to a second-order homogeneous linear differential equation is presented in a standard form that is valid for all orders. In comparison to other methods, the present one is shown to be leading in the order of iteration, and thus possibly has the ability of accelerating the convergence of the solution. The method is also extended for the solution of inhomogeneous equations. (author)
Cyclic approximation to stasis
Directory of Open Access Journals (Sweden)
Stewart D. Johnson
2009-06-01
Full Text Available Neighborhoods of points in $mathbb{R}^n$ where a positive linear combination of $C^1$ vector fields sum to zero contain, generically, cyclic trajectories that switch between the vector fields. Such points are called stasis points, and the approximating switching cycle can be chosen so that the timing of the switches exactly matches the positive linear weighting. In the case of two vector fields, the stasis points form one-dimensional $C^1$ manifolds containing nearby families of two-cycles. The generic case of two flows in $mathbb{R}^3$ can be diffeomorphed to a standard form with cubic curves as trajectories.
Approximate Euclidean Ramsey theorems
Directory of Open Access Journals (Sweden)
Adrian Dumitrescu
2011-04-01
Full Text Available According to a classical result of Szemerédi, every dense subset of 1,2,…,N contains an arbitrary long arithmetic progression, if N is large enough. Its analogue in higher dimensions due to Fürstenberg and Katznelson says that every dense subset of {1,2,…,N}d contains an arbitrary large grid, if N is large enough. Here we generalize these results for separated point sets on the line and respectively in the Euclidean space: (i every dense separated set of points in some interval [0,L] on the line contains an arbitrary long approximate arithmetic progression, if L is large enough. (ii every dense separated set of points in the d-dimensional cube [0,L]d in Rd contains an arbitrary large approximate grid, if L is large enough. A further generalization for any finite pattern in Rd is also established. The separation condition is shown to be necessary for such results to hold. In the end we show that every sufficiently large point set in Rd contains an arbitrarily large subset of almost collinear points. No separation condition is needed in this case.
Approximate Bayesian computation.
Directory of Open Access Journals (Sweden)
Mikael Sunnåker
Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.
The quasilocalized charge approximation
International Nuclear Information System (INIS)
Kalman, G J; Golden, K I; Donko, Z; Hartmann, P
2005-01-01
The quasilocalized charge approximation (QLCA) has been used for some time as a formalism for the calculation of the dielectric response and for determining the collective mode dispersion in strongly coupled Coulomb and Yukawa liquids. The approach is based on a microscopic model in which the charges are quasilocalized on a short-time scale in local potential fluctuations. We review the conceptual basis and theoretical structure of the QLC approach and together with recent results from molecular dynamics simulations that corroborate and quantify the theoretical concepts. We also summarize the major applications of the QLCA to various physical systems, combined with the corresponding results of the molecular dynamics simulations and point out the general agreement and instances of disagreement between the two
Approximate quantum Markov chains
Sutter, David
2018-01-01
This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2012-05-01
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.
Nagatomo, Shigenori; Okumura, Miki; Saito, Kazuya; Ogura, Takashi; Kitagawa, Teizo; Nagai, Masako
2017-03-07
Regulation of the oxygen affinity of human adult hemoglobin (Hb A) at high pH, known as the alkaline Bohr effect, is essential for its physiological function. In this study, structural mechanisms of the alkaline Bohr effect and pH-dependent O 2 affinity changes were investigated via 1 H nuclear magnetic resonance and visible and UV resonance Raman spectra of mutant Hbs, Hb M Iwate (αH87Y) and Hb M Boston (αH58Y). It was found that even though the binding of O 2 to the α subunits is forbidden in the mutant Hbs, the O 2 affinity was higher at alkaline pH than at neutral pH, and concomitantly, the Fe-His stretching frequency of the β subunits was shifted to higher values. Thus, it was confirmed for the β subunits that the stronger the Fe-His bond, the higher the O 2 affinity. It was found in this study that the quaternary structure of α(Fe 3+ )β(Fe 2+ -CO) of the mutant Hb is closer to T than to the ordinary R at neutral pH. The retained Aspβ94-Hisβ146 hydrogen bond makes the extent of proton release smaller upon ligand binding from Hisβ146, known as one of residues contributing to the alkaline Bohr effect. For these T structures, the Aspα94-Trpβ37 hydrogen bond in the hinge region and the Tyrα42-Aspβ99 hydrogen bond in the switch region of the α 1 -β 2 interface are maintained but elongated at alkaline pH. Thus, a decrease in tension in the Fe-His bond of the β subunits at alkaline pH causes a substantial increase in the change in global structure upon binding of CO to the β subunit.
International Nuclear Information System (INIS)
Busch, M.R.; Mace, J.E.; Ho, N.T.; Ho, Chien
1991-01-01
Assessment of the roles of the carboxyl-terminal β146 histidyl residues in the alkaline Bohr effect in human and normal adult hemoglobin by high-resolution proton nuclear magnetic resonance spectroscopy requires assignment of the resonances corresponding to these residues. By a careful spectroscopic study of human normal adult hemoglobin, enzymatically prepared des(His146β)-hemoglobin, and the mutant hemoglobins Cowtown (β146His → Leu) and York (β146His → Pro), the authors have resolved some of these conflicting results. By a close incremental variation of pH over a wide range in chloride-free 0.1 M N-(2-hydroxyethyl)piperazine-N'-2-ethanesulfonic acid buffer, a single resonance has been found to be consistently missing in the proton nuclear magnetic resonance spectra of these hemoglobin variants. The results indicate that the contribution of the β146 histidyl residues is 0.52 H + /hemoglobin tetramer at pH 7.6, markedly less than 0.8 H + /hemoglobin tetramer estimated by study of the mutant hemoglobin Cowtown (β146His → Leu) by Shih and Perutz. They have found that at least two histidyl residues in the carbonmonoxy form of this mutant have pK values that are perturbed, and they suggest that these pK differences may in part account for this discrepancy. The results show that the pK values of β146 histidyl residues in the carbonmonoxy form of hemoglobin are substantially affected by the presence of chloride and other anions in the solvent, and thus, the contribution of this amino acid residue to the alkaline Bohr effect can be shown to vary widely in magnitude, depending on the solvent composition. These results demonstrate that the detailed molecular mechanisms of the alkaline Bohr effect are not unique but are affected both by the hemoglobin structure and by the interactions with the solvent components in which the hemoglobin molecule resides
The Bohr Correspondence Principle
Indian Academy of Sciences (India)
Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 3. Current Issue Volume 23 | Issue 3. March 2018. Home · Volumes & Issues · Categories · Special Issues · Search · Editorial Board · Information for Authors · Subscription ...
Indian Academy of Sciences (India)
IAS Admin
*Text of the Rutherford Memorial Lecture delivered by Sir Rudolf Peierls, FRS, on 10 November 1987 at the National. Physical Laboratory, New Delhi. Reproduced from Current ..... felt that Langmuir's ideas were much too descriptive for the year of our Lord 1921. They might have served in 1911. See you in Brussels (at the ...
The Bohr Correspondence Principle
Indian Academy of Sciences (India)
Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 4. Current Issue Volume 23 | Issue 4. April 2018. Home · Volumes & Issues · Categories · Special Issues · Search · Editorial Board · Information for Authors · Subscription ...
International Conference Approximation Theory XV
Schumaker, Larry
2017-01-01
These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-07
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Comparative Study of Approximate Multipliers
Masadeh, Mahmoud; Hasan, Osman; Tahar, Sofiene
2018-01-01
Approximate multipliers are widely being advocated for energy-efficient computing in applications that exhibit an inherent tolerance to inaccuracy. However, the inclusion of accuracy as a key design parameter, besides the performance, area and power, makes the identification of the most suitable approximate multiplier quite challenging. In this paper, we identify three major decision making factors for the selection of an approximate multipliers circuit: (1) the type of approximate full adder...
Forms of Approximate Radiation Transport
Brunner, G
2002-01-01
Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.
International Conference Approximation Theory XIV
Schumaker, Larry
2014-01-01
This volume developed from papers presented at the international conference Approximation Theory XIV, held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
Directory of Open Access Journals (Sweden)
Furman W.I.
2012-02-01
Full Text Available Last data on angular correlations of fission fragments from slow (s-wave neutron induced binary fission of spin-aligned nuclei 235U are discussed in the context of JπK A. Bohrs channels. Special attention is paid to K = 0 channel. Reasons for its suppression are specified for compound nucleus states of negative parity. A brief overview of recent data on T-odd angular correlations in ternary and binary (with emission of a third particle, a neutron or γ-quantum fission induced by slow polarized neutrons is presented. On the basis of the developed theoretical approach it is shown that a valuable information on JπK fission channels at scission point can be inferred from these T-odd angular correlations.
Approximation by planar elastic curves
DEFF Research Database (Denmark)
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2016-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient-driven...
Anytime classification by ontology approximation
Schlobach, S.; Blaauw, E.; El Kebir, M.; Ten Teije, A.; Van Harmelen, F.; Bortoli, S.; Hobbelman, M.C.; Millian, K.; Ren, Y.; Stam, S.; Thomassen, P.; Van Het Schip, R.; Van Willigem, W.
2007-01-01
Reasoning with large or complex ontologies is one of the bottle-necks of the Semantic Web. In this paper we present an anytime algorithm for classification based on approximate subsumption. We give the formal definitions for approximate subsumption, and show its monotonicity and soundness; we show
Some results in Diophantine approximation
DEFF Research Database (Denmark)
Pedersen, Steffen Højris
This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...... the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered...... in the formal Laurent series over F3. The first paper is on intrinsic Diophantine approximation in the Cantor set in the formal Laurent series over F3. The summary contains a short motivation, the results of the paper and sketches of the proofs, mainly focusing on the ideas involved. The details of the proofs...
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Approximate Implicitization Using Linear Algebra
Directory of Open Access Journals (Sweden)
Oliver J. D. Barrowclough
2012-01-01
Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.
Rollout sampling approximate policy iteration
Dimitrakakis, C.; Lagoudakis, M.G.
2008-01-01
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a
Shearlets and Optimally Sparse Approximations
DEFF Research Database (Denmark)
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
2012-01-01
of such functions. Recently, cartoon-like images were introduced in 2D and 3D as a suitable model class, and approximation properties were measured by considering the decay rate of the $L^2$ error of the best $N$-term approximation. Shearlet systems are to date the only representation system, which provide...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....
Mathematical algorithms for approximate reasoning
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
Approximate number sense theory or approximate theory of magnitude?
Content, Alain; Velde, Michael Vande; Adriano, Andrea
2017-01-01
Leibovich et al. argue that the evidence in favor of a perceptual mechanism devoted to the extraction of numerosity from visual collections is unsatisfactory and propose to replace it with an unspecific mechanism capturing approximate magnitudes from continuous dimensions. We argue that their representation of the evidence is incomplete and that their theoretical proposal is too vague to be useful.
Approximate Matching of Hierarchial Data
DEFF Research Database (Denmark)
Augsten, Nikolaus
The goal of this thesis is to design, develop, and evaluate new methods for the approximate matching of hierarchical data represented as labeled trees. In approximate matching scenarios two items should be matched if they are similar. Computing the similarity between labeled trees is hard...... formally proof that the pq-gram index can be incrementally updated based on the log of edit operations without reconstructing intermediate tree versions. The incremental update is independent of the data size and scales to a large number of changes in the data. We introduce windowed pq...... as in addition to the data values also the structure must be considered. A well-known measure for comparing trees is the tree edit distance. It is computationally expensive and leads to a prohibitively high run time. Our solution for the approximate matching of hierarchical data are pq-grams. The pq...
Approximations to camera sensor noise
Jin, Xiaodan; Hirakawa, Keigo
2013-02-01
Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.
Face Recognition using Approximate Arithmetic
DEFF Research Database (Denmark)
Marso, Karol
Face recognition is image processing technique which aims to identify human faces and found its use in various diﬀerent ﬁelds for example in security. Throughout the years this ﬁeld evolved and there are many approaches and many diﬀerent algorithms which aim to make the face recognition as eﬀective...... as possible. The use of diﬀerent approaches such as neural networks and machine learning can lead to fast and eﬃcient solutions however, these solutions are expensive in terms of hardware resources and power consumption. A possible solution to this problem can be use of approximate arithmetic. In many image...... processing applications the results do not need to be completely precise and use of the approximate arithmetic can lead to reduction in terms of delay, space and power consumption. In this paper we examine possible use of approximate arithmetic in face recognition using Eigenfaces algorithm....
Approximate reasoning in physical systems
International Nuclear Information System (INIS)
Mutihac, R.
1991-01-01
The theory of fuzzy sets provides excellent ground to deal with fuzzy observations (uncertain or imprecise signals, wavelengths, temperatures,etc.) fuzzy functions (spectra and depth profiles) and fuzzy logic and approximate reasoning. First, the basic ideas of fuzzy set theory are briefly presented. Secondly, stress is put on application of simple fuzzy set operations for matching candidate reference spectra of a spectral library to an unknown sample spectrum (e.g. IR spectroscopy). Thirdly, approximate reasoning is applied to infer an unknown property from information available in a database (e.g. crystal systems). Finally, multi-dimensional fuzzy reasoning techniques are suggested. (Author)
Approximations to the Newton potential
International Nuclear Information System (INIS)
Warburton, A.E.A.; Hatfield, R.W.
1977-01-01
Explicit expressions are obtained for Newton's (Newton, R.G., J. Math. Phys., 3:75-82 (1962)) solution to the inverse scattering problem in the approximations where up to two phase shifts are treated exactly and the rest to first order. (author)
Approximation properties of haplotype tagging
Directory of Open Access Journals (Sweden)
Dreiseitl Stephan
2006-01-01
Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.
Approximate Reanalysis in Topology Optimization
DEFF Research Database (Denmark)
Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole
2009-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...
Ultrafast Approximation for Phylogenetic Bootstrap
Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and
APPROXIMATE MODELS FOR FLOOD ROUTING
African Journals Online (AJOL)
kinematic model and a nonlinear convection-diffusion model are extracted from a normalized form of the St. Venant equations, and applied to ... normal ﬂow condition is moderate. Keywords: approximate models, nonlinear kinematic ... The concern here is with the movement of an abnormal amount of water along a river or ...
On badly approximable complex numbers
DEFF Research Database (Denmark)
Esdahl-Schou, Rune; Kristensen, S.
We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...
Rational approximation of vertical segments
Salazar Celis, Oliver; Cuyt, Annie; Verdonk, Brigitte
2007-08-01
In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive.
All-Norm Approximation Algorithms
Azar, Yossi; Epstein, Leah; Richter, Yossi; Woeginger, Gerhard J.; Penttonen, Martti; Meineche Schmidt, Erik
2002-01-01
A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different ℓ p norms. We address this problem by introducing the concept of an All-norm ρ-approximation
Approximate Reasoning with Fuzzy Booleans
van den Broek, P.M.; Noppen, J.A.R.
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp
Zhang, Peng; Xing, Caihong; Rhodes, Steven D; He, Yongzheng; Deng, Kai; Li, Zhaomin; He, Fuhong; Zhu, Caiying; Nguyen, Lihn; Zhou, Yuan; Chen, Shi; Mohammad, Khalid S; Guise, Theresa A; Abdel-Wahab, Omar; Xu, Mingjiang; Wang, Qian-Fei; Yang, Feng-Chun
2016-06-14
De novo ASXL1 mutations are found in patients with Bohring-Opitz syndrome, a disease with severe developmental defects and early childhood mortality. The underlying pathologic mechanisms remain largely unknown. Using Asxl1-targeted murine models, we found that Asxl1 global loss as well as conditional deletion in osteoblasts and their progenitors led to significant bone loss and a markedly decreased number of bone marrow stromal cells (BMSCs) compared with wild-type littermates. Asxl1(-/-) BMSCs displayed impaired self-renewal and skewed differentiation, away from osteoblasts and favoring adipocytes. RNA-sequencing analysis revealed altered expression of genes involved in cell proliferation, skeletal development, and morphogenesis. Furthermore, gene set enrichment analysis showed decreased expression of stem cell self-renewal gene signature, suggesting a role of Asxl1 in regulating the stemness of BMSCs. Importantly, re-introduction of Asxl1 normalized NANOG and OCT4 expression and restored the self-renewal capacity of Asxl1(-/-) BMSCs. Our study unveils a pivotal role of ASXL1 in the maintenance of BMSC functions and skeletal development. Copyright © 2016 The Author(s). Published by Elsevier Inc. All rights reserved.
Hydrogen: Beyond the Classic Approximation
International Nuclear Information System (INIS)
Scivetti, Ivan
2003-01-01
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Hydrogen Beyond the Classic Approximation
Scivetti, I
2003-01-01
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Good points for diophantine approximation
Indian Academy of Sciences (India)
n=1 of real numbers in the interval [0, 1) and a sequence. (δn)∞ n=1 of positive numbers tending to zero, we consider the size of the set of numbers in [0, 1] which can be 'well approximated' by terms of the first sequence, namely, those y ∈ [0, 1] for which the inequality |y − xn| < δn holds for infinitely many positive integers n ...
Dimensionality Reduction with Adaptive Approximation
Kokiopoulou, Effrosyni; Frossard, Pascal
2007-01-01
In this paper, we propose the use of (adaptive) nonlinear approximation for dimensionality reduction. In particular, we propose a dimensionality reduction method for learning a parts based representation of signals using redundant dictionaries. A redundant dictionary is an overcomplete set of basis vectors that spans the signal space. The signals are jointly represented in a common subspace extracted from the redundant dictionary, using greedy pursuit algorithms for simultaneous sparse approx...
Ultrafast approximation for phylogenetic bootstrap.
Minh, Bui Quang; Nguyen, Minh Anh Thi; von Haeseler, Arndt
2013-05-01
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and the Shimodaira-Hasegawa-like approximate likelihood ratio test have been introduced to speed up the bootstrap. Here, we suggest an ultrafast bootstrap approximation approach (UFBoot) to compute the support of phylogenetic groups in maximum likelihood (ML) based trees. To achieve this, we combine the resampling estimated log-likelihood method with a simple but effective collection scheme of candidate trees. We also propose a stopping rule that assesses the convergence of branch support values to automatically determine when to stop collecting candidate trees. UFBoot achieves a median speed up of 3.1 (range: 0.66-33.3) to 10.2 (range: 1.32-41.4) compared with RAxML RBS for real DNA and amino acid alignments, respectively. Moreover, our extensive simulations show that UFBoot is robust against moderate model violations and the support values obtained appear to be relatively unbiased compared with the conservative standard bootstrap. This provides a more direct interpretation of the bootstrap support. We offer an efficient and easy-to-use software (available at http://www.cibiv.at/software/iqtree) to perform the UFBoot analysis with ML tree inference.
Initially Approximated Quasi Equilibrium Manifold
International Nuclear Information System (INIS)
Shahzad, M.; Arif, H.; Gulistan, M.; Sajid, M.
2015-01-01
Most commonly, kinetics model reduction techniques are based on exploiting time scale separation into fast and slow reaction processes. Then, a researcher approximates the system dynamically with dimension reduction for slow ones eliminating the fast modes. The main idea behind the construction of the lower dimension manifold is based on finding its initial approximation using Quasi Equilibrium Manifold (QEM). Here, we provide an efficient numerical method, which allow us to calculate low dimensional manifolds of chemical reaction systems. This computation technique is not restricted to our specific complex problem, but it can also be applied to other reacting flows or dynamic systems provided with the condition that a large number of extra (decaying) components can be eliminated from the system. Through computational approach, we approximate low dimensional manifold for a mechanism of six chemical species to simplify complex chemical kinetics. A reduced descriptive form of slow invariant manifold is obtained from dissipative system. This method is applicable for higher dimensions and is applied over an oxidation of CO/Pt. (author)
Approximate Inference for Wireless Communications
DEFF Research Database (Denmark)
Hansen, Morten
to the optimal one, which usually requires an unacceptable high complexity. Some of the treated approximate methods are based on QL-factorization of the channel matrix. In the work presented in this thesis it is proven how the QL-factorization of frequency-selective channels asymptotically provides the minimum......-phase and all-pass filters. This enables us to view Sphere Detection (SD) as an adaptive variant of minimum-phase prefiltered reduced-state sequence estimation. Thus, a novel way of computing the minimum-phase filter and its associated all-pass filter using the numerically stable QL-factorization is suggested...
Generalized Gradient Approximation Made Simple
International Nuclear Information System (INIS)
Perdew, J.P.; Burke, K.; Ernzerhof, M.
1996-01-01
Generalized gradient approximations (GGA close-quote s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. copyright 1996 The American Physical Society
Wavelet Approximation in Data Assimilation
Tangborn, Andrew; Atlas, Robert (Technical Monitor)
2002-01-01
Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.
Plasma Physics Approximations in Ares
International Nuclear Information System (INIS)
Managan, R. A.
2015-01-01
Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, Fn( μ/θ ), the chemical potential, μ or ζ = ln(1+e μ/θ ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A α (ζ ),A β (ζ ), ζ, f(ζ ) = (1 + e -μ/θ )F 1/2 (μ/θ), F 1/2 '/F 1/2 , F c α , and F c β . In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.
Approximation by double Walsh polynomials
Directory of Open Access Journals (Sweden)
Ferenc Móricz
1992-01-01
Full Text Available We study the rate of approximation by rectangular partial sums, Cesàro means, and de la Vallée Poussin means of double Walsh-Fourier series of a function in a homogeneous Banach space X. In particular, X may be Lp(I2, where 1≦p<∞ and I2=[0,1×[0,1, or CW(I2, the latter being the collection of uniformly W-continuous functions on I2. We extend the results by Watari, Fine, Yano, Jastrebova, Bljumin, Esfahanizadeh and Siddiqi from univariate to multivariate cases. As by-products, we deduce sufficient conditions for convergence in Lp(I2-norm and uniform convergence on I2 as well as characterizations of Lipschitz classes of functions. At the end, we raise three problems.
Approximating the minimum cycle mean
Directory of Open Access Journals (Sweden)
Krishnendu Chatterjee
2013-07-01
Full Text Available We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1 First we show that the algorithmic question is reducible in O(n^2 time to the problem of a logarithmic number of min-plus matrix multiplications of n-by-n matrices, where n is the number of vertices of the graph. (2 Second, when the weights are nonnegative, we present the first (1 + ε-approximation algorithm for the problem and the running time of our algorithm is ilde(O(n^ω log^3(nW/ε / ε, where O(n^ω is the time required for the classic n-by-n matrix multiplication and W is the maximum value of the weights.
Nonlinear approximation with dictionaries I. Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2004-01-01
We study various approximation classes associated with m-term approximation by elements from a (possibly) redundant dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation w...
Li, Chen; Requist, Ryan; Gross, E K U
2018-02-28
We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length R = R c , where an avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the R-dependent electronic structure of LiF within a two-site Hubbard model, we find that nonadiabatic electron-nuclear coupling produces a sizable elongation of the critical R c by 0.5 bohr. This effect is very accurately captured by a simple and rigorously derived correction, with an M -1 prefactor, to the exchange-correlation potential in density functional theory, M = reduced nuclear mass. Since this nonadiabatic term depends on gradients of the nuclear wave function and conditional electronic density, ∇ R χ(R) and ∇ R n(r, R), it couples the Kohn-Sham equations at neighboring R points. Motivated by an observed localization of nonadiabatic effects in nuclear configuration space, we propose a local conditional density approximation-an approximation that reduces the search for nonadiabatic density functionals to the search for a single function y(n).
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
is called the metric invariant translation approximation property for a countable dis- crete metric space. Moreover ... Uniform Roe algebras; fine hyperbolic graph; metric invariant translation approximation property. ..... ate Studies in Mathematics, Volume 88 (2008) (Rhode Island: American Mathematical. Society Providence).
Approximate Uniqueness Estimates for Singular Correlation Matrices.
Finkbeiner, C. T.; Tucker, L. R.
1982-01-01
The residual variance is often used as an approximation to the uniqueness in factor analysis. An upper bound approximation to the residual variance is presented for the case when the correlation matrix is singular. (Author/JKS)
Reduction of Linear Programming to Linear Approximation
Vaserstein, Leonid N.
2006-01-01
It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.
HE11 radiation patterns and gaussian approximations
International Nuclear Information System (INIS)
Rebuffi, L.; Crenn, J.P.
1986-12-01
The possibility of approximating the HE11 radiation pattern with a Gaussian distribution is presented. A numerical comparison between HE11 far-field theoretical patterns and Abrams and Crenn approximations permits an evaluation of the validity of these two approximations. A new numerically optimized HE11 Gaussian approximation for the far-field, extended to great part of the near field, has been found. In particular, the value given for the beam radius at the waist, has been demonstrated to give the best HE11 Gaussian approximation in the far-field. The Crenn approximation is found to be very close to this optimal approximation, while the Abrams approximation is shown to be less precise. Universal curves for intensity, amplitude and power distribution are given for the HE11 radiated mode. These results are of interest for laser waveguide applications and for plasma ECRH transmission systems
Analytical approximations of Chandrasekhar's H-Function
International Nuclear Information System (INIS)
Simovic, R.; Vukanic, J.
1995-01-01
Analytical approximations of Chandrasekhar's H-function are derived in this paper by using ordinary and modified DPN methods. The accuracy of the approximations is discussed and the energy dependent albedo problem is treated. (author)
Axiomatic Characterizations of IVF Rough Approximation Operators
Directory of Open Access Journals (Sweden)
Guangji Yu
2014-01-01
Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.
Truth Approximation, Social Epistemology, and Opinion Dynamics
Douven, Igor; Kelp, Christoph
This paper highlights some connections between work on truth approximation and work in social epistemology, in particular work on peer disagreement. In some of the literature on truth approximation, questions have been addressed concerning the efficiency of research strategies for approximating the
Operator approximant problems arising from quantum theory
Maher, Philip J
2017-01-01
This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.
Approximate Nearest Neighbor Queries among Parallel Segments
DEFF Research Database (Denmark)
Emiris, Ioannis Z.; Malamatos, Theocharis; Tsigaridas, Elias
2010-01-01
We develop a data structure for answering efficiently approximate nearest neighbor queries over a set of parallel segments in three dimensions. We connect this problem to approximate nearest neighbor searching under weight constraints and approximate nearest neighbor searching on historical data...
Nonlinear approximation with dictionaries I. Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2004-01-01
We study various approximation classes associated with m-term approximation by elements from a (possibly) redundant dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation...... with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove...... that assuming a certain structure of the dictionary is sufficient and (almost) necessary to obtain stronger results. We give examples of classical dictionaries in L^p spaces and modulation spaces where our results recover some known Jackson type estimates, and discuss som new estimates they provide....
Nonlinear approximation with dictionaries, I: Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
We study various approximation classes associated with $m$-term approximation by elements from a (possibly redundant) dictionary in a Banach space. The standard approximation class associated with the best $m$-term approximation is compared to new classes defined by considering $m......$-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space......, and we prove that assuming a certain structure of the dictionary is sufficient and (almost) necessary to obtain stronger results. We give examples of classical dictionaries in $L^p$ spaces and modulation spaces where our results recover some known Jackson type estimates, and discuss som new estimates...
Bounded-Degree Approximations of Stochastic Networks
Energy Technology Data Exchange (ETDEWEB)
Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar
2017-06-01
We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.
Mapping moveout approximations in TI media
Stovas, Alexey
2013-11-21
Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.
Multilevel Monte Carlo in Approximate Bayesian Computation
Jasra, Ajay
2017-02-13
In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.
Approximate unitary equivalence of normaloid type operators
Zhu, Sen
2015-01-01
In this paper, we explore approximate unitary equivalence of normaloid operators and classify several normaloid type operators including transaloid operators, polynomial-normaloid operators and von Neumann operators up to approximate unitary equivalence. As an application, we explore approximation of transaloid operators with closed numerical ranges. Among other things, it is proved that those transaloid operators with closed numerical ranges are norm dense in the class of transaloid operators.
Uniform analytic approximation of Wigner rotation matrices
Hoffmann, Scott E.
2018-02-01
We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.
A Note on Generalized Approximation Property
Directory of Open Access Journals (Sweden)
Antara Bhar
2013-01-01
Full Text Available We introduce a notion of generalized approximation property, which we refer to as --AP possessed by a Banach space , corresponding to an arbitrary Banach sequence space and a convex subset of , the class of bounded linear operators on . This property includes approximation property studied by Grothendieck, -approximation property considered by Sinha and Karn and Delgado et al., and also approximation property studied by Lissitsin et al. We characterize a Banach space having --AP with the help of -compact operators, -nuclear operators, and quasi--nuclear operators. A particular case for ( has also been characterized.
Local density approximations for relativistic exchange energies
International Nuclear Information System (INIS)
MacDonald, A.H.
1986-01-01
The use of local density approximations to approximate exchange interactions in relativistic electron systems is reviewed. Particular attention is paid to the physical content of these exchange energies by discussing results for the uniform relativistic electron gas from a new point of view. Work on applying these local density approximations in atoms and solids is reviewed and it is concluded that good accuracy is usually possible provided self-interaction corrections are applied. The local density approximations necessary for spin-polarized relativistic systems are discussed and some new results are presented
Approximate maximum parsimony and ancestral maximum likelihood.
Alon, Noga; Chor, Benny; Pardi, Fabio; Rapoport, Anat
2010-01-01
We explore the maximum parsimony (MP) and ancestral maximum likelihood (AML) criteria in phylogenetic tree reconstruction. Both problems are NP-hard, so we seek approximate solutions. We formulate the two problems as Steiner tree problems under appropriate distances. The gist of our approach is the succinct characterization of Steiner trees for a small number of leaves for the two distances. This enables the use of known Steiner tree approximation algorithms. The approach leads to a 16/9 approximation ratio for AML and asymptotically to a 1.55 approximation ratio for MP.
O modelo atômico de Bohr e as suas limitações na interpretação do espectro do átomo de hélio
Directory of Open Access Journals (Sweden)
Danielle Nicolodelli Tenfen
2017-05-01
Full Text Available A inserção de tópicos de física moderna e contemporânea na Educação Básica já não é mais algo tão distante. Os livros didáticos aprovados no último Plano Nacional contemplam, de formas distintas, discussões a esse respeito. Porém, sabe-se que a efetiva implementação desses conteúdos em sala de aula depende da formação – tanto conceitual quanto pedagógica – dos professores. Nesse sentido, o presente artigo visa contribuir com professores e estudantes de graduação em Física, apresentando um breve delineamento histórico que enfatiza o contexto de surgimento do modelo atômico de Niels Bohr, conhecido por situar-se em um período de transição entre Física Clássica e Moderna. Ainda, mostram-se detalhadamente as limitações do modelo de Bohr, evidenciando a necessidade das explicações oriundas da nova Mecânica Quântica para uma descrição adequada do espectro do átomo de hélio. Por fim, apresenta-se uma proposta experimental que consiste na construção de um espectroscópio de baixo custo e problematizam-se alguns dados coletados a partir desse aparato.
Non-Linear Approximation of Bayesian Update
Litvinenko, Alexander
2016-06-23
We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.
Diagonal Pade approximations for initial value problems
International Nuclear Information System (INIS)
Reusch, M.F.; Ratzan, L.; Pomphrey, N.; Park, W.
1987-06-01
Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained. 20 refs., 3 figs., 1 tab
Simultaneous approximation in scales of Banach spaces
International Nuclear Information System (INIS)
Bramble, J.H.; Scott, R.
1978-01-01
The problem of verifying optimal approximation simultaneously in different norms in a Banach scale is reduced to verification of optimal approximation in the highest order norm. The basic tool used is the Banach space interpolation method developed by Lions and Peetre. Applications are given to several problems arising in the theory of finite element methods
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use ... Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, People's Republic of China ...
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...
Quirks of Stirling's Approximation
Macrae, Roderick M.; Allgeier, Benjamin M.
2013-01-01
Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…
On approximating multi-criteria TSP
Manthey, Bodo; Albers, S.; Marion, J.-Y.
2009-01-01
We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP), whose performances are independent of the number $k$ of criteria and come close to the approximation ratios obtained for TSP with a single objective function. We present randomized
On approximating multi-criteria TSP
Manthey, Bodo
We present approximation algorithms for almost all variants of the multicriteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multicriteria maximum traveling salesman problems (Max-TSP). For multicriteria Max-STSP where the edge weights have to be
Boundary Value Problems and Approximate Solutions ...
African Journals Online (AJOL)
In this paper, we discuss about some basic things of boundary value problems. Secondly, we study boundary conditions involving derivatives and obtain finite difference approximations of partial derivatives of boundary value problems. The last section is devoted to determine an approximate solution for boundary value ...
Polynomial approximation approach to transient heat conduction ...
African Journals Online (AJOL)
This work reports polynomial approximation approach to transient heat conduction in a long slab, long cylinder and sphere with linear internal heat generation. It has been shown that the polynomial approximation method is able to calculate average temperature as a function of time for higher value of Biot numbers.
Approximation algorithms for guarding holey polygons ...
African Journals Online (AJOL)
Guarding edges of polygons is a version of art gallery problem.The goal is finding the minimum number of guards to cover the edges of a polygon. This problem is NP-hard, and to our knowledge there are approximation algorithms just for simple polygons. In this paper we present two approximation algorithms for guarding ...
Similarity based approximate reasoning: fuzzy control
Raha, S.; Hossain, A.; Ghosh, S.
2008-01-01
This paper presents an approach to similarity based approximate reasoning that elucidates the connection between similarity and existing approaches to inference in approximate reasoning methodology. A set of axioms is proposed to get a reasonable measure of similarity between two fuzzy sets. The
Improved Dutch Roll Approximation for Hypersonic Vehicle
Directory of Open Access Journals (Sweden)
Liang-Liang Yin
2014-06-01
Full Text Available An improved dutch roll approximation for hypersonic vehicle is presented. From the new approximations, the dutch roll frequency is shown to be a function of the stability axis yaw stability and the dutch roll damping is mainly effected by the roll damping ratio. In additional, an important parameter called roll-to-yaw ratio is obtained to describe the dutch roll mode. Solution shows that large-roll-to-yaw ratio is the generate character of hypersonic vehicle, which results the large error for the practical approximation. Predictions from the literal approximations derived in this paper are compared with actual numerical values for s example hypersonic vehicle, results show the approximations work well and the error is below 10 %.
Approximate error conjugation gradient minimization methods
Kallman, Jeffrey S
2013-05-21
In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.
The tendon approximator device in traumatic injuries.
Forootan, Kamal S; Karimi, Hamid; Forootan, Nazilla-Sadat S
2015-01-01
Precise and tension-free approximation of two tendon endings is the key predictor of outcomes following tendon lacerations and repairs. We evaluate the efficacy of a new tendon approximator device in tendon laceration repairs. In a comparative study, we used our new tendon approximator device in 99 consecutive patients with laceration of 266 tendons who attend a university hospital and evaluated the operative time to repair the tendons, surgeons' satisfaction as well as patient's outcomes in a long-term follow-up. Data were compared with the data of control patients undergoing tendon repair by conventional method. Totally 266 tendons were repaired by approximator device and 199 tendons by conventional technique. 78.7% of patients in first group were male and 21.2% were female. In approximator group 38% of patients had secondary repair of cut tendons and 62% had primary repair. Patients were followed for a mean period of 3years (14-60 months). Time required for repair of each tendon was significantly reduced with the approximator device (2 min vs. 5.5 min, ptendon repair were identical in the two groups and were not significantly different. 1% of tendons in group A and 1.2% in group B had rupture that was not significantly different. The new nerve approximator device is cheap, feasible to use and reduces the time of tendon repair with sustained outcomes comparable to the conventional methods.
Hardness and Approximation for Network Flow Interdiction
Chestnut, Stephen R.; Zenklusen, Rico
2015-01-01
In the Network Flow Interdiction problem an adversary attacks a network in order to minimize the maximum s-t-flow. Very little is known about the approximatibility of this problem despite decades of interest in it. We present the first approximation hardness, showing that Network Flow Interdiction and several of its variants cannot be much easier to approximate than Densest k-Subgraph. In particular, any $n^{o(1)}$-approximation algorithm for Network Flow Interdiction would imply an $n^{o(1)}...
Regression with Sparse Approximations of Data
DEFF Research Database (Denmark)
Noorzad, Pardis; Sturm, Bob L.
2012-01-01
We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based...
Approximately Liner Phase IIR Digital Filter Banks
Directory of Open Access Journals (Sweden)
J. D. Ćertić
2013-11-01
Full Text Available In this paper, uniform and nonuniform digital filter banks based on approximately linear phase IIR filters and frequency response masking technique (FRM are presented. Both filter banks are realized as a connection of an interpolated half-band approximately linear phase IIR filter as a first stage of the FRM design and an appropriate number of masking filters. The masking filters are half-band IIR filters with an approximately linear phase. The resulting IIR filter banks are compared with linear-phase FIR filter banks exhibiting similar magnitude responses. The effects of coefficient quantization are analyzed.
Mathematical analysis, approximation theory and their applications
Gupta, Vijay
2016-01-01
Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.
Approximation of the semi-infinite interval
Directory of Open Access Journals (Sweden)
A. McD. Mercer
1980-01-01
Full Text Available The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞ based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(uxkα+β−1Γ(kα+βf(kαuThe present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.
Pion-nucleus cross sections approximation
International Nuclear Information System (INIS)
Barashenkov, V.S.; Polanski, A.; Sosnin, A.N.
1990-01-01
Analytical approximation of pion-nucleus elastic and inelastic interaction cross-section is suggested, with could be applied in the energy range exceeding several dozens of MeV for nuclei heavier than beryllium. 3 refs.; 4 tabs
Square well approximation to the optical potential
International Nuclear Information System (INIS)
Jain, A.K.; Gupta, M.C.; Marwadi, P.R.
1976-01-01
Approximations for obtaining T-matrix elements for a sum of several potentials in terms of T-matrices for individual potentials are studied. Based on model calculations for S-wave for a sum of two separable non-local potentials of Yukawa type form factors and a sum of two delta function potentials, it is shown that the T-matrix for a sum of several potentials can be approximated satisfactorily over all the energy regions by the sum of T-matrices for individual potentials. Based on this, an approximate method for finding T-matrix for any local potential by approximating it by a sum of suitable number of square wells is presented. This provides an interesting way to calculate the T-matrix for any arbitary potential in terms of Bessel functions to a good degree of accuracy. The method is applied to the Saxon-Wood potentials and good agreement with exact results is found. (author)
Seismic wave extrapolation using lowrank symbol approximation
Fomel, Sergey
2012-04-30
We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.
Steepest descent approximations for accretive operator equations
International Nuclear Information System (INIS)
Chidume, C.E.
1993-03-01
A necessary and sufficient condition is established for the strong convergence of the steepest descent approximation to a solution of equations involving quasi-accretive operators defined on a uniformly smooth Banach space. (author). 49 refs
Degree of Approximation and Green Potential
Directory of Open Access Journals (Sweden)
M. Simkani
2009-03-01
Full Text Available We will relate the degree of rational approximation of a meromorphic function f to the minimum value, on the natural boundary of f, of Green potential of the weak∗ limit of the normalized pole-counting measures
Low Rank Approximation Algorithms, Implementation, Applications
Markovsky, Ivan
2012-01-01
Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
APPROXIMATE DEVELOPMENTS FOR SURFACES OF REVOLUTION
Directory of Open Access Journals (Sweden)
Mădălina Roxana Buneci
2016-12-01
Full Text Available The purpose of this paper is provide a set of Maple procedures to construct approximate developments of a general surface of revolution generalizing the well-known gore method for sphere
An overview on Approximate Bayesian computation*
Directory of Open Access Journals (Sweden)
Baragatti Meïli
2014-01-01
Full Text Available Approximate Bayesian computation techniques, also called likelihood-free methods, are one of the most satisfactory approach to intractable likelihood problems. This overview presents recent results since its introduction about ten years ago in population genetics.
Approximation for the adjoint neutron spectrum
International Nuclear Information System (INIS)
Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da
2002-01-01
The proposal of this work is the determination of an analytical approximation which is capable to reproduce the adjoint neutron flux for the energy range of the narrow resonances (NR). In a previous work we developed a method for the calculation of the adjoint spectrum which was calculated from the adjoint neutron balance equations, that were obtained by the collision probabilities method, this method involved a considerable quantity of numerical calculation. In the analytical method some approximations were done, like the multiplication of the escape probability in the fuel by the adjoint flux in the moderator, and after these approximations, taking into account the case of the narrow resonances, were substituted in the adjoint neutron balance equation for the fuel, resulting in an analytical approximation for the adjoint flux. The results obtained in this work were compared to the results generated with the reference method, which demonstrated a good and precise results for the adjoint neutron flux for the narrow resonances. (author)
TMB: Automatic differentiation and laplace approximation
DEFF Research Database (Denmark)
Kristensen, Kasper; Nielsen, Anders; Berg, Casper Willestofte
2016-01-01
are automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (approximate to 10(6)) and parameters (approximate to 10...... computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects......(3)). Computation times using ADMB and TMB are compared on a suite of examples ranging from simple models to large spatial models where the random effects are a Gaussian random field. Speedups ranging from 1.5 to about 100 are obtained with increasing gains for large problems...
Approximations of Stochastic Partial Differential Equations
Di Nunno, Giulia; Zhang, Tusheng
2014-01-01
In this paper we show that solutions of stochastic partial differ- ential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks. Applications to stochastic Burgers equations are discussed.
Saddlepoint approximation methods in financial engineering
Kwok, Yue Kuen
2018-01-01
This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables. The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quanti...
Approximative solutions of stochastic optimization problem
Czech Academy of Sciences Publication Activity Database
Lachout, Petr
2010-01-01
Roč. 46, č. 3 (2010), s. 513-523 ISSN 0023-5954 R&D Projects: GA ČR GA201/08/0539 Institutional research plan: CEZ:AV0Z10750506 Keywords : Stochastic optimization problem * sensitivity * approximative solution Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/SI/lachout-approximative solutions of stochastic optimization problem.pdf
Nonlinear approximation with nonstationary Gabor frames
DEFF Research Database (Denmark)
Ottosen, Emil Solsbæk; Nielsen, Morten
2018-01-01
We consider sparseness properties of adaptive time-frequency representations obtained using nonstationary Gabor frames (NSGFs). NSGFs generalize classical Gabor frames by allowing for adaptivity in either time or frequency. It is known that the concept of painless nonorthogonal expansions...... resolution. Based on this characterization we prove an upper bound on the approximation error occurring when thresholding the coefficients of the corresponding frame expansions. We complement the theoretical results with numerical experiments, estimating the rate of approximation obtained from thresholding...
Lattice quantum chromodynamics with approximately chiral fermions
Energy Technology Data Exchange (ETDEWEB)
Hierl, Dieter
2008-05-15
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, s.
1999-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G(1) surface consisting of pieces of cones or cylinders of revolution or a G(r) NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produ...... robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in shipbuilding. (C) 1999 Academic Press....
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, S.
1998-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G_1 surface consisting of pieces of cones or cylinders of revolution or a G_r NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...... robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in shipbuilding....
Lattice quantum chromodynamics with approximately chiral fermions
International Nuclear Information System (INIS)
Hierl, Dieter
2008-05-01
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the Θ + pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
Nonlinear Stochastic PDEs: Analysis and Approximations
2016-05-23
Approximation to Nonlinear SPDEs with Discrete Random Variables , SIAM J Scientific Computing, (08 2015): 1872. doi: R. Mikulevicius, B. Rozovskii. On...multiplicative discrete random variables , ( ) S. Lototsky, B. Rozovsky. Stochastic Partial Differential Equations, (09 2015) B. Rozovsky, R...B. Rozovsky and G.E. Karniadakis, "Adaptive Wick-Malliavin approximation to nonlinear SPDEs with discrete random variables ," SIAM J. Sci. Comput., 37
Polynomial approximation of functions in Sobolev spaces
International Nuclear Information System (INIS)
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces
Approximation properties ofλ-Bernstein operators.
Cai, Qing-Bo; Lian, Bo-Yong; Zhou, Guorong
2018-01-01
In this paper, we introduce a new type λ -Bernstein operators with parameter [Formula: see text], we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Finally, we give some graphs and numerical examples to show the convergence of [Formula: see text] to [Formula: see text], and we see that in some cases the errors are smaller than [Formula: see text] to f .
Rough Sets Approximations for Learning Outcomes
Encheva, Sylvia; Tumin, Sharil
Discovering dependencies between students' responses and their level of mastering of a particular skill is very important in the process of developing intelligent tutoring systems. This work is an approach to attain a higher level of certainty while following students' learning progress. Rough sets approximations are applied for assessing students understanding of a concept. Consecutive responses from each individual learner to automated tests are placed in corresponding rough sets approximations. The resulting path provides strong indication about the current level of learning outcomes.
Approximations for the Erlang Loss Function
DEFF Research Database (Denmark)
Mejlbro, Leif
1998-01-01
Theoretically, at least three formulae are needed for arbitrarily good approximates of the Erlang Loss Function. In the paper, for convenience five formulae are presented guaranteeing a relative error <1E-2, and methods are indicated for improving this bound.......Theoretically, at least three formulae are needed for arbitrarily good approximates of the Erlang Loss Function. In the paper, for convenience five formulae are presented guaranteeing a relative error
Approximating centrality in evolving graphs: toward sublinearity
Priest, Benjamin W.; Cybenko, George
2017-05-01
The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.
The Grammar of Approximating Number Pairs
Eriksson, Kimmo; Bailey, Drew H.; Geary, David C.
2009-01-01
We studied approximating pairs of numbers (a, b) used to estimate quantity in a single phrase (“two, three years ago”). Pollmann and Jansen (1996) found that only a few of the many possible pairs are actually used, suggesting an interaction between the ways in which people estimate quantity and their use of quantitative phrases in colloquial speech. They proposed a set of rules that describe which approximating pairs are used in Dutch phrases. We revisit this issue in an analysis of Swedish and American language corpora and in a series of three experiments in which Swedish and American adults rated the acceptability of various approximating pairs, and created approximating pairs of their own in response to various estimation tasks. We find evidence for Pollmann’s and Jansen’s rules in both Swedish and English phrases, but also identify additional rules and substantial individual and cross-language variation. We discuss implications for the origin of this loose “grammar” of approximating pairs. PMID:20234023
'LTE-diffusion approximation' for arc calculations
International Nuclear Information System (INIS)
Lowke, J J; Tanaka, M
2006-01-01
This paper proposes the use of the 'LTE-diffusion approximation' for predicting the properties of electric arcs. Under this approximation, local thermodynamic equilibrium (LTE) is assumed, with a particular mesh size near the electrodes chosen to be equal to the 'diffusion length', based on D e /W, where D e is the electron diffusion coefficient and W is the electron drift velocity. This approximation overcomes the problem that the equilibrium electrical conductivity in the arc near the electrodes is almost zero, which makes accurate calculations using LTE impossible in the limit of small mesh size, as then voltages would tend towards infinity. Use of the LTE-diffusion approximation for a 200 A arc with a thermionic cathode gives predictions of total arc voltage, electrode temperatures, arc temperatures and radial profiles of heat flux density and current density at the anode that are in approximate agreement with more accurate calculations which include an account of the diffusion of electric charges to the electrodes, and also with experimental results. Calculations, which include diffusion of charges, agree with experimental results of current and heat flux density as a function of radius if the Milne boundary condition is used at the anode surface rather than imposing zero charge density at the anode
Approximate Bayesian evaluations of measurement uncertainty
Possolo, Antonio; Bodnar, Olha
2018-04-01
The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.
Semiclassical initial value approximation for Green's function.
Kay, Kenneth G
2010-06-28
A semiclassical initial value approximation is obtained for the energy-dependent Green's function. For a system with f degrees of freedom the Green's function expression has the form of a (2f-1)-dimensional integral over points on the energy surface and an integral over time along classical trajectories initiated from these points. This approximation is derived by requiring an integral ansatz for Green's function to reduce to Gutzwiller's semiclassical formula when the integrations are performed by the stationary phase method. A simpler approximation is also derived involving only an (f-1)-dimensional integral over momentum variables on a Poincare surface and an integral over time. The relationship between the present expressions and an earlier initial value approximation for energy eigenfunctions is explored. Numerical tests for two-dimensional systems indicate that good accuracy can be obtained from the initial value Green's function for calculations of autocorrelation spectra and time-independent wave functions. The relative advantages of initial value approximations for the energy-dependent Green's function and the time-dependent propagator are discussed.
Trajectory averaging for stochastic approximation MCMC algorithms
Liang, Faming
2010-10-01
The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.
The grammar of approximating number pairs.
Eriksson, Kimmo; Bailey, Drew H; Geary, David C
2010-04-01
In the present article, we studied approximating pairs of numbers (a, b) that were used to estimate quantity in a single phrase ("two, three years ago"). Pollmann and Jansen (1996) found that only a few of the many possible pairs are actually used, suggesting an interaction between the ways in which people estimate quantity and their use of quantitative phrases in colloquial speech. They proposed a set of rules that describe which approximating pairs are used in Dutch phrases. We revisited this issue in an analysis of Swedish and American language corpora and in a series of three experiments in which Swedish and American adults rated the acceptability of various approximating pairs and created approximating pairs of their own in response to various estimation tasks. We found evidence for Pollmann and Jansen's rules in both Swedish and English phrases, but we also identified additional rules and substantial individual and cross-language variation. We will discuss implications for the origin of this loose "grammar" of approximating pairs.
Multilevel weighted least squares polynomial approximation
Haji-Ali, Abdul-Lateef
2017-06-30
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.
Numerical approximation of partial differential equations
Bartels, Sören
2016-01-01
Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular ...
Fast wavelet based sparse approximate inverse preconditioner
Energy Technology Data Exchange (ETDEWEB)
Wan, W.L. [Univ. of California, Los Angeles, CA (United States)
1996-12-31
Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.
Piecewise-Cubic Approximation in Autotracking Mode
Dikoussar, N D
2004-01-01
A method for piecewise-cubic approximation within the frame of four-point transforms is proposed. The knots of the segments are detected in autotracking mode using a digitized curve. A three-point cubic parametric spline (TPS) is used as a model of a local approximant. A free parameter $\\theta$ (a coefficient at $x^{3}$) is found in a line following mode, using step-by-step averaging. A formula for expression of the free parameter via a length of the segment and values of a function and derivatives in joining points is received. The $C^{1}$-smoothness depends on the accuracy of the $\\theta$-estimate. The stability of the method w.r.t. input errors is shown as well. The key parameters of the approximation are: the parameters of the basic functions, the variance of the input errors, and a sampling step. The efficiency of the method is shown by numerical calculations on test examples.
On transparent potentials: a Born approximation study
International Nuclear Information System (INIS)
Coudray, C.
1980-01-01
In the frame of the scattering inverse problem at fixed energy, a class of potentials transparent in Born approximation is obtained. All these potentials are spherically symmetric and are oscillating functions of the reduced radial variable. Amongst them, the Born approximation of the transparent potential of the Newton-Sabatier method is found. In the same class, quasi-transparent potentials are exhibited. Very general features of potentials transparent in Born approximation are then stated. And bounds are given for the exact scattering amplitudes corresponding to most of the potentials previously exhibited. These bounds, obtained at fixed energy, and for large values of the angular momentum, are found to be independent on the energy
The adiabatic approximation in multichannel scattering
International Nuclear Information System (INIS)
Schulte, A.M.
1978-01-01
Using two-dimensional models, an attempt has been made to get an impression of the conditions of validity of the adiabatic approximation. For a nucleon bound to a rotating nucleus the Coriolis coupling is neglected and the relation between this nuclear Coriolis coupling and the classical Coriolis force has been examined. The approximation for particle scattering from an axially symmetric rotating nucleus based on a short duration of the collision, has been combined with an approximation based on the limitation of angular momentum transfer between particle and nucleus. Numerical calculations demonstrate the validity of the new combined method. The concept of time duration for quantum mechanical collisions has also been studied, as has the collective description of permanently deformed nuclei. (C.F.)
The binary collision approximation: Background and introduction
International Nuclear Information System (INIS)
Robinson, M.T.
1992-08-01
The binary collision approximation (BCA) has long been used in computer simulations of the interactions of energetic atoms with solid targets, as well as being the basis of most analytical theory in this area. While mainly a high-energy approximation, the BCA retains qualitative significance at low energies and, with proper formulation, gives useful quantitative information as well. Moreover, computer simulations based on the BCA can achieve good statistics in many situations where those based on full classical dynamical models require the most advanced computer hardware or are even impracticable. The foundations of the BCA in classical scattering are reviewed, including methods of evaluating the scattering integrals, interaction potentials, and electron excitation effects. The explicit evaluation of time at significant points on particle trajectories is discussed, as are scheduling algorithms for ordering the collisions in a developing cascade. An approximate treatment of nearly simultaneous collisions is outlined and the searching algorithms used in MARLOWE are presented
Minimal entropy approximation for cellular automata
International Nuclear Information System (INIS)
Fukś, Henryk
2014-01-01
We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim. (paper)
APPROXIMATE INTEGRATION OF HIGHLY OSCILLATING FUNCTIONS
Directory of Open Access Journals (Sweden)
I. N. Melashko
2017-01-01
Full Text Available Elementary approximate formulae for numerical integration of functions containing oscillating factors of a special form with a parameter have been proposed in the paper. In this case general quadrature formulae can be used only at sufficiently small values of the parameter. Therefore, it is necessary to consider in advance presence of strongly oscillating factors in order to obtain formulae for numerical integration which are suitable in the case when the parameter is changing within wide limits. This can be done by taking into account such factors as weighting functions. Moreover, since the parameter can take values which cannot always be predicted in advance, approximate formulae for calculation of such integrals should be constructed in such a way that they contain this parameter in a letter format and they are suitable for calculation at any and particularly large values of the parameter. Computational rules with such properties are generally obtained by dividing an interval of integration into elementary while making successive approximation of the integral density at each elementary interval with polynomials of the first, second and third degrees and taking the oscillating factors as weighting functions. The paper considers the variant when density of the integrals at each elementary interval is approximated by a polynomial of zero degree that is a constant which is equal to the value of density in the middle of the interval. At the same time one approximate formula for calculation of an improper integral with infinite interval of the function with oscillating factor of a special type has been constructed in the paper. In this case it has been assumed that density of the improper integral rather quickly goes to zero when an argument module is increasing indefinitely. In other words it is considered as small to negligible outside some finite interval. Uniforms in parameter used for evaluation of errors in approximate formulae have been
Stopping Rules for Linear Stochastic Approximation
Wada, Takayuki; Itani, Takamitsu; Fujisaki, Yasumasa
Stopping rules are developed for stochastic approximation which is an iterative method for solving an unknown equation based on its consecutive residuals corrupted by additive random noise. It is assumed that the equation is linear and the noise is independent and identically distributed random vectors with zero mean and a bounded covariance. Then, the number of iterations for achieving a given probabilistic accuracy of the resultant solution is derived, which gives a rigorous stopping rule for the stochastic approximation. This number is polynomial of the problem size.
Computational topology for approximations of knots
Directory of Open Access Journals (Sweden)
Ji Li
2014-10-01
• a sum of total curvature and derivative. High degree Bézier curves are often used as smooth representations, where computational efficiency is a practical concern. Subdivision can produce PL approximations for a given B\\'ezier curve, fulfilling the above two conditions. The primary contributions are: (i a priori bounds on the number of subdivision iterations sufficient to achieve a PL approximation that is ambient isotopic to the original B\\'ezier curve, and (ii improved iteration bounds over those previously established.
On the dipole approximation with error estimates
Boßmann, Lea; Grummt, Robert; Kolb, Martin
2018-01-01
The dipole approximation is employed to describe interactions between atoms and radiation. It essentially consists of neglecting the spatial variation of the external field over the atom. Heuristically, this is justified by arguing that the wavelength is considerably larger than the atomic length scale, which holds under usual experimental conditions. We prove the dipole approximation in the limit of infinite wavelengths compared to the atomic length scale and estimate the rate of convergence. Our results include N-body Coulomb potentials and experimentally relevant electromagnetic fields such as plane waves and laser pulses.
Static correlation beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian Sommer
2014-01-01
derived from Hedin's equations (Random Phase Approximation (RPA), Time-dependent Hartree-Fock (TDHF), Bethe-Salpeter equation (BSE), and Time-Dependent GW) all reproduce the correct dissociation limit. We also show that the BSE improves the correlation energies obtained within RPA and TDHF significantly...... for intermediate binding distances. A Hubbard model for the dimer allows us to obtain exact analytical results for the various approximations, which is readily compared with the exact diagonalization of the model. Moreover, the model is shown to reproduce all the qualitative results from the ab initio calculations...
Faster and Simpler Approximation of Stable Matchings
Directory of Open Access Journals (Sweden)
Katarzyna Paluch
2014-04-01
Full Text Available We give a 3 2 -approximation algorithm for finding stable matchings that runs in O(m time. The previous most well-known algorithm, by McDermid, has the same approximation ratio but runs in O(n3/2m time, where n denotes the number of people andm is the total length of the preference lists in a given instance. In addition, the algorithm and the analysis are much simpler. We also give the extension of the algorithm for computing stable many-to-many matchings.
An approximate analytical approach to resampling averages
DEFF Research Database (Denmark)
Malzahn, Dorthe; Opper, M.
2004-01-01
Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach for appr......Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach...
APPROXIMATION OF PROBABILITY DISTRIBUTIONS IN QUEUEING MODELS
Directory of Open Access Journals (Sweden)
T. I. Aliev
2013-03-01
Full Text Available For probability distributions with variation coefficient, not equal to unity, mathematical dependences for approximating distributions on the basis of first two moments are derived by making use of multi exponential distributions. It is proposed to approximate distributions with coefficient of variation less than unity by using hypoexponential distribution, which makes it possible to generate random variables with coefficient of variation, taking any value in a range (0; 1, as opposed to Erlang distribution, having only discrete values of coefficient of variation.
Approximate Controllability of Fractional Integrodifferential Evolution Equations
Directory of Open Access Journals (Sweden)
R. Ganesh
2013-01-01
Full Text Available This paper addresses the issue of approximate controllability for a class of control system which is represented by nonlinear fractional integrodifferential equations with nonlocal conditions. By using semigroup theory, p-mean continuity and fractional calculations, a set of sufficient conditions, are formulated and proved for the nonlinear fractional control systems. More precisely, the results are established under the assumption that the corresponding linear system is approximately controllable and functions satisfy non-Lipschitz conditions. The results generalize and improve some known results.
Approximated Fractional Order Chebyshev Lowpass Filters
Directory of Open Access Journals (Sweden)
Todd Freeborn
2015-01-01
Full Text Available We propose the use of nonlinear least squares optimization to approximate the passband ripple characteristics of traditional Chebyshev lowpass filters with fractional order steps in the stopband. MATLAB simulations of (1+α, (2+α, and (3+α order lowpass filters with fractional steps from α = 0.1 to α = 0.9 are given as examples. SPICE simulations of 1.2, 1.5, and 1.8 order lowpass filters using approximated fractional order capacitors in a Tow-Thomas biquad circuit validate the implementation of these filter circuits.
Approximate Inference and Deep Generative Models
CERN. Geneva
2018-01-01
Advances in deep generative models are at the forefront of deep learning research because of the promise they offer for allowing data-efficient learning, and for model-based reinforcement learning. In this talk I'll review a few standard methods for approximate inference and introduce modern approximations which allow for efficient large-scale training of a wide variety of generative models. Finally, I'll demonstrate several important application of these models to density estimation, missing data imputation, data compression and planning.
Approximation result toward nearest neighbor heuristic
Directory of Open Access Journals (Sweden)
Monnot Jér"me
2002-01-01
Full Text Available In this paper, we revisit the famous heuristic called nearest neighbor (N N for the traveling salesman problem under maximization and minimization goal. We deal with variants where the edge costs belong to interval Ša;taĆ for a>0 and t>1, which certainly corresponds to practical cases of these problems. We prove that NN is a (t+1/2t-approximation for maxTSPŠa;taĆ and a 2/(t+1-approximation for minTSPŠa;taĆ under the standard performance ratio. Moreover, we show that these ratios are tight for some instances.
Radiation forces in the discrete dipole approximation
Hoekstra, A.G.; Frijlink, M.O.; Waters, L.B.F.M.; Sloot, P.M.A.
2001-01-01
The theory of the discrete-dipole approximation (DDA) for light scattering is extended to allow for the calculation of radiation forces on each dipole in the DDA model. Starting with the theory of Draine and Weingartner [Astrophys. J. 470, 551 (1996)] we derive an expression for the radiation force
Perturbation of operators and approximation of spectrum
Indian Academy of Sciences (India)
The pure linear algebraic approach is the main advantage of the results here. Keywords. Operator .... The paper is organized as follows. In §2, the approximation results are extended to the case of a one-parameter norm continuous family of operators. In §3, the spectral gap prediction results are proved with some examples.
Isotopic Approximation of Implicit Curves and Surfaces
Plantinga, Simon; Vegter, Gert
2004-01-01
Implicit surfaces are defined as the zero set of a function F: R3 → R. Although several algorithms exist for generating piecewise linear approximations, most of them are based on a user-defined stepsize or bounds to indicate the precision, and therefore cannot guarantee topological correctness.
A rational approximation of the effectiveness factor
DEFF Research Database (Denmark)
Wedel, Stig; Luss, Dan
1980-01-01
A fast, approximate method of calculating the effectiveness factor for arbitrary rate expressions is presented. The method does not require any iterative or interpolative calculations. It utilizes the well known asymptotic behavior for small and large Thiele moduli to derive a rational function w...
An approximate analytical approach to resampling averages
DEFF Research Database (Denmark)
Malzahn, Dorthe; Opper, M.
2004-01-01
Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach for appr...
Approximate solutions to variational inequalities and applications
Directory of Open Access Journals (Sweden)
M. Beatrice Lignola
1994-11-01
Full Text Available The aim of this paper is to investigate two concepts of approximate solutions to parametric variational inequalities in topological vector spaces for which the corresponding solution map is closed graph and/or lower semicontinuous and to apply the results to the stability of optimization problems with variational inequality constrains.
Nanostructures: Scattering beyond the Born approximation
Grigoriev, S.V.; Syromyatnikov, A. V.; Chumakov, A. P.; Grigoryeva, N.A.; Napolskii, K.S.; Roslyakov, I. V.; Eliseev, A.A.; Petukhov, A.V.; Eckerlebe, H.
2010-01-01
The neutron scattering on a two-dimensional ordered nanostructure with the third nonperiodic dimension can go beyond the Born approximation. In our model supported by the exact theoretical solution a well-correlated hexagonal porous structure of anodic aluminum oxide films acts as a peculiar
Large hierarchies from approximate R symmetries
International Nuclear Information System (INIS)
Kappl, Rolf; Ratz, Michael; Vaudrevange, Patrick K.S.
2008-12-01
We show that hierarchically small vacuum expectation values of the superpotential in supersymmetric theories can be a consequence of an approximate R symmetry. We briefly discuss the role of such small constants in moduli stabilization and understanding the huge hierarchy between the Planck and electroweak scales. (orig.)
Approximability and Parameterized Complexity of Minmax Values
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Hansen, Thomas Dueholm; Miltersen, Peter Bro
2008-01-01
We consider approximating the minmax value of a multi player game in strategic form. Tightening recent bounds by Borgs et al., we observe that approximating the value with a precision of ε log n digits (for any constant ε > 0) is NP-hard, where n is the size of the game. On the other hand......, approximating the value with a precision of c log log n digits (for any constant c ≥ 1) can be done in quasi-polynomial time. We consider the parameterized complexity of the problem, with the parameter being the number of pure strategies k of the player for which the minmax value is computed. We show...... that if there are three players, k = 2 and there are only two possible rational payoffs, the minmax value is a rational number and can be computed exactly in linear time. In the general case, we show that the value can be approximated wigh any polynomial number of digits of accuracy in time n^O(k) . On the other hand, we...
An Approximate Bayesian Fundamental Frequency Estimator
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Jensen, Søren Holdt
2012-01-01
Joint fundamental frequency and model order estimation is an important problem in several applications such as speech and music processing. In this paper, we develop an approximate estimation algorithm of these quantities using Bayesian inference. The inference about the fundamental frequency...
Pade approximant calculations for neutron escape probability
International Nuclear Information System (INIS)
El Wakil, S.A.; Saad, E.A.; Hendi, A.A.
1984-07-01
The neutron escape probability from a non-multiplying slab containing internal source is defined in terms of a functional relation for the scattering function for the diffuse reflection problem. The Pade approximant technique is used to get numerical results which compare with exact results. (author)
Uniform semiclassical approximation for absorptive scattering systems
International Nuclear Information System (INIS)
Hussein, M.S.; Pato, M.P.
1987-07-01
The uniform semiclassical approximation of the elastic scattering amplitude is generalized to absorptive systems. An integral equation is derived which connects the absorption modified amplitude to the absorption free one. Division of the amplitude into a diffractive and refractive components is then made possible. (Author) [pt
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-11-30
We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.
Nonlinear approximation with dictionaries. II. Inverse Estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2006-01-01
In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block...
Nonlinear approximation with dictionaries,.. II: Inverse estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
In this paper we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for separated decomposable dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually...
Generalized Lower and Upper Approximations in Quantales
Directory of Open Access Journals (Sweden)
Qimei Xiao
2012-01-01
Full Text Available We introduce the concepts of set-valued homomorphism and strong set-valued homomorphism of a quantale which are the extended notions of congruence and complete congruence, respectively. The properties of generalized lower and upper approximations, constructed by a set-valued mapping, are discussed.
Uncertainty relations for approximation and estimation
Energy Technology Data Exchange (ETDEWEB)
Lee, Jaeha, E-mail: jlee@post.kek.jp [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Tsutsui, Izumi, E-mail: izumi.tsutsui@kek.jp [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan)
2016-05-27
We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for proxy functions used for the approximation is given by Aharonov's weak value, which also determines the classical Fisher information in parameter estimation, turning our inequality into the genuine Cramér–Rao inequality. Since the standard form of the uncertainty relation arises as a special case of our inequality, and since the parameter estimation is available as well, our inequality can treat both the position–momentum and the time–energy relations in one framework albeit handled differently. - Highlights: • Several inequalities interpreted as uncertainty relations for approximation/estimation are derived from a single ‘versatile inequality’. • The ‘versatile inequality’ sets a limit on the approximation of an observable and/or the estimation of a parameter by another observable. • The ‘versatile inequality’ turns into an elaboration of the Robertson–Kennard (Schrödinger) inequality and the Cramér–Rao inequality. • Both the position–momentum and the time–energy relation are treated in one framework. • In every case, Aharonov's weak value arises as a key geometrical ingredient, deciding the optimal choice for the proxy functions.
An approximate classical unimolecular reaction rate theory
Zhao, Meishan; Rice, Stuart A.
1992-05-01
We describe a classical theory of unimolecular reaction rate which is derived from the analysis of Davis and Gray by use of simplifying approximations. These approximations concern the calculation of the locations of, and the fluxes of phase points across, the bottlenecks to fragmentation and to intramolecular energy transfer. The bottleneck to fragment separation is represented as a vibration-rotation state dependent separatrix, which approximation is similar to but extends and improves the approximations for the separatrix introduced by Gray, Rice, and Davis and by Zhao and Rice. The novel feature in our analysis is the representation of the bottlenecks to intramolecular energy transfer as dividing surfaces in phase space; the locations of these dividing surfaces are determined by the same conditions as locate the remnants of robust tori with frequency ratios related to the golden mean (in a two degree of freedom system these are the cantori). The flux of phase points across each dividing surface is calculated with an analytic representation instead of a stroboscopic mapping. The rate of unimolecular reaction is identified with the net rate at which phase points escape from the region of quasiperiodic bounded motion to the region of free fragment motion by consecutively crossing the dividing surfaces for intramolecular energy exchange and the separatrix. This new theory generates predictions of the rates of predissociation of the van der Waals molecules HeI2, NeI2 and ArI2 which are in very good agreement with available experimental data.
Markov operators, positive semigroups and approximation processes
Altomare, Francesco; Leonessa, Vita; Rasa, Ioan
2015-01-01
In recent years several investigations have been devoted to the study of large classes of (mainly degenerate) initial-boundary value evolution problems in connection with the possibility to obtain a constructive approximation of the associated positive C_0-semigroups. In this research monograph we present the main lines of a theory which finds its root in the above-mentioned research field.
Orthorhombic rational approximants for decagonal quasicrystals
Indian Academy of Sciences (India)
Unknown
An important exercise in the study of rational approximants is to derive their metric, especially in relation to the corresponding quasicrystal or the underlying clusters. Kuo's model has ..... the smaller diagonal of the fat rhombus in the Penrose tiling. This length scale is obtained by a section along a1 in the Penrose tiling and ...
Uncertainty relations for approximation and estimation
International Nuclear Information System (INIS)
Lee, Jaeha; Tsutsui, Izumi
2016-01-01
We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for proxy functions used for the approximation is given by Aharonov's weak value, which also determines the classical Fisher information in parameter estimation, turning our inequality into the genuine Cramér–Rao inequality. Since the standard form of the uncertainty relation arises as a special case of our inequality, and since the parameter estimation is available as well, our inequality can treat both the position–momentum and the time–energy relations in one framework albeit handled differently. - Highlights: • Several inequalities interpreted as uncertainty relations for approximation/estimation are derived from a single ‘versatile inequality’. • The ‘versatile inequality’ sets a limit on the approximation of an observable and/or the estimation of a parameter by another observable. • The ‘versatile inequality’ turns into an elaboration of the Robertson–Kennard (Schrödinger) inequality and the Cramér–Rao inequality. • Both the position–momentum and the time–energy relation are treated in one framework. • In every case, Aharonov's weak value arises as a key geometrical ingredient, deciding the optimal choice for the proxy functions.
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
groups have invariant translation approximation property (ITAP, see Definition 2.2). He also pointed out that there was no serious difficulty in extending the main theorem to fine hyperbolic graphs, but he did not outline the proof. So in this paper, we first give a proof for this extension, see Theorem 1.1 below. Then we define ...
Approximate Dynamic Programming by Practical Examples
Mes, Martijn R.K.; Perez Rivera, Arturo Eduardo; Boucherie, Richard; van Dijk, Nico M.
2017-01-01
Computing the exact solution of an MDP model is generally difficult and possibly intractable for realistically sized problem instances. A powerful technique to solve the large scale discrete time multistage stochastic control processes is Approximate Dynamic Programming (ADP). Although ADP is used
Approximation Algorithms for Model-Based Diagnosis
Feldman, A.B.
2010-01-01
Model-based diagnosis is an area of abductive inference that uses a system model, together with observations about system behavior, to isolate sets of faulty components (diagnoses) that explain the observed behavior, according to some minimality criterion. This thesis presents greedy approximation
Quasilinear theory without the random phase approximation
International Nuclear Information System (INIS)
Weibel, E.S.; Vaclavik, J.
1980-08-01
The system of quasilinear equations is derived without making use of the random phase approximation. The fluctuating quantities are described by the autocorrelation function of the electric field using the techniques of Fourier analysis. The resulting equations posses the necessary conservation properties, but comprise new terms which hitherto have been lost in the conventional derivations
Statistical model semiquantitatively approximates arabinoxylooligosaccharides' structural diversity
DEFF Research Database (Denmark)
Dotsenko, Gleb; Nielsen, Michael Krogsgaard; Lange, Lene
2016-01-01
(wheat flour arabinoxylan (arabinose/xylose, A/X = 0.47); grass arabinoxylan (A/X = 0.24); wheat straw arabinoxylan (A/X = 0.15); and hydrothermally pretreated wheat straw arabinoxylan (A/X = 0.05)), is semiquantitatively approximated using the proposed model. The suggested approach can be applied...
Upper Bounds on Numerical Approximation Errors
DEFF Research Database (Denmark)
Raahauge, Peter
2004-01-01
This paper suggests a method for determining rigorous upper bounds on approximationerrors of numerical solutions to infinite horizon dynamic programming models.Bounds are provided for approximations of the value function and the policyfunction as well as the derivatives of the value function...
Multi-Interpretation Operators and Approximate Classification
Engelfriet, J.; Treur, J.
2003-01-01
In this paper non-classical logical techniques are introduced to formalize the analysis of multi-interpretable observation information, in particular in approximate classification processes where information on attributes of an object is to be inferred on the basis of observable properties of the
Approximate Furthest Neighbor in High Dimensions
DEFF Research Database (Denmark)
Pagh, Rasmus; Silvestri, Francesco; Sivertsen, Johan von Tangen
2015-01-01
-dimensional Euclidean space. We build on the technique of Indyk (SODA 2003), storing random projections to provide sublinear query time for AFN. However, we introduce a different query algorithm, improving on Indyk’s approximation factor and reducing the running time by a logarithmic factor. We also present a variation...
Padé approximations and diophantine geometry.
Chudnovsky, D V; Chudnovsky, G V
1985-04-01
Using methods of Padé approximations we prove a converse to Eisenstein's theorem on the boundedness of denominators of coefficients in the expansion of an algebraic function, for classes of functions, parametrized by meromorphic functions. This result is applied to the Tate conjecture on the effective description of isogenies for elliptic curves.
tt in the soft-gluon approximation
Indian Academy of Sciences (India)
April 2002 physics pp. 575–590. QCD corrections to decay-lepton polar and azimuthal angular distributions in ee+ee- t t in the soft-gluon approximation. SAURABH D RINDANI ... accurate determination of its couplings will have to await the construction of a linear e ·e collider. ..... is the azimuthal angle of the l· momentum.
Stability of approximate factorization with $ heta $-methods
W. Hundsdorfer (Willem)
1997-01-01
textabstractApproximate factorization seems for certain problems a viable alternative to time splitting. Since a splitting error is avoided, accuracy will in general be favourable compared to time splitting methods. However, it is not clear to what extent stability is affected by factorization.
Decision-theoretic troubleshooting: Hardness of approximation
Czech Academy of Sciences Publication Activity Database
Lín, Václav
2014-01-01
Roč. 55, č. 4 (2014), s. 977-988 ISSN 0888-613X R&D Projects: GA ČR GA13-20012S Institutional support: RVO:67985556 Keywords : Decision-theoretic troubleshooting * Hardness of approximation * NP-completeness Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.451, year: 2014
Comparison of Two Approaches to Approximated Reasoning
van den Broek, P.M.; Wagenknecht, Michael; Hampel, Rainer
A comparison is made of two approaches to approximate reasoning: Mamdani's interpolation method and the implication method. Both approaches are variants of Zadeh's compositional rule of inference. It is shown that the approaches are not equivalent. A correspondence between the approaches is
Lognormal Approximations of Fault Tree Uncertainty Distributions.
El-Shanawany, Ashraf Ben; Ardron, Keith H; Walker, Simon P
2018-01-26
Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed-form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling-based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed-form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks's method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models. © 2018 Society for Risk Analysis.
Counting independent sets using the Bethe approximation
Energy Technology Data Exchange (ETDEWEB)
Chertkov, Michael [Los Alamos National Laboratory; Chandrasekaran, V [MIT; Gamarmik, D [MIT; Shah, D [MIT; Sin, J [MIT
2009-01-01
The authors consider the problem of counting the number of independent sets or the partition function of a hard-core model in a graph. The problem in general is computationally hard (P hard). They study the quality of the approximation provided by the Bethe free energy. Belief propagation (BP) is a message-passing algorithm can be used to compute fixed points of the Bethe approximation; however, BP is not always guarantee to converge. As the first result, they propose a simple message-passing algorithm that converges to a BP fixed pont for any grapy. They find that their algorithm converges within a multiplicative error 1 + {var_epsilon} of a fixed point in {Omicron}(n{sup 2}E{sup -4} log{sup 3}(nE{sup -1})) iterations for any bounded degree graph of n nodes. In a nutshell, the algorithm can be thought of as a modification of BP with 'time-varying' message-passing. Next, they analyze the resulting error to the number of independent sets provided by such a fixed point of the Bethe approximation. Using the recently developed loop calculus approach by Vhertkov and Chernyak, they establish that for any bounded graph with large enough girth, the error is {Omicron}(n{sup -{gamma}}) for some {gamma} > 0. As an application, they find that for random 3-regular graph, Bethe approximation of log-partition function (log of the number of independent sets) is within o(1) of corret log-partition - this is quite surprising as previous physics-based predictions were expecting an error of o(n). In sum, their results provide a systematic way to find Bethe fixed points for any graph quickly and allow for estimating error in Bethe approximation using novel combinatorial techniques.
Analytical Ballistic Trajectories with Approximately Linear Drag
Directory of Open Access Journals (Sweden)
Giliam J. P. de Carpentier
2014-01-01
Full Text Available This paper introduces a practical analytical approximation of projectile trajectories in 2D and 3D roughly based on a linear drag model and explores a variety of different planning algorithms for these trajectories. Although the trajectories are only approximate, they still capture many of the characteristics of a real projectile in free fall under the influence of an invariant wind, gravitational pull, and terminal velocity, while the required math for these trajectories and planners is still simple enough to efficiently run on almost all modern hardware devices. Together, these properties make the proposed approach particularly useful for real-time applications where accuracy and performance need to be carefully balanced, such as in computer games.
Analysing organic transistors based on interface approximation
International Nuclear Information System (INIS)
Akiyama, Yuto; Mori, Takehiko
2014-01-01
Temperature-dependent characteristics of organic transistors are analysed thoroughly using interface approximation. In contrast to amorphous silicon transistors, it is characteristic of organic transistors that the accumulation layer is concentrated on the first monolayer, and it is appropriate to consider interface charge rather than band bending. On the basis of this model, observed characteristics of hexamethylenetetrathiafulvalene (HMTTF) and dibenzotetrathiafulvalene (DBTTF) transistors with various surface treatments are analysed, and the trap distribution is extracted. In turn, starting from a simple exponential distribution, we can reproduce the temperature-dependent transistor characteristics as well as the gate voltage dependence of the activation energy, so we can investigate various aspects of organic transistors self-consistently under the interface approximation. Small deviation from such an ideal transistor operation is discussed assuming the presence of an energetically discrete trap level, which leads to a hump in the transfer characteristics. The contact resistance is estimated by measuring the transfer characteristics up to the linear region
Nonlinear analysis approximation theory, optimization and applications
2014-01-01
Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.
Simple Lie groups without the approximation property
DEFF Research Database (Denmark)
Haagerup, Uffe; de Laat, Tim
2013-01-01
For a locally compact group G, let A(G) denote its Fourier algebra, and let M0A(G) denote the space of completely bounded Fourier multipliers on G. The group G is said to have the Approximation Property (AP) if the constant function 1 can be approximated by a net in A(G) in the weak-∗ topology...... on the space M0A(G). Recently, Lafforgue and de la Salle proved that SL(3,R) does not have the AP, implying the first example of an exact discrete group without it, namely, SL(3,Z). In this paper we prove that Sp(2,R) does not have the AP. It follows that all connected simple Lie groups with finite center...... and real rank greater than or equal to two do not have the AP. This naturally gives rise to many examples of exact discrete groups without the AP....
The optimal XFEM approximation for fracture analysis
International Nuclear Information System (INIS)
Jiang Shouyan; Du Chengbin; Ying Zongquan
2010-01-01
The extended finite element method (XFEM) provides an effective tool for analyzing fracture mechanics problems. A XFEM approximation consists of standard finite elements which are used in the major part of the domain and enriched elements in the enriched sub-domain for capturing special solution properties such as discontinuities and singularities. However, two issues in the standard XFEM should specially be concerned: efficient numerical integration methods and an appropriate construction of the blending elements. In the paper, an optimal XFEM approximation is proposed to overcome the disadvantage mentioned above in the standard XFEM. The modified enrichment functions are presented that can reproduced exactly everywhere in the domain. The corresponding FORTRAN program is developed for fracture analysis. A classic problem of fracture mechanics is used to benchmark the program. The results indicate that the optimal XFEM can alleviate the errors and improve numerical precision.
Approximated solutions to Born-Infeld dynamics
Energy Technology Data Exchange (ETDEWEB)
Ferraro, Rafael [Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA),Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina); Nigro, Mauro [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina)
2016-02-01
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.
Incomplete Sparse Approximate Inverses for Parallel Preconditioning
International Nuclear Information System (INIS)
Anzt, Hartwig; University of Tennessee, Knoxville, TN; Huckle, Thomas K.; Bräckle, Jürgen; Dongarra, Jack
2017-01-01
In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as an attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.
Approximate Solutions in Planted 3-SAT
Hsu, Benjamin; Laumann, Christopher; Moessner, Roderich; Sondhi, Shivaji
2013-03-01
In many computational settings, there exists many instances where finding a solution requires a computing time that grows exponentially in the number of variables. Concrete examples occur in combinatorial optimization problems and cryptography in computer science or glassy systems in physics. However, while exact solutions are often known to require exponential time, a related and important question is the running time required to find approximate solutions. Treating this problem as a problem in statistical physics at finite temperature, we examine the computational running time in finding approximate solutions in 3-satisfiability for randomly generated 3-SAT instances which are guaranteed to have a solution. Analytic predictions are corroborated by numerical evidence using stochastic local search algorithms. A first order transition is found in the running time of these algorithms.
Time Stamps for Fixed-Point Approximation
DEFF Research Database (Denmark)
Damian, Daniela
2001-01-01
Time stamps were introduced in Shivers's PhD thesis for approximating the result of a control-flow analysis. We show them to be suitable for computing program analyses where the space of results (e.g., control-flow graphs) is large. We formalize time-stamping as a top-down, fixed-point approximat......Time stamps were introduced in Shivers's PhD thesis for approximating the result of a control-flow analysis. We show them to be suitable for computing program analyses where the space of results (e.g., control-flow graphs) is large. We formalize time-stamping as a top-down, fixed...
Traveltime approximations for inhomogeneous HTI media
Alkhalifah, Tariq Ali
2011-01-01
Traveltimes information is convenient for parameter estimation especially if the medium is described by an anisotropic set of parameters. This is especially true if we could relate traveltimes analytically to these medium parameters, which is generally hard to do in inhomogeneous media. As a result, I develop traveltimes approximations for horizontaly transversely isotropic (HTI) media as simplified and even linear functions of the anisotropic parameters. This is accomplished by perturbing the solution of the HTI eikonal equation with respect to η and the azimuthal symmetry direction (usually used to describe the fracture direction) from a generally inhomogeneous elliptically anisotropic background medium. The resulting approximations can provide accurate analytical description of the traveltime in a homogenous background compared to other published moveout equations out there. These equations will allow us to readily extend the inhomogenous background elliptical anisotropic model to an HTI with a variable, but smoothly varying, η and horizontal symmetry direction values. © 2011 Society of Exploration Geophysicists.
The approximability of the String Barcoding problem
Directory of Open Access Journals (Sweden)
Rizzi Romeo
2006-08-01
Full Text Available Abstract The String Barcoding (SBC problem, introduced by Rash and Gusfield (RECOMB, 2002, consists in finding a minimum set of substrings that can be used to distinguish between all members of a set of given strings. In a computational biology context, the given strings represent a set of known viruses, while the substrings can be used as probes for an hybridization experiment via microarray. Eventually, one aims at the classification of new strings (unknown viruses through the result of the hybridization experiment. In this paper we show that SBC is as hard to approximate as Set Cover. Furthermore, we show that the constrained version of SBC (with probes of bounded length is also hard to approximate. These negative results are tight.
Approximations in the PE-method
DEFF Research Database (Denmark)
Arranz, Marta Galindo
1996-01-01
Two differenct sources of errors may occur in the implementation of the PE methods; a phase error introduced in the approximation of a pseudo-differential operator and an amplitude error generated from the starting field. First, the inherent phase errors introduced in the solution are analyzed...... for a case where the normal mode solution to the wave equation is valid, when the sound is propagated in a downward refracting atmosphere. The angular limitations for the different parabolic approximations are deduced, and calculations showing shifts in the starter as the second source of error...... is investigated. Numerical and analytical starters are compared for source locations close to the ground. The spectral properties of several starters are presented....
A Varifold Approach to Surface Approximation
Buet, Blanche; Leonardi, Gian Paolo; Masnou, Simon
2017-11-01
We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we introduce the notion of approximate mean curvature and show various convergence results that hold, in particular, for sequences of discrete varifolds associated with point clouds or pixel/voxel-type discretizations of d-surfaces in the Euclidean n-space, without restrictions on dimension and codimension. The variational nature of the approach also allows us to consider surfaces with singularities, and in that case the approximate mean curvature is consistent with the generalized mean curvature of the limit surface. A series of numerical tests are provided in order to illustrate the effectiveness and generality of the method.
Approximations and Solution Estimates in Optimization
2016-04-06
for applications in machine learning and stochastic optimization . In this paper, we quantify the error in optimal values, optimal solutions, near...problem from that of another rather different problem is especially important in stochastic optimization , optimal control, and semi-infinite...approximate solutions to convex stochastic programs. SIAM J. Optimization , 18(3):961–979, 2007. [26] J. O. Royset and R. J-B Wets. From data to
Finite element approximation of the Isaacs equation
Salgado, Abner J.; Zhang, Wujun
2015-01-01
We propose and analyze a two-scale finite element method for the Isaacs equation. The fine scale is given by the mesh size $h$ whereas the coarse scale $\\varepsilon$ is dictated by an integro-differential approximation of the partial differential equation. We show that the method satisfies the discrete maximum principle provided that the mesh is weakly acute. This, in conjunction with weak operator consistency of the finite element method, allows us to establish convergence of the numerical s...
Mean-field approximation minimizes relative entropy
International Nuclear Information System (INIS)
Bilbro, G.L.; Snyder, W.E.; Mann, R.C.
1991-01-01
The authors derive the mean-field approximation from the information-theoretic principle of minimum relative entropy instead of by minimizing Peierls's inequality for the Weiss free energy of statistical physics theory. They show that information theory leads to the statistical mechanics procedure. As an example, they consider a problem in binary image restoration. They find that mean-field annealing compares favorably with the stochastic approach
Fast Approximate Joint Diagonalization Incorporating Weight Matrices
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Yeredor, A.
2009-01-01
Roč. 57, č. 3 (2009), s. 878-891 ISSN 1053-587X R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : autoregressive processes * blind source separation * nonstationary random processes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.212, year: 2009 http://library.utia.cas.cz/separaty/2009/SI/tichavsky-fast approximate joint diagonalization incorporating weight matrices.pdf
Fast approximate convex decomposition using relative concavity
Ghosh, Mukulika
2013-02-01
Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31]. © 2012 Elsevier Ltd. All rights reserved.
Approximations of Two-Attribute Utility Functions
1976-09-01
06320 i Technology Cambridge, Massachusetts 02139 Dr. Jack R. Borsting, Chairman Dept. of Operations Research and Professor Oskar Morgenstern ... Morgenstern utility functions u defined on two attributes from the viewpoint of mathematical --roxi-n’tion theory.r It focuses on approximations v of u that...von Neumann and Morgenstern (1947) or an equivalent system (Herstein and Milnor, 1953; Fishburn, 1970) so that there exists u: T + Re such that P - Q
Approximate Inverse Preconditioners with Adaptive Dropping
Czech Academy of Sciences Publication Activity Database
Kopal, J.; Rozložník, Miroslav; Tůma, Miroslav
2015-01-01
Roč. 84, June (2015), s. 13-20 ISSN 0965-9978 R&D Projects: GA ČR(CZ) GAP108/11/0853; GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : approximate inverse * Gram-Schmidt orthogonalization * incomplete decomposition * preconditioned conjugate gradient method * algebraic preconditioning * pivoting Subject RIV: BA - General Mathematics Impact factor: 1.673, year: 2015
Solving Math Problems Approximately: A Developmental Perspective.
Directory of Open Access Journals (Sweden)
Dana Ganor-Stern
Full Text Available Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults' ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger than the exact answer and when it was far (vs. close from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner.
Optical pulse propagation with minimal approximations
Kinsler, Paul
2008-01-01
Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations -- including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single first order propagation equation using a minimum of approximations and a straightforward "factorization" mathematical scheme. The approach generates exact coupled bi-directional equations, after which it is clear that the description can be reduced to a singl...
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-07
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-05
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.
Solving Math Problems Approximately: A Developmental Perspective.
Ganor-Stern, Dana
2016-01-01
Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults' ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner.
Markdown Optimization via Approximate Dynamic Programming
Directory of Open Access Journals (Sweden)
Cos?gun
2013-02-01
Full Text Available We consider the markdown optimization problem faced by the leading apparel retail chain. Because of substitution among products the markdown policy of one product affects the sales of other products. Therefore, markdown policies for product groups having a significant crossprice elasticity among each other should be jointly determined. Since the state space of the problem is very huge, we use Approximate Dynamic Programming. Finally, we provide insights on the behavior of how each product price affects the markdown policy.
Factorized Approximate Inverses With Adaptive Dropping
Czech Academy of Sciences Publication Activity Database
Kopal, Jiří; Rozložník, Miroslav; Tůma, Miroslav
2016-01-01
Roč. 38, č. 3 (2016), A1807-A1820 ISSN 1064-8275 R&D Projects: GA ČR GA13-06684S Grant - others:GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : approximate inverses * incomplete factorization * Gram–Schmidt orthogonalization * preconditioned iterative methods Subject RIV: BA - General Mathematics Impact factor: 2.195, year: 2016
An analytical approximation for resonance integral
International Nuclear Information System (INIS)
Magalhaes, C.G. de; Martinez, A.S.
1985-01-01
It is developed a method which allows to obtain an analytical solution for the resonance integral. The problem formulation is completely theoretical and based in concepts of physics of general character. The analytical expression for integral does not involve any empiric correlation or parameter. Results of approximation are compared with pattern values for each individual resonance and for sum of all resonances. (M.C.K.) [pt
Fast algorithms for approximate circular string matching.
Barton, Carl; Iliopoulos, Costas S; Pissis, Solon P
2014-03-22
Circular string matching is a problem which naturally arises in many biological contexts. It consists in finding all occurrences of the rotations of a pattern of length m in a text of length n. There exist optimal average-case algorithms for exact circular string matching. Approximate circular string matching is a rather undeveloped area. In this article, we present a suboptimal average-case algorithm for exact circular string matching requiring time O(n). Based on our solution for the exact case, we present two fast average-case algorithms for approximate circular string matching with k-mismatches, under the Hamming distance model, requiring time O(n) for moderate values of k, that is k=O(m/logm). We show how the same results can be easily obtained under the edit distance model. The presented algorithms are also implemented as library functions. Experimental results demonstrate that the functions provided in this library accelerate the computations by more than three orders of magnitude compared to a naïve approach. We present two fast average-case algorithms for approximate circular string matching with k-mismatches; and show that they also perform very well in practice. The importance of our contribution is underlined by the fact that the provided functions may be seamlessly integrated into any biological pipeline. The source code of the library is freely available at http://www.inf.kcl.ac.uk/research/projects/asmf/.
Approximate particle number projection in hot nuclei
International Nuclear Information System (INIS)
Kosov, D.S.; Vdovin, A.I.
1995-01-01
Heated finite systems like, e.g., hot atomic nuclei have to be described by the canonical partition function. But this is a quite difficult technical problem and, as a rule, the grand canonical partition function is used in the studies. As a result, some shortcomings of the theoretical description appear because of the thermal fluctuations of the number of particles. Moreover, in nuclei with pairing correlations the quantum number fluctuations are introduced by some approximate methods (e.g., by the standard BCS method). The exact particle number projection is very cumbersome and an approximate number projection method for T ≠ 0 basing on the formalism of thermo field dynamics is proposed. The idea of the Lipkin-Nogami method to perform any operator as a series in the number operator powers is used. The system of equations for the coefficients of this expansion is written and the solution of the system in the next approximation after the BCS one is obtained. The method which is of the 'projection after variation' type is applied to a degenerate single j-shell model. 14 refs., 1 tab
Feedforward Approximations to Dynamic Recurrent Network Architectures.
Muir, Dylan R
2018-02-01
Recurrent neural network architectures can have useful computational properties, with complex temporal dynamics and input-sensitive attractor states. However, evaluation of recurrent dynamic architectures requires solving systems of differential equations, and the number of evaluations required to determine their response to a given input can vary with the input or can be indeterminate altogether in the case of oscillations or instability. In feedforward networks, by contrast, only a single pass through the network is needed to determine the response to a given input. Modern machine learning systems are designed to operate efficiently on feedforward architectures. We hypothesized that two-layer feedforward architectures with simple, deterministic dynamics could approximate the responses of single-layer recurrent network architectures. By identifying the fixed-point responses of a given recurrent network, we trained two-layer networks to directly approximate the fixed-point response to a given input. These feedforward networks then embodied useful computations, including competitive interactions, information transformations, and noise rejection. Our approach was able to find useful approximations to recurrent networks, which can then be evaluated in linear and deterministic time complexity.
Impulse approximation versus elementary particle method
International Nuclear Information System (INIS)
Klieb, L.
1982-01-01
Calculations are made for radiative muon capture in 3 He, both in impulse approximation and with the elementary particle method, and results are compared. It is argued that a diagrammatic method which takes a selected set of Feynman diagrams into account only provides insufficient warrant that effects not included are small. Therefore low-energy theorems are employed, as first given by Adler and Dothan, to determine the amplitude up to and including all terms linear in photon momentum and momentum transfer at the weak vertex. This amplitude is applied to radiative muon capture with the elementary particle method (EPM). The various form factors needed are discussed. It is shown that the results are particularly sensitive to the π- 3 He- 3 H coupling constant of which many contradictory determinations have been described in the literature. The classification of the nuclear wave function employed in the impulse approximation (IA) is summarized. The ν-decay of 3 H and (radiative muon capture in 3 He is treated and numerical results are given. Next, pion photoproduction and radiative pion capture are considered. IA and EPM for radiative muon capture are compared more closely. It is concluded that two-step processes are inherently difficult; the elementary particle method has convergence problems, and unknown parameters are present. In the impulse approximation, which is perhaps conceptually more difficult, the two-step interaction for the nucleon is considered as effectively point-like with small non-local corrections. (Auth.)
Ranking Support Vector Machine with Kernel Approximation
Directory of Open Access Journals (Sweden)
Kai Chen
2017-01-01
Full Text Available Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels can give higher accuracy than linear RankSVM (RankSVM with a linear kernel for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.
CMB-lensing beyond the Born approximation
International Nuclear Information System (INIS)
Marozzi, Giovanni; Fanizza, Giuseppe; Durrer, Ruth; Dio, Enea Di
2016-01-01
We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles ℓ ∼< 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.
Function approximation of tasks by neural networks
International Nuclear Information System (INIS)
Gougam, L.A.; Chikhi, A.; Mekideche-Chafa, F.
2008-01-01
For several years now, neural network models have enjoyed wide popularity, being applied to problems of regression, classification and time series analysis. Neural networks have been recently seen as attractive tools for developing efficient solutions for many real world problems in function approximation. The latter is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. In a previous contribution, we have used a well known simplified architecture to show that it provides a reasonably efficient, practical and robust, multi-frequency analysis. We have investigated the universal approximation theory of neural networks whose transfer functions are: sigmoid (because of biological relevance), Gaussian and two specified families of wavelets. The latter have been found to be more appropriate to use. The aim of the present contribution is therefore to use a m exican hat wavelet a s transfer function to approximate different tasks relevant and inherent to various applications in physics. The results complement and provide new insights into previously published results on this problem
Simultaneous perturbation stochastic approximation for tidal models
Altaf, M.U.
2011-05-12
The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.
Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin
2016-01-01
What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright
Photoelectron spectroscopy and the dipole approximation
Energy Technology Data Exchange (ETDEWEB)
Hemmers, O.; Hansen, D.L.; Wang, H. [Univ. of Nevada, Las Vegas, NV (United States)] [and others
1997-04-01
Photoelectron spectroscopy is a powerful technique because it directly probes, via the measurement of photoelectron kinetic energies, orbital and band structure in valence and core levels in a wide variety of samples. The technique becomes even more powerful when it is performed in an angle-resolved mode, where photoelectrons are distinguished not only by their kinetic energy, but by their direction of emission as well. Determining the probability of electron ejection as a function of angle probes the different quantum-mechanical channels available to a photoemission process, because it is sensitive to phase differences among the channels. As a result, angle-resolved photoemission has been used successfully for many years to provide stringent tests of the understanding of basic physical processes underlying gas-phase and solid-state interactions with radiation. One mainstay in the application of angle-resolved photoelectron spectroscopy is the well-known electric-dipole approximation for photon interactions. In this simplification, all higher-order terms, such as those due to electric-quadrupole and magnetic-dipole interactions, are neglected. As the photon energy increases, however, effects beyond the dipole approximation become important. To best determine the range of validity of the dipole approximation, photoemission measurements on a simple atomic system, neon, where extra-atomic effects cannot play a role, were performed at BL 8.0. The measurements show that deviations from {open_quotes}dipole{close_quotes} expectations in angle-resolved valence photoemission are observable for photon energies down to at least 0.25 keV, and are quite significant at energies around 1 keV. From these results, it is clear that non-dipole angular-distribution effects may need to be considered in any application of angle-resolved photoelectron spectroscopy that uses x-ray photons of energies as low as a few hundred eV.
Product-State Approximations to Quantum States
Brandão, Fernando G. S. L.; Harrow, Aram W.
2016-02-01
We show that for any many-body quantum state there exists an unentangled quantum state such that most of the two-body reduced density matrices are close to those of the original state. This is a statement about the monogamy of entanglement, which cannot be shared without limit in the same way as classical correlation. Our main application is to Hamiltonians that are sums of two-body terms. For such Hamiltonians we show that there exist product states with energy that is close to the ground-state energy whenever the interaction graph of the Hamiltonian has high degree. This proves the validity of mean-field theory and gives an explicitly bounded approximation error. If we allow states that are entangled within small clusters of systems but product across clusters then good approximations exist when the Hamiltonian satisfies one or more of the following properties: (1) high degree, (2) small expansion, or (3) a ground state where the blocks in the partition have sublinear entanglement. Previously this was known only in the case of small expansion or in the regime where the entanglement was close to zero. Our approximations allow an extensive error in energy, which is the scale considered by the quantum PCP (probabilistically checkable proof) and NLTS (no low-energy trivial-state) conjectures. Thus our results put restrictions on the possible Hamiltonians that could be used for a possible proof of the qPCP or NLTS conjectures. By contrast the classical PCP constructions are often based on constraint graphs with high degree. Likewise we show that the parallel repetition that is possible with classical constraint satisfaction problems cannot also be possible for quantum Hamiltonians, unless qPCP is false. The main technical tool behind our results is a collection of new classical and quantum de Finetti theorems which do not make any symmetry assumptions on the underlying states.
Dynamic system evolution and markov chain approximation
Directory of Open Access Journals (Sweden)
Roderick V. Nicholas Melnik
1998-01-01
Full Text Available In this paper computational aspects of the mathematical modelling of dynamic system evolution have been considered as a problem in information theory. The construction of mathematical models is treated as a decision making process with limited available information.The solution of the problem is associated with a computational model based on heuristics of a Markov Chain in a discrete space–time of events. A stable approximation of the chain has been derived and the limiting cases are discussed. An intrinsic interconnection of constructive, sequential, and evolutionary approaches in related optimization problems provides new challenges for future work.
The EH Interpolation Spline and Its Approximation
Directory of Open Access Journals (Sweden)
Jin Xie
2014-01-01
Full Text Available A new interpolation spline with two parameters, called EH interpolation spline, is presented in this paper, which is the extension of the standard cubic Hermite interpolation spline, and inherits the same properties of the standard cubic Hermite interpolation spline. Given the fixed interpolation conditions, the shape of the proposed splines can be adjusted by changing the values of the parameters. Also, the introduced spline could approximate to the interpolated function better than the standard cubic Hermite interpolation spline and the quartic Hermite interpolation splines with single parameter by a new algorithm.
On one approximation in quantum chromodynamics
International Nuclear Information System (INIS)
Alekseev, A.I.; Bajkov, V.A.; Boos, Eh.Eh.
1982-01-01
Form of a complete fermion propagator near the mass shell is investigated. Considered is a nodel of quantum chromodynamics (MQC) where in the fermion section the Block-Nordsic approximation has been made, i. e. u-numbers are substituted for ν matrices. The model was investigated by means of the Schwinger-Dyson equation for a quark propagator in the infrared region. The Schwinger-Dyson equation was managed to reduce to a differential equation which is easily solved. At that, the Green function is suitable to represent as integral transformation
Topics in multivariate approximation and interpolation
Jetter, Kurt
2005-01-01
This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for gr
Shape theory categorical methods of approximation
Cordier, J M
2008-01-01
This in-depth treatment uses shape theory as a ""case study"" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras.A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes and
Mean field approximation to QCD, 1
International Nuclear Information System (INIS)
Tezuka, Hirokazu.
1987-09-01
We apply mean field approximation to the gluon field in the equations of motion derived from the QCD lagrangian. The gluon mean field is restricted to the time-independent 0th component, and color exchange components are ignored. The equation of motion for the gluon mean field turns into a Poisson equation, and that for the quark field into a Dirac equation with a potential term. For example, assuming spherical symmetric box-like distribution and Gauss-like distribution to quarks, we try to solve these two equations simultaneously. (author)
Nonlinear higher quasiparticle random phase approximation
Smetana, Adam; Šimkovic, Fedor; Štefánik, Dušan; Krivoruchenko, Mikhail
2017-10-01
We develop a new approach to describe nuclear states of multiphonon origin, motivated by the necessity for a more accurate description of matrix elements of neutrinoless double-beta decay. Our approach is an extension of the Quasiparticle Random Phase Approximation (QRPA), in which nonlinear phonon operators play an essential role. Before applying the nonlinear higher QRPA (nhQRPA) to realistic problems, we test its efficiency with exactly solvable models. The first considered model is equivalent to a harmonic oscillator. The nhQRPA solutions follow from the standard QRPA equation, but for nonlinear phonon operators defined for each individual excited state separately. The second exactly solvable model is the proton-neutron Lipkin model that describes successfully not only energy spectrum of nuclei, but also beta-decay transitions. Again, we reproduce exactly the numerical solutions in the nhQRPA framework. We show in particular that truncation of the nonlinear phonon operators leads to an approximation similar to the self-consistent second QRPA, given the phonon operators are defined with a constant term. The test results demonstrate that the proposed nhQRPA is a promising tool for a realistic calculation of energy spectra and nuclear transitions.
Fast approximate hierarchical clustering using similarity heuristics
Directory of Open Access Journals (Sweden)
Kull Meelis
2008-09-01
Full Text Available Abstract Background Agglomerative hierarchical clustering (AHC is a common unsupervised data analysis technique used in several biological applications. Standard AHC methods require that all pairwise distances between data objects must be known. With ever-increasing data sizes this quadratic complexity poses problems that cannot be overcome by simply waiting for faster computers. Results We propose an approximate AHC algorithm HappieClust which can output a biologically meaningful clustering of a large dataset more than an order of magnitude faster than full AHC algorithms. The key to the algorithm is to limit the number of calculated pairwise distances to a carefully chosen subset of all possible distances. We choose distances using a similarity heuristic based on a small set of pivot objects. The heuristic efficiently finds pairs of similar objects and these help to mimic the greedy choices of full AHC. Quality of approximate AHC as compared to full AHC is studied with three measures. The first measure evaluates the global quality of the achieved clustering, while the second compares biological relevance using enrichment of biological functions in every subtree of the clusterings. The third measure studies how well the contents of subtrees are conserved between the clusterings. Conclusion The HappieClust algorithm is well suited for large-scale gene expression visualization and analysis both on personal computers as well as public online web applications. The software is available from the URL http://www.quretec.com/HappieClust
Traveling cluster approximation for uncorrelated amorphous systems
International Nuclear Information System (INIS)
Kaplan, T.; Sen, A.K.; Gray, L.J.; Mills, R.
1985-01-01
In this paper, the authors apply the TCA concepts to spatially disordered, uncorrelated systems (e.g., fluids or amorphous metals without short-range order). This is the first approximation scheme for amorphous systems that takes cluster effects into account while preserving the Herglotz property for any amount of disorder. They have performed some computer calculations for the pair TCA, for the model case of delta-function potentials on a one-dimensional random chain. These results are compared with exact calculations (which, in principle, taken into account all cluster effects) and with the CPA, which is the single-site TCA. The density of states for the pair TCA clearly shows some improvement over the CPA, and yet, apparently, the pair approximation distorts some of the features of the exact results. They conclude that the effects of large clusters are much more important in an uncorrelated liquid metal than in a substitutional alloy. As a result, the pair TCA, which does quite a nice job for alloys, is not adequate for the liquid. Larger clusters must be treated exactly, and therefore an n-TCA with n > 2 must be used
APPROXIMATING INNOVATION POTENTIAL WITH NEUROFUZZY ROBUST MODEL
Directory of Open Access Journals (Sweden)
Kasa, Richard
2015-01-01
Full Text Available In a remarkably short time, economic globalisation has changed the world’s economic order, bringing new challenges and opportunities to SMEs. These processes pushed the need to measure innovation capability, which has become a crucial issue for today’s economic and political decision makers. Companies cannot compete in this new environment unless they become more innovative and respond more effectively to consumers’ needs and preferences – as mentioned in the EU’s innovation strategy. Decision makers cannot make accurate and efficient decisions without knowing the capability for innovation of companies in a sector or a region. This need is forcing economists to develop an integrated, unified and complete method of measuring, approximating and even forecasting the innovation performance not only on a macro but also a micro level. In this recent article a critical analysis of the literature on innovation potential approximation and prediction is given, showing their weaknesses and a possible alternative that eliminates the limitations and disadvantages of classical measuring and predictive methods.
Analytic approximate radiation effects due to Bremsstrahlung
Energy Technology Data Exchange (ETDEWEB)
Ben-Zvi I.
2012-02-01
The purpose of this note is to provide analytic approximate expressions that can provide quick estimates of the various effects of the Bremsstrahlung radiation produced relatively low energy electrons, such as the dumping of the beam into the beam stop at the ERL or field emission in superconducting cavities. The purpose of this work is not to replace a dependable calculation or, better yet, a measurement under real conditions, but to provide a quick but approximate estimate for guidance purposes only. These effects include dose to personnel, ozone generation in the air volume exposed to the radiation, hydrogen generation in the beam dump water cooling system and radiation damage to near-by magnets. These expressions can be used for other purposes, but one should note that the electron beam energy range is limited. In these calculations the good range is from about 0.5 MeV to 10 MeV. To help in the application of this note, calculations are presented as a worked out example for the beam dump of the R&D Energy Recovery Linac.
Approximate reversal of quantum Gaussian dynamics
Lami, Ludovico; Das, Siddhartha; Wilde, Mark M.
2018-03-01
Recently, there has been focus on determining the conditions under which the data processing inequality for quantum relative entropy is satisfied with approximate equality. The solution of the exact equality case is due to Petz, who showed that the quantum relative entropy between two quantum states stays the same after the action of a quantum channel if and only if there is a reversal channel that recovers the original states after the channel acts. Furthermore, this reversal channel can be constructed explicitly and is now called the Petz recovery map. Recent developments have shown that a variation of the Petz recovery map works well for recovery in the case of approximate equality of the data processing inequality. Our main contribution here is a proof that bosonic Gaussian states and channels possess a particular closure property, namely, that the Petz recovery map associated to a bosonic Gaussian state σ and a bosonic Gaussian channel N is itself a bosonic Gaussian channel. We furthermore give an explicit construction of the Petz recovery map in this case, in terms of the mean vector and covariance matrix of the state σ and the Gaussian specification of the channel N .
Approximating Markov Chains: What and why
International Nuclear Information System (INIS)
Pincus, S.
1996-01-01
Much of the current study of dynamical systems is focused on geometry (e.g., chaos and bifurcations) and ergodic theory. Yet dynamical systems were originally motivated by an attempt to open-quote open-quote solve,close-quote close-quote or at least understand, a discrete-time analogue of differential equations. As such, numerical, analytical solution techniques for dynamical systems would seem desirable. We discuss an approach that provides such techniques, the approximation of dynamical systems by suitable finite state Markov Chains. Steady state distributions for these Markov Chains, a straightforward calculation, will converge to the true dynamical system steady state distribution, with appropriate limit theorems indicated. Thus (i) approximation by a computable, linear map holds the promise of vastly faster steady state solutions for nonlinear, multidimensional differential equations; (ii) the solution procedure is unaffected by the presence or absence of a probability density function for the attractor, entirely skirting singularity, fractal/multifractal, and renormalization considerations. The theoretical machinery underpinning this development also implies that under very general conditions, steady state measures are weakly continuous with control parameter evolution. This means that even though a system may change periodicity, or become chaotic in its limiting behavior, such statistical parameters as the mean, standard deviation, and tail probabilities change continuously, not abruptly with system evolution. copyright 1996 American Institute of Physics
Analytic approximate radiation effects due to Bremsstrahlung
International Nuclear Information System (INIS)
Ben-Zvi, I.
2012-01-01
The purpose of this note is to provide analytic approximate expressions that can provide quick estimates of the various effects of the Bremsstrahlung radiation produced relatively low energy electrons, such as the dumping of the beam into the beam stop at the ERL or field emission in superconducting cavities. The purpose of this work is not to replace a dependable calculation or, better yet, a measurement under real conditions, but to provide a quick but approximate estimate for guidance purposes only. These effects include dose to personnel, ozone generation in the air volume exposed to the radiation, hydrogen generation in the beam dump water cooling system and radiation damage to near-by magnets. These expressions can be used for other purposes, but one should note that the electron beam energy range is limited. In these calculations the good range is from about 0.5 MeV to 10 MeV. To help in the application of this note, calculations are presented as a worked out example for the beam dump of the R and D Energy Recovery Linac.
On some applications of diophantine approximations.
Chudnovsky, G V
1984-03-01
Siegel's results [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1] on the transcendence and algebraic independence of values of E-functions are refined to obtain the best possible bound for the measures of irrationality and linear independence of values of arbitrary E-functions at rational points. Our results show that values of E-functions at rational points have measures of diophantine approximations typical to "almost all" numbers. In particular, any such number has the "2 + epsilon" exponent of irrationality: Theta - p/q > q(-2-epsilon) for relatively prime rational integers p,q, with q >/= q(0) (Theta, epsilon). These results answer some problems posed by Lang. The methods used here are based on the introduction of graded Padé approximations to systems of functions satisfying linear differential equations with rational function coefficients. The constructions and proofs of this paper were used in the functional (nonarithmetic case) in a previous paper [Chudnovsky, D. V. & Chudnovsky, G. V. (1983) Proc. Natl. Acad. Sci. USA 80, 5158-5162].
Regularity and approximability of electronic wave functions
Yserentant, Harry
2010-01-01
The electronic Schrödinger equation describes the motion of N-electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, with three spatial dimensions for each electron. Approximating these solutions is thus inordinately challenging, and it is generally believed that a reduction to simplified models, such as those of the Hartree-Fock method or density functional theory, is the only tenable approach. This book seeks to show readers that this conventional wisdom need not be ironclad: the regularity of the solutions, which increases with the number of electrons, the decay behavior of their mixed derivatives, and the antisymmetry enforced by the Pauli principle contribute properties that allow these functions to be approximated with an order of complexity which comes arbitrarily close to that for a system of one or two electrons. The text is accessible to a mathematical audience at the beginning graduate level as...
Adaptive and Approximate Orthogonal Range Counting
DEFF Research Database (Denmark)
Chan, Timothy M.; Wilkinson, Bryan Thomas
2013-01-01
-case optimal query time O(log_w n). We give an O(n loglog n)-space adaptive data structure that improves the query time to O(loglog n + log_w k), where k is the output count. When k=O(1), our bounds match the state of the art for the 2-D orthogonal range emptiness problem [Chan, Larsen, and Pătraşcu, SoCG 2011......]. •We give an O(n loglog n)-space data structure for approximate 2-D orthogonal range counting that can compute a (1+δ)-factor approximation to the count in O(loglog n) time for any fixed constant δ>0. Again, our bounds match the state of the art for the 2-D orthogonal range emptiness problem. •Lastly......Close Abstract We present three new results on one of the most basic problems in geometric data structures, 2-D orthogonal range counting. All the results are in the w-bit word RAM model. •It is well known that there are linear-space data structures for 2-D orthogonal range counting with worst...
DEFF Research Database (Denmark)
Sadegh, Payman
1997-01-01
This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...... of the optimization parameters. It is shown that, under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point, The procedure is illustrated by a numerical example, (C) 1997 Elsevier Science Ltd....
Hydromagnetic turbulence in the direct interaction approximation
International Nuclear Information System (INIS)
Nagarajan, S.
1975-01-01
The dissertation is concerned with the nature of turbulence in a medium with large electrical conductivity. Three distinct though inter-related questions are asked. Firstly, the evolution of a weak, random initial magnetic field in a highly conducting, isotropically turbulent fluid is discussed. This was first discussed in the paper 'Growth of Turbulent Magnetic Fields' by Kraichnan and Nagargian. The Physics of Fluids, volume 10, number 4, 1967. Secondly, the direct interaction approximation for hydromagnetic turbulence maintained by stationary, isotropic, random stirring forces is formulated in the wave-number-frequency domain. Thirdly, the dynamical evolution of a weak, random, magnetic excitation in a turbulent electrically conducting fluid is examined under varying kinematic conditions. (G.T.H.)
Discrete Spectrum Reconstruction Using Integral Approximation Algorithm.
Sizikov, Valery; Sidorov, Denis
2017-07-01
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of linear-nonlinear equations (SLNE) with respect to intensities and frequencies of the discrete spectral lines. The SLNE is linear with respect to lines' intensities and nonlinear with respect to the lines' frequencies. The integral approximation algorithm is proposed for the solution of this SLNE. The algorithm combines solution of linear integral equations with solution of a system of linear algebraic equations and avoids nonlinear equations. Numerical examples of the application of the technique, both to synthetic and experimental spectra, demonstrate the efficacy of the proposed approach in enabling an effective enhancement of the spectrometer's resolution.
Nanostructures: Scattering beyond the Born approximation
Grigoriev, S. V.; Syromyatnikov, A. V.; Chumakov, A. P.; Grigoryeva, N. A.; Napolskii, K. S.; Roslyakov, I. V.; Eliseev, A. A.; Petukhov, A. V.; Eckerlebe, H.
2010-03-01
The neutron scattering on a two-dimensional ordered nanostructure with the third nonperiodic dimension can go beyond the Born approximation. In our model supported by the exact theoretical solution a well-correlated hexagonal porous structure of anodic aluminum oxide films acts as a peculiar two-dimensional grating for the coherent neutron wave. The thickness of the film L (length of pores) plays important role in the transition from the weak to the strong scattering regimes. It is shown that the coherency of the standard small-angle neutron scattering setups suits to the geometry of the studied objects and often affects the intensity of scattering. The proposed theoretical solution can be applied in the small-angle neutron diffraction experiments with flux lines in superconductors, periodic arrays of magnetic or superconducting nanowires, as well as in small-angle diffraction experiments on synchrotron radiation.
UFBoot2: Improving the Ultrafast Bootstrap Approximation.
Hoang, Diep Thi; Chernomor, Olga; von Haeseler, Arndt; Minh, Bui Quang; Vinh, Le Sy
2018-02-01
The standard bootstrap (SBS), despite being computationally intensive, is widely used in maximum likelihood phylogenetic analyses. We recently proposed the ultrafast bootstrap approximation (UFBoot) to reduce computing time while achieving more unbiased branch supports than SBS under mild model violations. UFBoot has been steadily adopted as an efficient alternative to SBS and other bootstrap approaches. Here, we present UFBoot2, which substantially accelerates UFBoot and reduces the risk of overestimating branch supports due to polytomies or severe model violations. Additionally, UFBoot2 provides suitable bootstrap resampling strategies for phylogenomic data. UFBoot2 is 778 times (median) faster than SBS and 8.4 times (median) faster than RAxML rapid bootstrap on tested data sets. UFBoot2 is implemented in the IQ-TREE software package version 1.6 and freely available at http://www.iqtree.org. © The Author 2017. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.
Approximation by max-product type operators
Bede, Barnabás; Gal, Sorin G
2016-01-01
This monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called "max-product" type operators. The exposition highlights the max-product operators as those which allow one to obtain, in many cases, more valuable estimates than those obtained by classical approaches. The text considers a wide variety of operators which are studied for a number of interesting problems such as quantitative estimates, convergence, saturation results, localization, to name several. Additionally, the book discusses the perfect analogies between the probabilistic approaches of the classical Bernstein type operators and of the classical convolution operators (non-periodic and periodic cases), and the possibilistic approaches of the max-product variants of these operators. These approaches allow for two natural interpretations of the max-product Bernstein type operators and convolution type operators: firstly, as possibilistic expectations of some fuzzy variables, and secondly,...
PROX: Approximated Summarization of Data Provenance.
Ainy, Eleanor; Bourhis, Pierre; Davidson, Susan B; Deutch, Daniel; Milo, Tova
2016-03-01
Many modern applications involve collecting large amounts of data from multiple sources, and then aggregating and manipulating it in intricate ways. The complexity of such applications, combined with the size of the collected data, makes it difficult to understand the application logic and how information was derived. Data provenance has been proven helpful in this respect in different contexts; however, maintaining and presenting the full and exact provenance may be infeasible, due to its size and complex structure. For that reason, we introduce the notion of approximated summarized provenance, where we seek a compact representation of the provenance at the possible cost of information loss. Based on this notion, we have developed PROX, a system for the management, presentation and use of data provenance for complex applications. We propose to demonstrate PROX in the context of a movies rating crowd-sourcing system, letting participants view provenance summarization and use it to gain insights on the application and its underlying data.
Exact and Approximate Probabilistic Symbolic Execution
Luckow, Kasper; Pasareanu, Corina S.; Dwyer, Matthew B.; Filieri, Antonio; Visser, Willem
2014-01-01
Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.
Approximate analytical modeling of leptospirosis infection
Ismail, Nur Atikah; Azmi, Amirah; Yusof, Fauzi Mohamed; Ismail, Ahmad Izani
2017-11-01
Leptospirosis is an infectious disease carried by rodents which can cause death in humans. The disease spreads directly through contact with feces, urine or through bites of infected rodents and indirectly via water contaminated with urine and droppings from them. Significant increase in the number of leptospirosis cases in Malaysia caused by the recent severe floods were recorded during heavy rainfall season. Therefore, to understand the dynamics of leptospirosis infection, a mathematical model based on fractional differential equations have been developed and analyzed. In this paper an approximate analytical method, the multi-step Laplace Adomian decomposition method, has been used to conduct numerical simulations so as to gain insight on the spread of leptospirosis infection.
Analytical approximations for wide and narrow resonances
International Nuclear Information System (INIS)
Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da
2005-01-01
This paper aims at developing analytical expressions for the adjoint neutron spectrum in the resonance energy region, taking into account both narrow and wide resonance approximations, in order to reduce the numerical computations involved. These analytical expressions, besides reducing computing time, are very simple from a mathematical point of view. The results obtained with this analytical formulation were compared to a reference solution obtained with a numerical method previously developed to solve the neutron balance adjoint equations. Narrow and wide resonances of U 238 were treated and the analytical procedure gave satisfactory results as compared with the reference solution, for the resonance energy range. The adjoint neutron spectrum is useful to determine the neutron resonance absorption, so that multigroup adjoint cross sections used by the adjoint diffusion equation can be obtained. (author)
Analytical approximations for wide and narrow resonances
Energy Technology Data Exchange (ETDEWEB)
Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]. E-mail: aquilino@lmp.ufrj.br
2005-07-01
This paper aims at developing analytical expressions for the adjoint neutron spectrum in the resonance energy region, taking into account both narrow and wide resonance approximations, in order to reduce the numerical computations involved. These analytical expressions, besides reducing computing time, are very simple from a mathematical point of view. The results obtained with this analytical formulation were compared to a reference solution obtained with a numerical method previously developed to solve the neutron balance adjoint equations. Narrow and wide resonances of U{sup 238} were treated and the analytical procedure gave satisfactory results as compared with the reference solution, for the resonance energy range. The adjoint neutron spectrum is useful to determine the neutron resonance absorption, so that multigroup adjoint cross sections used by the adjoint diffusion equation can be obtained. (author)
Evaluating methods for approximating stochastic differential equations.
Brown, Scott D; Ratcliff, Roger; Smith, Philip L
2006-08-01
Models of decision making and response time (RT) are often formulated using stochastic differential equations (SDEs). Researchers often investigate these models using a simple Monte Carlo method based on Euler's method for solving ordinary differential equations. The accuracy of Euler's method is investigated and compared to the performance of more complex simulation methods. The more complex methods for solving SDEs yielded no improvement in accuracy over the Euler method. However, the matrix method proposed by Diederich and Busemeyer (2003) yielded significant improvements. The accuracy of all methods depended critically on the size of the approximating time step. The large (∼10 ms) step sizes often used by psychological researchers resulted in large and systematic errors in evaluating RT distributions.
Efficient Approximate OLAP Querying Over Time Series
DEFF Research Database (Denmark)
Perera, Kasun Baruhupolage Don Kasun Sanjeewa; Hahmann, Martin; Lehner, Wolfgang
2016-01-01
The ongoing trend for data gathering not only produces larger volumes of data, but also increases the variety of recorded data types. Out of these, especially time series, e.g. various sensor readings, have attracted attention in the domains of business intelligence and decision making. As OLAP...... queries play a major role in these domains, it is desirable to also execute them on time series data. While this is not a problem on the conceptual level, it can become a bottleneck with regards to query run-time. In general, processing OLAP queries gets more computationally intensive as the volume...... are either costly or require continuous maintenance. In this paper we propose an approach for approximate OLAP querying of time series that offers constant latency and is maintenance-free. To achieve this, we identify similarities between aggregation cuboids and propose algorithms that eliminate...
Approximate truncation robust computed tomography—ATRACT
International Nuclear Information System (INIS)
Dennerlein, Frank; Maier, Andreas
2013-01-01
We present an approximate truncation robust algorithm to compute tomographic images (ATRACT). This algorithm targets at reconstructing volumetric images from cone-beam projections in scenarios where these projections are highly truncated in each dimension. It thus facilitates reconstructions of small subvolumes of interest, without involving prior knowledge about the object. Our method is readily applicable to medical C-arm imaging, where it may contribute to new clinical workflows together with a considerable reduction of x-ray dose. We give a detailed derivation of ATRACT that starts from the conventional Feldkamp filtered-backprojection algorithm and that involves, as one component, a novel original formula for the inversion of the two-dimensional Radon transform. Discretization and numerical implementation are discussed and reconstruction results from both, simulated projections and first clinical data sets are presented. (paper)
Approximate Sensory Data Collection: A Survey
Directory of Open Access Journals (Sweden)
Siyao Cheng
2017-03-01
Full Text Available With the rapid development of the Internet of Things (IoTs, wireless sensor networks (WSNs and related techniques, the amount of sensory data manifests an explosive growth. In some applications of IoTs and WSNs, the size of sensory data has already exceeded several petabytes annually, which brings too many troubles and challenges for the data collection, which is a primary operation in IoTs and WSNs. Since the exact data collection is not affordable for many WSN and IoT systems due to the limitations on bandwidth and energy, many approximate data collection algorithms have been proposed in the last decade. This survey reviews the state of the art of approximatedatacollectionalgorithms. Weclassifythemintothreecategories: themodel-basedones, the compressive sensing based ones, and the query-driven ones. For each category of algorithms, the advantages and disadvantages are elaborated, some challenges and unsolved problems are pointed out, and the research prospects are forecasted.
Approximate Sensory Data Collection: A Survey.
Cheng, Siyao; Cai, Zhipeng; Li, Jianzhong
2017-03-10
With the rapid development of the Internet of Things (IoTs), wireless sensor networks (WSNs) and related techniques, the amount of sensory data manifests an explosive growth. In some applications of IoTs and WSNs, the size of sensory data has already exceeded several petabytes annually, which brings too many troubles and challenges for the data collection, which is a primary operation in IoTs and WSNs. Since the exact data collection is not affordable for many WSN and IoT systems due to the limitations on bandwidth and energy, many approximate data collection algorithms have been proposed in the last decade. This survey reviews the state of the art of approximatedatacollectionalgorithms. Weclassifythemintothreecategories: themodel-basedones, the compressive sensing based ones, and the query-driven ones. For each category of algorithms, the advantages and disadvantages are elaborated, some challenges and unsolved problems are pointed out, and the research prospects are forecasted.
The Bloch Approximation in Periodically Perforated Media
International Nuclear Information System (INIS)
Conca, C.; Gomez, D.; Lobo, M.; Perez, E.
2005-01-01
We consider a periodically heterogeneous and perforated medium filling an open domain Ω of R N . Assuming that the size of the periodicity of the structure and of the holes is O(ε),we study the asymptotic behavior, as ε → 0, of the solution of an elliptic boundary value problem with strongly oscillating coefficients posed in Ω ε (Ω ε being Ω minus the holes) with a Neumann condition on the boundary of the holes. We use Bloch wave decomposition to introduce an approximation of the solution in the energy norm which can be computed from the homogenized solution and the first Bloch eigenfunction. We first consider the case where Ωis R N and then localize the problem for abounded domain Ω, considering a homogeneous Dirichlet condition on the boundary of Ω
Coated sphere scattering by geometric optics approximation.
Mengran, Zhai; Qieni, Lü; Hongxia, Zhang; Yinxin, Zhang
2014-10-01
A new geometric optics model has been developed for the calculation of light scattering by a coated sphere, and the analytic expression for scattering is presented according to whether rays hit the core or not. The ray of various geometric optics approximation (GOA) terms is parameterized by the number of reflections in the coating/core interface, the coating/medium interface, and the number of chords in the core, with the degeneracy path and repeated path terms considered for the rays striking the core, which simplifies the calculation. For the ray missing the core, the various GOA terms are dealt with by a homogeneous sphere. The scattering intensity of coated particles are calculated and then compared with those of Debye series and Aden-Kerker theory. The consistency of the results proves the validity of the method proposed in this work.
DEFF Research Database (Denmark)
Sadegh, Payman; Spall, J. C.
1998-01-01
The simultaneous perturbation stochastic approximation (SPSA) algorithm has attracted considerable attention for challenging optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient...... simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...... process. The objective is to minimize the mean square error of the estimate. The authors also consider maximization of the likelihood that the estimate be confined within a bounded symmetric region of the true parameter. The optimal distribution for the components of the simultaneous perturbation vector...
DEFF Research Database (Denmark)
Sadegh, Payman; Spall, J. C.
1997-01-01
The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient...... simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...... process. The objective is to minimize the mean square error of the estimate. We also consider maximization of the likelihood that the estimate be confined within a bounded symmetric region of the true parameter. The optimal distribution for the components of the simultaneous perturbation vector is found...
Some properties of dual and approximate dual of fusion frames
Arefijamaal, Ali Akbar; Neyshaburi, Fahimeh Arabyani
2016-01-01
In this paper we extend the notion of approximate dual to fusion frames and present some approaches to obtain dual and approximate alternate dual fusion frames. Also, we study the stability of dual and approximate alternate dual fusion frames.
Approximate Model for Turbulent Stagnation Point Flow.
Energy Technology Data Exchange (ETDEWEB)
Dechant, Lawrence [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
Here we derive an approximate turbulent self-similar model for a class of favorable pressure gradient wedge-like flows, focusing on the stagnation point limit. While the self-similar model provides a useful gross flow field estimate this approach must be combined with a near wall model is to determine skin friction and by Reynolds analogy the heat transfer coefficient. The combined approach is developed in detail for the stagnation point flow problem where turbulent skin friction and Nusselt number results are obtained. Comparison to the classical Van Driest (1958) result suggests overall reasonable agreement. Though the model is only valid near the stagnation region of cylinders and spheres it nonetheless provides a reasonable model for overall cylinder and sphere heat transfer. The enhancement effect of free stream turbulence upon the laminar flow is used to derive a similar expression which is valid for turbulent flow. Examination of free stream enhanced laminar flow suggests that the rather than enhancement of a laminar flow behavior free stream disturbance results in early transition to turbulent stagnation point behavior. Excellent agreement is shown between enhanced laminar flow and turbulent flow behavior for high levels, e.g. 5% of free stream turbulence. Finally the blunt body turbulent stagnation results are shown to provide realistic heat transfer results for turbulent jet impingement problems.
Configuring Airspace Sectors with Approximate Dynamic Programming
Bloem, Michael; Gupta, Pramod
2010-01-01
In response to changing traffic and staffing conditions, supervisors dynamically configure airspace sectors by assigning them to control positions. A finite horizon airspace sector configuration problem models this supervisor decision. The problem is to select an airspace configuration at each time step while considering a workload cost, a reconfiguration cost, and a constraint on the number of control positions at each time step. Three algorithms for this problem are proposed and evaluated: a myopic heuristic, an exact dynamic programming algorithm, and a rollouts approximate dynamic programming algorithm. On problem instances from current operations with only dozens of possible configurations, an exact dynamic programming solution gives the optimal cost value. The rollouts algorithm achieves costs within 2% of optimal for these instances, on average. For larger problem instances that are representative of future operations and have thousands of possible configurations, excessive computation time prohibits the use of exact dynamic programming. On such problem instances, the rollouts algorithm reduces the cost achieved by the heuristic by more than 15% on average with an acceptable computation time.
Adaptive approximation of higher order posterior statistics
Lee, Wonjung
2014-02-01
Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively. © 2013 Elsevier Inc.
Rainbows: Mie computations and the Airy approximation.
Wang, R T; van de Hulst, H C
1991-01-01
Efficient and accurate computation of the scattered intensity pattern by the Mie formulas is now feasible for size parameters up to x = 50,000 at least, which in visual light means spherical drops with diameters up to 6 mm. We present a method for evaluating the Mie coefficients from the ratios between Riccati-Bessel and Neumann functions of successive order. We probe the applicability of the Airy approximation, which we generalize to rainbows of arbitrary p (number of internal reflections = p - 1), by comparing the Mie and Airy intensity patterns. Millimeter size water drops show a match in all details, including the position and intensity of the supernumerary maxima and the polarization. A fairly good match is still seen for drops of 0.1 mm. A small spread in sizes helps to smooth out irrelevant detail. The dark band between the rainbows is used to test more subtle features. We conclude that this band contains not only externally reflected light (p = 0) but also a sizable contribution f rom the p = 6 and p = 7 rainbows, which shift rapidly with wavelength. The higher the refractive index, the closer both theories agree on the first primary rainbow (p = 2) peak for drop diameters as small as 0.02 mm. This may be useful in supporting experimental work.
Approximate von Neumann entropy for directed graphs.
Ye, Cheng; Wilson, Richard C; Comin, César H; Costa, Luciano da F; Hancock, Edwin R
2014-05-01
In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks.
Bond selective chemistry beyond the adiabatic approximation
Energy Technology Data Exchange (ETDEWEB)
Butler, L.J. [Univ. of Chicago, IL (United States)
1993-12-01
One of the most important challenges in chemistry is to develop predictive ability for the branching between energetically allowed chemical reaction pathways. Such predictive capability, coupled with a fundamental understanding of the important molecular interactions, is essential to the development and utilization of new fuels and the design of efficient combustion processes. Existing transition state and exact quantum theories successfully predict the branching between available product channels for systems in which each reaction coordinate can be adequately described by different paths along a single adiabatic potential energy surface. In particular, unimolecular dissociation following thermal, infrared multiphoton, or overtone excitation in the ground state yields a branching between energetically allowed product channels which can be successfully predicted by the application of statistical theories, i.e. the weakest bond breaks. (The predictions are particularly good for competing reactions in which when there is no saddle point along the reaction coordinates, as in simple bond fission reactions.) The predicted lack of bond selectivity results from the assumption of rapid internal vibrational energy redistribution and the implicit use of a single adiabatic Born-Oppenheimer potential energy surface for the reaction. However, the adiabatic approximation is not valid for the reaction of a wide variety of energetic materials and organic fuels; coupling between the electronic states of the reacting species play a a key role in determining the selectivity of the chemical reactions induced. The work described below investigated the central role played by coupling between electronic states in polyatomic molecules in determining the selective branching between energetically allowed fragmentation pathways in two key systems.
Hydration thermodynamics beyond the linear response approximation.
Raineri, Fernando O
2016-10-19
The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, [Formula: see text] and [Formula: see text], with the solvent environment. Throughout the A [Formula: see text] B transformation of the solute, the solvation system is described by a Hamiltonian [Formula: see text] that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density [Formula: see text] that the dimensionless perturbational solute-solvent interaction energy [Formula: see text] has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both [Formula: see text] and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density [Formula: see text]. The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in which either (1) the solute
Coronal Loops: Evolving Beyond the Isothermal Approximation
Schmelz, J. T.; Cirtain, J. W.; Allen, J. D.
2002-05-01
Are coronal loops isothermal? A controversy over this question has arisen recently because different investigators using different techniques have obtained very different answers. Analysis of SOHO-EIT and TRACE data using narrowband filter ratios to obtain temperature maps has produced several key publications that suggest that coronal loops may be isothermal. We have constructed a multi-thermal distribution for several pixels along a relatively isolated coronal loop on the southwest limb of the solar disk using spectral line data from SOHO-CDS taken on 1998 Apr 20. These distributions are clearly inconsistent with isothermal plasma along either the line of sight or the length of the loop, and suggested rather that the temperature increases from the footpoints to the loop top. We speculated originally that these differences could be attributed to pixel size -- CDS pixels are larger, and more `contaminating' material would be expected along the line of sight. To test this idea, we used CDS iron line ratios from our data set to mimic the isothermal results from the narrowband filter instruments. These ratios indicated that the temperature gradient along the loop was flat, despite the fact that a more complete analysis of the same data showed this result to be false! The CDS pixel size was not the cause of the discrepancy; rather, the problem lies with the isothermal approximation used in EIT and TRACE analysis. These results should serve as a strong warning to anyone using this simplistic method to obtain temperature. This warning is echoed on the EIT web page: ``Danger! Enter at your own risk!'' In other words, values for temperature may be found, but they may have nothing to do with physical reality. Solar physics research at the University of Memphis is supported by NASA grant NAG5-9783. This research was funded in part by the NASA/TRACE MODA grant for Montana State University.
Kim, SungKun; Lee, Hunpyo
2017-06-01
Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.
Approximate solutions of the Wei Hua oscillator using the Pekeris ...
Indian Academy of Sciences (India)
The analytical exact solutions of the wave equation with some exponential-type potentials are impossible for l = 0 states. So, the next best thing to do is to find approximate analytical solutions of a given potential by appropriate approximation techniques. Therefore, approximate schemes like the Pekeris approximation [6–8] ...
Approximate Implicitization of Parametric Curves Using Cubic Algebraic Splines
Directory of Open Access Journals (Sweden)
Xiaolei Zhang
2009-01-01
Full Text Available This paper presents an algorithm to solve the approximate implicitization of planar parametric curves using cubic algebraic splines. It applies piecewise cubic algebraic curves to give a global G2 continuity approximation to planar parametric curves. Approximation error on approximate implicitization of rational curves is given. Several examples are provided to prove that the proposed method is flexible and efficient.
Niels Bohr and the Atomic Structure
Indian Academy of Sciences (India)
IAS Admin
the electrons such as optical spectroscopy or chemical reactivity. This picture of the .... body of uncorrelated data, and thus could get to the heart of the problem. Second, he appreciated the distinction between atomic processes and the nuclear processes. .... theory needed new concepts and mathematical tools, but classical.
Niels Bohr and the Atomic Structure
Indian Academy of Sciences (India)
IAS Admin
that succeeded in explaining the spectral features of hydrogen atom. In the process, he incorporated some non-classical features such as discrete energy levels for the bound electrons, and quantization of their angular ... element in the periodic table is determined by the nuclear charge. The particle has a mass of four ...
Cheon, Sooyoung
2013-02-16
Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.
Peng, Degao; Yang, Yang; Zhang, Peng; Yang, Weitao
2014-12-07
In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N(4)). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as ⟨Ŝ(2)⟩ are also developed and tested.
Coefficients Calculation in Pascal Approximation for Passive Filter Design
Directory of Open Access Journals (Sweden)
George B. Kasapoglu
2018-02-01
Full Text Available The recently modified Pascal function is further exploited in this paper in the design of passive analog filters. The Pascal approximation has non-equiripple magnitude, in contrast of the most well-known approximations, such as the Chebyshev approximation. A novelty of this work is the introduction of a precise method that calculates the coefficients of the Pascal function. Two examples are presented for the passive design to illustrate the advantages and the disadvantages of the Pascal approximation. Moreover, the values of the passive elements can be taken from tables, which are created to define the normalized values of these elements for the Pascal approximation, as Zverev had done for the Chebyshev, Elliptic, and other approximations. Although Pascal approximation can be implemented to both passive and active filter designs, a passive filter design is addressed in this paper, and the benefits and shortcomings of Pascal approximation are presented and discussed.
Comparison of four support-vector based function approximators
de Kruif, B.J.; de Vries, Theodorus J.A.
2004-01-01
One of the uses of the support vector machine (SVM), as introduced in V.N. Vapnik (2000), is as a function approximator. The SVM and approximators based on it, approximate a relation in data by applying interpolation between so-called support vectors, being a limited number of samples that have been
Meta-Regression Approximations to Reduce Publication Selection Bias
Stanley, T. D.; Doucouliagos, Hristos
2014-01-01
Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with…
Three-loop Phi-derivable approximation in QED
Andersen, J.O.; Strickland, M.
2005-01-01
In this paper we examine 9Φ-derivable approximations in QED, General theorems tell us that the gauge dependence of the n-loop Φ-derivable approximation shows up at order g2n where g is the coupling constant. We consider the gauge dependence of the two-loop Φ-derivable approximation to the Debye mass
On Love's approximation for fluid-filled elastic tubes
International Nuclear Information System (INIS)
Caroli, E.; Mainardi, F.
1980-01-01
A simple procedure is set up to introduce Love's approximation for wave propagation in thin-walled fluid-filled elastic tubes. The dispersion relation for linear waves and the radial profile for fluid pressure are determined in this approximation. It is shown that the Love approximation is valid in the low-frequency regime. (author)
Approximation Properties of Certain Summation Integral Type Operators
Directory of Open Access Journals (Sweden)
Patel P.
2015-03-01
Full Text Available In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.
Iterative Approximate Solutions of Kinetic Equations for Reversible Enzyme Reactions
Khoshnaw, S.
2012-01-01
We study kinetic models of reversible enzyme reactions and compare two techniques for analytic approximate solutions of the model. Analytic approximate solutions of non-linear reaction equations for reversible enzyme reactions are calculated using the Homotopy Perturbation Method (HPM) and the Simple Iteration Method (SIM). The results of the approximations are similar. The Matlab programs are included in appendices.
2014-03-01
Almost dry but never dull: ASE 2014 EuroPhysicsFun shows physics to Europe Institute of Physics for Africa (IOPfA) South Sudan Report October 2013 Celebrating the centenary of x-ray diffraction The Niels Bohr Institute—an EPS Historical Site Nordic Research Symposium on Science Education (NFSUN) 2014: inquiry-based science education in technology-rich environments Physics World Cup 2013
Approximate Noether symmetries and collineations for regular perturbative Lagrangians
Paliathanasis, Andronikos; Jamal, Sameerah
2018-01-01
Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying manifold. In particular we determine the generic Noether symmetry conditions for the approximate point symmetries and we find that for a class of perturbed Lagrangians, Noether symmetries are related to the elements of the Homothetic algebra of the metric which is defined by the unperturbed Lagrangian. Moreover, we discuss how exact symmetries become approximate symmetries. Finally, some applications are presented.
Perturbative corrections for approximate inference in gaussian latent variable models
DEFF Research Database (Denmark)
Opper, Manfred; Paquet, Ulrich; Winther, Ole
2013-01-01
Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact b...... illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution. © 2013 Manfred Opper, Ulrich Paquet and Ole Winther....
Methods of Approximation Theory in Complex Analysis and Mathematical Physics
Saff, Edward
1993-01-01
The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...
Discrete extrinsic curvatures and approximation of surfaces by polar polyhedra
Garanzha, V. A.
2010-01-01
Duality principle for approximation of geometrical objects (also known as Eu-doxus exhaustion method) was extended and perfected by Archimedes in his famous tractate “Measurement of circle”. The main idea of the approximation method by Archimedes is to construct a sequence of pairs of inscribed and circumscribed polygons (polyhedra) which approximate curvilinear convex body. This sequence allows to approximate length of curve, as well as area and volume of the bodies and to obtain error estimates for approximation. In this work it is shown that a sequence of pairs of locally polar polyhedra allows to construct piecewise-affine approximation to spherical Gauss map, to construct convergent point-wise approximations to mean and Gauss curvature, as well as to obtain natural discretizations of bending energies. The Suggested approach can be applied to nonconvex surfaces and in the case of multiple dimensions.
Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length
Directory of Open Access Journals (Sweden)
Jun Tao
2015-01-01
Full Text Available In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up to Oβ2. We also show that if the slope of the potential at a turning point is too steep, the WKB connection formula is no longer valid around the turning point. The effects of the minimal length on the classical motions are investigated using the Hamilton-Jacobi method. We also use the Bohr-Sommerfeld quantization to study statistical physics in deformed spaces with the minimal length.
Approximate solutions for certain bidomain problems in electrocardiography
Johnston, Peter R.
2008-10-01
The simulation of problems in electrocardiography using the bidomain model for cardiac tissue often creates issues with satisfaction of the boundary conditions required to obtain a solution. Recent studies have proposed approximate methods for solving such problems by satisfying the boundary conditions only approximately. This paper presents an analysis of their approximations using a similar method, but one which ensures that the boundary conditions are satisfied during the whole solution process. Also considered are additional functional forms, used in the approximate solutions, which are more appropriate to specific boundary conditions. The analysis shows that the approximations introduced by Patel and Roth [Phys. Rev. E 72, 051931 (2005)] generally give accurate results. However, there are certain situations where functional forms based on the geometry of the problem under consideration can give improved approximations. It is also demonstrated that the recent methods are equivalent to different approaches to solving the same problems introduced 20years earlier.
On approximation of flat Banach modules by free modules
International Nuclear Information System (INIS)
Aristov, O Yu
2005-01-01
The local structure of flat Banach modules is considered; in particular, it is shown that if a flat module has the approximation property, then it is freely approximable, that is, the identity operator on it is approximated by operators each of which admits factorization through a free Banach module satisfying a natural finiteness condition. Among the maps involved in the factorization, the first is approximately multiplicative up to ε on compact sets, and the second is exactly a morphism of modules. The properties of freely approximable and approximately projective modules are studied. It is proved that the standard complex for calculating the derived functor Ext is locally asymptotically exact in the first term for an arbitrary second argument if and only if its first argument is a flat Banach module.
Precise analytic approximations for the Bessel function J1 (x)
Maass, Fernando; Martin, Pablo
2018-03-01
Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.
Space-efficient path-reporting approximate distance oracles
DEFF Research Database (Denmark)
Elkin, Michael; Neiman, Ofer; Wulff-Nilsen, Christian
2016-01-01
We consider approximate path-reporting distance oracles, distance labeling and labeled routing with extremely low space requirements, for general undirected graphs. For distance oracles, we show how to break the nlogn space bound of Thorup and Zwick if approximate paths rather than distances need...... to be reported. For approximate distance labeling and labeled routing, we break the previously best known space bound of O(logn) words per vertex. The cost for such space efficiency is an increased stretch....
Approximation for a large-angle simple pendulum period
International Nuclear Information System (INIS)
Belendez, A; Rodes, J J; Belendez, T; Hernandez, A
2009-01-01
An approximation scheme to obtain the period for large amplitude oscillations of a simple pendulum is analysed and discussed. The analytical approximate formula for the period is the same as that suggested by Hite (2005 Phys. Teach. 43 290), but it is now obtained analytically by means of a term-by-term comparison of the power-series expansion for the approximate period with the corresponding series for the exact period. (letters and comments)
Multijet final states: exact results and the leading pole approximation
International Nuclear Information System (INIS)
Ellis, R.K.; Owens, J.F.
1984-09-01
Exact results for the process gg → ggg are compared with those obtained using the leading pole approximation. Regions of phase space where the approximation breaks down are discussed. A specific example relevant for background estimates to W boson production is presented. It is concluded that in this instance the leading pole approximation may underestimate the standard QCD background by more than a factor of two in certain kinematic regions of physical interest
Fractal image coding by an approximation of the collage error
Salih, Ismail; Smith, Stanley H.
1998-12-01
In fractal image compression an image is coded as a set of contractive transformations, and is guaranteed to generate an approximation to the original image when iteratively applied to any initial image. In this paper we present a method for mapping similar regions within an image by an approximation of the collage error; that is, range blocks can be approximated by a linear combination of domain blocks.
Upper bounds on minimum cardinality of exact and approximate reducts
Chikalov, Igor
2010-01-01
In the paper, we consider the notions of exact and approximate decision reducts for binary decision tables. We present upper bounds on minimum cardinality of exact and approximate reducts depending on the number of rows (objects) in the decision table. We show that the bound for exact reducts is unimprovable in the general case, and the bound for approximate reducts is almost unimprovable in the general case. © 2010 Springer-Verlag Berlin Heidelberg.
LCAO approximation for scaling properties of the Menger sponge fractal.
Sakoda, Kazuaki
2006-11-13
The electromagnetic eigenmodes of a three-dimensional fractal called the Menger sponge were analyzed by the LCAO (linear combination of atomic orbitals) approximation and a first-principle calculation based on the FDTD (finite-difference time-domain) method. Due to the localized nature of the eigenmodes, the LCAO approximation gives a good guiding principle to find scaled eigenfunctions and to observe the approximate self-similarity in the spectrum of the localized eigenmodes.
Analysis of the dynamical cluster approximation for the Hubbard model
Aryanpour, K.; Hettler, M. H.; Jarrell, M.
2002-01-01
We examine a central approximation of the recently introduced Dynamical Cluster Approximation (DCA) by example of the Hubbard model. By both analytical and numerical means we study non-compact and compact contributions to the thermodynamic potential. We show that approximating non-compact diagrams by their cluster analogs results in a larger systematic error as compared to the compact diagrams. Consequently, only the compact contributions should be taken from the cluster, whereas non-compact ...
Approximation theorems by Meyer-Koenig and Zeller type operators
International Nuclear Information System (INIS)
Ali Ozarslan, M.; Duman, Oktay
2009-01-01
This paper is mainly connected with the approximation properties of Meyer-Koenig and Zeller (MKZ) type operators. We first introduce a general sequence of MKZ operators based on q-integers and then obtain a Korovkin-type approximation theorem for these operators. We also compute their rates of convergence by means of modulus of continuity and the elements of Lipschitz class functionals. Furthermore, we give an rth order generalization of our operators in order to get some explicit approximation results.
Co-Occuring Directions Sketching for Approximate Matrix Multiply
Mroueh, Youssef; Marcheret, Etienne; Goel, Vaibhava
2016-01-01
We introduce co-occurring directions sketching, a deterministic algorithm for approximate matrix product (AMM), in the streaming model. We show that co-occuring directions achieves a better error bound for AMM than other randomized and deterministic approaches for AMM. Co-occurring directions gives a $1 + \\epsilon$ -approximation of the optimal low rank approximation of a matrix product. Empirically our algorithm outperforms competing methods for AMM, for a small sketch size. We validate empi...
Exchange energy in the local Airy gas approximation
DEFF Research Database (Denmark)
Vitos, Levente; Johansson, B.; Kollár, J.
2000-01-01
The Airy gas model of the edge electron gas is used to construct an exchange-energy functional that is an alternative to those obtained in the local-density and generalized-gradient approximations. Test calculations for rare-gas atoms, molecules, solids, and surfaces show that the Airy gas...... functional performs better than the local-density approximation in all cases and better than the generalized-gradient approximation for solids and surfaces....
A simple approximation for eigenvalues in quantum theory
International Nuclear Information System (INIS)
Mitter, H.; Yamazaki, K.
1983-01-01
An approximation method for the determination of energy levels in quantum theory is discussed, which starts from a scaled set of eigenstates of a solvable model. It is shown, that the lowest approximation fulfills certain relations, which hold also exactly. The approximation is tested by comparison with numerically computed eigenvalues in several cases. The errors turn out to be moderate in most of these and depend very little on typical coupling constants. (Author)
Perturbative corrections for approximate inference in gaussian latent variable models
DEFF Research Database (Denmark)
Opper, Manfred; Paquet, Ulrich; Winther, Ole
2013-01-01
orders, corrections of increasing polynomial complexity can be applied to the approximation. The second order provides a correction in quadratic time, which we apply to an array of Gaussian process and Ising models. The corrections generalize to arbitrarily complex approximating families, which we...... illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution. © 2013 Manfred Opper, Ulrich Paquet and Ole Winther....
Algorithms For Approximation IV. Proceedings of the 2001 International Symposium
National Research Council Canada - National Science Library
Levesley, Jeremy
2002-01-01
...: Algorithms- Approximation of Functions, Data Fitting, Geometric and Surface Modelling, Splines, Wavelets, Radial Basis Functions, Support Vector Machines, Norms and Metrics, Errors in Data, Uncertainty Estimation...
Recursive B-spline approximation using the Kalman filter
Directory of Open Access Journals (Sweden)
Jens Jauch
2017-02-01
Full Text Available This paper proposes a novel recursive B-spline approximation (RBA algorithm which approximates an unbounded number of data points with a B-spline function and achieves lower computational effort compared with previous algorithms. Conventional recursive algorithms based on the Kalman filter (KF restrict the approximation to a bounded and predefined interval. Conversely RBA includes a novel shift operation that enables to shift estimated B-spline coefficients in the state vector of a KF. This allows to adapt the interval in which the B-spline function can approximate data points during run-time.
Scattering theory and effective medium approximations to heterogeneous materials
International Nuclear Information System (INIS)
Gubernatis, J.E.
1977-01-01
The formal analogy existing between problems studied in the microscopic theory of disordered alloys and problems concerned with the effective (macroscopic) behavior of heterogeneous materials is discussed. Attention is focused on (1) analogous approximations (effective medium approximations) developed for the microscopic problems by scattering theory concepts and techniques, but for the macroscopic problems principally by intuitive means, (2) the link, provided by scattering theory, of the intuitively developed approximations to a well-defined perturbative analysis, (3) the possible presence of conditionally convergent integrals in effective medium approximations
Approximation of quadrilaterals by rational quadrilaterals in the plane
Indian Academy of Sciences (India)
Keywords. Rational triangles and quadrilaterals; rational approximability of polygons; rational points on quartic curves; elliptic curves; torsion points; rational points on varieties and their density.
Embedding impedance approximations in the analysis of SIS mixers
Kerr, A. R.; Pan, S.-K.; Withington, S.
1992-01-01
Future millimeter-wave radio astronomy instruments will use arrays of many SIS receivers, either as focal plane arrays on individual radio telescopes, or as individual receivers on the many antennas of radio interferometers. Such applications will require broadband integrated mixers without mechanical tuners. To produce such mixers, it will be necessary to improve present mixer design techniques, most of which use the three-frequency approximation to Tucker's quantum mixer theory. This paper examines the adequacy of three approximations to Tucker's theory: (1) the usual three-frequency approximation which assumes a sinusoidal LO voltage at the junction, and a short-circuit at all frequencies above the upper sideband; (2) a five-frequency approximation which allows two LO voltage harmonics and five small-signal sidebands; and (3) a quasi five-frequency approximation in which five small-signal sidebands are allowed, but the LO voltage is assumed sinusoidal. These are compared with a full harmonic-Newton solution of Tucker's equations, including eight LO harmonics and their corresponding sidebands, for realistic SIS mixer circuits. It is shown that the accuracy of the three approximations depends strongly on the value of omega R(sub N)C for the SIS junctions used. For large omega R(sub N)C, all three approximations approach the eight-harmonic solution. For omega R(sub N)C values in the range 0.5 to 10, the range of most practical interest, the quasi five-frequency approximation is a considerable improvement over the three-frequency approximation, and should be suitable for much design work. For the realistic SIS mixers considered here, the five-frequency approximation gives results very close to those of the eight-harmonic solution. Use of these approximations, where appropriate, considerably reduces the computational effort needed to analyze an SIS mixer, and allows the design and optimization of mixers using a personal computer.
Efficient approximation of black-box functions and Pareto sets
Rennen, G.
2009-01-01
In the case of time-consuming simulation models or other so-called black-box functions, we determine a metamodel which approximates the relation between the input- and output-variables of the simulation model. To solve multi-objective optimization problems, we approximate the Pareto set, i.e. the
Approximation of the inverse G-frame operator
Indian Academy of Sciences (India)
In this paper, we introduce the concept of (strong) projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we ...
On Approximations of Compact Sets of Functions by Algebraic Surfaces
Kudryavtsev, S. N.
1986-06-01
This article deals with approximations of certain compact sets of smooth and analytic functions by families of functions depending in a polynomial fashion on parameters. The connection between the accuracy of the approximations of the compact sets by such families and the number of parameters and their degree is studied. Bibliography: 3 titles.
The modified signed likelihood statistic and saddlepoint approximations
DEFF Research Database (Denmark)
Jensen, Jens Ledet
1992-01-01
SUMMARY: For a number of tests in exponential families we show that the use of a normal approximation to the modified signed likelihood ratio statistic r * is equivalent to the use of a saddlepoint approximation. This is also true in a large deviation region where the signed likelihood ratio...... statistic r is of order √ n. © 1992 Biometrika Trust....
Approximation of the inverse G-frame operator
Indian Academy of Sciences (India)
... projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we like using finite-dimensional linear algebra.
Performance approximation of pick-to-belt orderpicking systems
M.B.M. de Koster (René)
1994-01-01
textabstractIn this paper, an approximation method is discussed for the analysis of pick-to-belt orderpicking systems. The aim of the approximation method is to provide an instrument for obtaining rapid insight in the performance of designs of pick-to-belt orderpicking systems. It can be used to
An approximate confidence interval for recombination fraction in ...
African Journals Online (AJOL)
user
2011-02-14
Feb 14, 2011 ... proposed a two stage Markov Chain Monte Carlo (MCMC) method to calculate an approximate confidence interval (ACI) ... Key words: Markov Chain Monte Carlo (MCMC), Gibbs sampler, approximate confidence interval, simulation size. ... from local conditional distributions at parameter valuesθ , given the ...
Approximation properties of the neuro-fuzzy minimum function
Gottschling, Andreas; Kreuter, Christof
1999-01-01
The integration of fuzzy logic systems and neural networks in data driven nonlinear modeling applications has generally been limited to functions based upon the multiplicative fuzzy implication rule for theoretical and computational reasons. We derive a universal approximation result for the minimum fuzzy implication rule as well as a differentiable substitute function that allows fast optimization and function approximation with neuro-fuzzy networks.
Finite approximate controllability for semilinear heat equations in noncylindrical domains
Directory of Open Access Journals (Sweden)
Menezes Silvano B. de
2004-01-01
Full Text Available We investigate finite approximate controllability for semilinear heat equation in noncylindrical domains. First we study the linearized problem and then by an application of the fixed point result of Leray-Schauder we obtain the finite approximate controllability for the semilinear state equation.
A simple approximation method for dilute Ising systems
International Nuclear Information System (INIS)
Saber, M.
1996-10-01
We describe a simple approximate method to analyze dilute Ising systems. The method takes into consideration the fluctuations of the effective field, and is based on a probability distribution of random variables which correctly accounts for all the single site kinematic relations. It is shown that the simplest approximation gives satisfactory results when compared with other methods. (author). 12 refs, 2 tabs
Topology optimization of dynamics problems with Padé approximants
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2007-01-01
An efficient procedure for topology optimization of dynamics problems is proposed. The method is based on frequency responses represented by Padé approximants and analytical sensitivity analysis derived using the adjoint method. This gives an accurate approximation of the frequency response over ...
The generalized Mayer theorem in the approximating hamiltonian method
International Nuclear Information System (INIS)
Bakulev, A.P.; Bogoliubov, N.N. Jr.; Kurbatov, A.M.
1982-07-01
With the help of the generalized Mayer theorem we obtain the improved inequality for free energies of model and approximating systems, where only ''connected parts'' over the approximating hamiltonian are taken into account. For the concrete system we discuss the problem of convergency of appropriate series of ''connected parts''. (author)
On a saddlepoint approximation to the Markov binomial distribution
DEFF Research Database (Denmark)
Jensen, Jens Ledet
A nonstandard saddlepoint approximation to the distribution of a sum of Markov dependent trials is introduced. The relative error of the approximation is studied, not only for the number of summands tending to infinity, but also for the parameter approaching the boundary of its definition range. ...
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
Gordon, Sheldon P.; Yang, Yajun
2017-01-01
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…
On approximation of Lie groups by discrete subgroups
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... The notion of approximation of Lie groups by discrete subgroups was introduced by Tôyama in Kodai Math. Sem. Rep. 1 (1949) 36–37 and investigated in detail by Kuranishi in Nagoya Math. J. 2 (1951) 63–71. It is known as a theorem of Tôyama that any connected Lie group approximated by discrete ...
Approximate solutions of the Wei Hua oscillator using the Pekeris ...
Indian Academy of Sciences (India)
The approximate analytical bound-state solutions of the Schrödinger equation for the. Wei Hua oscillator are carried out in N-dimensional space by taking Pekeris approximation scheme to the orbital centrifugal term. Solutions of the corresponding hyper-radial equation are obtained using the conventional Nikiforov–Uvarov ...
Reply to Steele & Ferrer: Modeling Oscillation, Approximately or Exactly?
Oud, Johan H. L.; Folmer, Henk
2011-01-01
This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure…
Merging Belief Propagation and the Mean Field Approximation
DEFF Research Database (Denmark)
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro
2010-01-01
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence...
OPTICAL QUANTITATION AND RADIOGRAPHIC DIAGNOSIS OF INCIPIENT APPROXIMAL CARIES LESIONS
VERDONSCHOT, EH; VANDERIJKE, JW; BROUWER, W; TENBOSCH, JJ; TRUIN, GJ
1991-01-01
The objectives of this study were to test the applicability of photocell measurements in approximal caries diagnosis and to evaluate the use of radiographs as validating criterion. Forty extracted premolars were selected, and the progression of the approximal lesions was graded clinically and
Function approximation using combined unsupervised and supervised learning.
Andras, Peter
2014-03-01
Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data.
The high intensity approximation applied to multiphoton ionization
International Nuclear Information System (INIS)
Brandi, H.S.; Davidovich, L.; Zagury, N.
1980-08-01
It is shown that the most commonly used high intensity approximations as applied to ionization by strong electromagnetic fields are related. The applicability of the steepest descent method in these approximations, and the relation between them and first-order perturbation theory, are also discussed. (Author) [pt
A Multi-wavelet type limiter for discontinuous Galerkin approximations
Cheruvu, V.; Ryan, J.K.
2010-01-01
In this report, we present a multi-wavelet type limiter for the discontinuous Galerkin method for limiting the solution when spurious oscillations develop near a shock. This limiting leads to a loss of information in the approximation that can be detrimental to a higher order approximation (k > 2).
The second Born approximation of electron–argon elastic scattering ...
Indian Academy of Sciences (India)
We study the elastic scattering of atomic argon by electron in the presence of a bichromatic laser ﬁeld in the second Born approximation. The target atom is approximated by a simple screening potential and the continuum states of the impinging and emitting electrons are described as Volkov states. We evaluate the S-matrix ...
The second Born approximation of electron–argon elastic scattering ...
Indian Academy of Sciences (India)
Abstract. We study the elastic scattering of atomic argon by electron in the presence of a bichro- matic laser field in the second Born approximation. The target atom is approximated by a simple screening potential and the continuum states of the impinging and emitting electrons are described as Volkov states. We evaluate ...
Practical error analysis of the quasi-steady-state approximation ...
African Journals Online (AJOL)
The Quasi-Steady-State Approximation (QSSA) is a method of getting approximate solutions to differential equations, developed heuristically in biochemistry early this century. It can produce acceptable and important results even when formal analytic and numerical procedures fail. It has become associated with singular ...
A-Statistical extension of the Korovkin type approximation theorem
Indian Academy of Sciences (India)
imation, in various areas of functional analysis [1,3,5,12,15]. The study of the Korovkin type approximation theory is a well-established area of research, which deals with the problem of approximating a function f by means of a sequence {Lnf } of positive lin- ear operators. Statistical convergence, which was introduced nearly ...
A periodic basis system of the smooth approximation space
Czech Academy of Sciences Publication Activity Database
Segeth, Karel
2015-01-01
Roč. 267, 15 September (2015), s. 436-444 ISSN 0096-3003 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : smooth approximation * data approximation * data interpolation * Fourier transform Subject RIV: BA - General Mathematics Impact factor: 1.345, year: 2015 http://www.sciencedirect.com/science/article/pii/S0096300315001526
Fifth International Conference on "Approximation and Optimization in the Caribbean"
Approximation, Optimization and Mathematical Economic
2001-01-01
The articles in this proceedings volume reflect the current trends in the theory of approximation, optimization and mathematical economics, and include numerous applications. The book will be of interest to researchers and graduate students involved in functional analysis, approximation theory, mathematical programming and optimization, game theory, mathematical finance and economics.
On root mean square approximation by exponential functions
Sharipov, Ruslan
2014-01-01
The problem of root mean square approximation of a square integrable function by finite linear combinations of exponential functions is considered. It is subdivided into linear and nonlinear parts. The linear approximation problem is solved. Then the nonlinear problem is studied in some particular example.
Approximate first integrals of a chaotic Hamiltonian system | Unal ...
African Journals Online (AJOL)
Approximate first integrals (conserved quantities) of a Hamiltonian dynamical system with two-degrees of freedom which arises in the modeling of galaxy have been obtained based on the approximate Noether symmetries for the resonance ω1 = ω2. Furthermore, Kolmogorov-Arnold-Moser (KAM) curves have been ...
The Log-Linear Return Approximation, Bubbles, and Predictability
DEFF Research Database (Denmark)
Engsted, Tom; Pedersen, Thomas Quistgaard; Tanggaard, Carsten
2012-01-01
We study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividend-price ratio. Next, we simulate various rational bubbles which have explosive conditional expe...
Approximate furthest neighbor with application to annulus query
DEFF Research Database (Denmark)
Pagh, Rasmus; Silvestri, Francesco; Sivertsen, Johan von Tangen
2016-01-01
Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries and present a simple, fast, and highly practical data structure for answering AFN queries in high-dimensional Euclid......Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries and present a simple, fast, and highly practical data structure for answering AFN queries in high...... a variation based on a query-independent ordering of the database points; while this does not have the provable approximation factor of the query-dependent data structure, it offers significant improvement in time and space complexity. We give a theoretical analysis and experimental results. As an application...
The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes
Blas, Diego; Tram, Thomas
2011-01-01
Boltzmann codes are used extensively by several groups for constraining cosmological parameters with Cosmic Microwave Background and Large Scale Structure data. This activity is computationally expensive, since a typical project requires from 10'000 to 100'000 Boltzmann code executions. The newly released code CLASS (Cosmic Linear Anisotropy Solving System) incorporates improved approximation schemes leading to a simultaneous gain in speed and precision. We describe here the three approximations used by CLASS for basic LambdaCDM models, namely: a baryon-photon tight-coupling approximation which can be set to first order, second order or to a compromise between the two; an ultra-relativistic fluid approximation which had not been implemented in public distributions before; and finally a radiation streaming approximation taking reionisation into account.
Ordering, symbols and finite-dimensional approximations of path integrals
International Nuclear Information System (INIS)
Kashiwa, Taro; Sakoda, Seiji; Zenkin, S.V.
1994-01-01
We derive general form of finite-dimensional approximations of path integrals for both bosonic and fermionic canonical systems in terms of symbols of operators determined by operator ordering. We argue that for a system with a given quantum Hamiltonian such approximations are independent of the type of symbols up to terms of O(ε), where ε of is infinitesimal time interval determining the accuracy of the approximations. A new class of such approximations is found for both c-number and Grassmannian dynamical variables. The actions determined by the approximations are non-local and have no classical continuum limit except the cases of pq- and qp-ordering. As an explicit example the fermionic oscillator is considered in detail. (author)
Approximate models for broken clouds in stochastic radiative transfer theory
International Nuclear Information System (INIS)
Doicu, Adrian; Efremenko, Dmitry S.; Loyola, Diego; Trautmann, Thomas
2014-01-01
This paper presents approximate models in stochastic radiative transfer theory. The independent column approximation and its modified version with a solar source computed in a full three-dimensional atmosphere are formulated in a stochastic framework and for arbitrary cloud statistics. The nth-order stochastic models describing the independent column approximations are equivalent to the nth-order stochastic models for the original radiance fields in which the gradient vectors are neglected. Fast approximate models are further derived on the basis of zeroth-order stochastic models and the independent column approximation. The so-called “internal mixing” models assume a combination of the optical properties of the cloud and the clear sky, while the “external mixing” models assume a combination of the radiances corresponding to completely overcast and clear skies. A consistent treatment of internal and external mixing models is provided, and a new parameterization of the closure coefficient in the effective thickness approximation is given. An efficient computation of the closure coefficient for internal mixing models, using a previously derived vector stochastic model as a reference, is also presented. Equipped with appropriate look-up tables for the closure coefficient, these models can easily be integrated into operational trace gas retrieval systems that exploit absorption features in the near-IR solar spectrum. - Highlights: • Independent column approximation in a stochastic setting. • Fast internal and external mixing models for total and diffuse radiances. • Efficient optimization of internal mixing models to match reference models
Dynamic flow-driven erosion - An improved approximate solution
Yu, Bofu; Guo, Dawei; Rose, Calvin W.
2017-09-01
Rose et al. (2007) published an approximate solution of dynamic sediment concentration for steady and uniform flows, and this approximate solution shows a peak sediment concentration at the early stage of a runoff event, which can be used to describe and explain the first flush effect, a commonly observed phenomenon, especially in the urban environment. However the approximate solution does not converge to the steady state solution that is known exactly. The purpose of the note is to improve the approximate solution of Rose et al. (2007) by maintaining its functional form while forcing its steady state behaviour for sediment concentration to converge to the known steady state solution. The quality of the new approximate solution was assessed by comparing the new approximate solution with an exact solution for the single size class case, and with the numerical solution for the multiple size classes. It was found that 1) the relative error, or discrepancy, decreases as the stream power increases for all three soils considered; 2) the largest discrepancy occurs for the peak sediment concentration, and the average discrepancy in the peak concentration is less than 10% for the three soils considered; 3) for the majority of the 27 slope-flow combinations and for the three soils considered, the new approximate solution modestly underestimates the peak sediment concentration.
Confidence Intervals for Asbestos Fiber Counts: Approximate Negative Binomial Distribution.
Bartley, David; Slaven, James; Harper, Martin
2017-03-01
The negative binomial distribution is adopted for analyzing asbestos fiber counts so as to account for both the sampling errors in capturing only a finite number of fibers and the inevitable human variation in identifying and counting sampled fibers. A simple approximation to this distribution is developed for the derivation of quantiles and approximate confidence limits. The success of the approximation depends critically on the use of Stirling's expansion to sufficient order, on exact normalization of the approximating distribution, on reasonable perturbation of quantities from the normal distribution, and on accurately approximating sums by inverse-trapezoidal integration. Accuracy of the approximation developed is checked through simulation and also by comparison to traditional approximate confidence intervals in the specific case that the negative binomial distribution approaches the Poisson distribution. The resulting statistics are shown to relate directly to early research into the accuracy of asbestos sampling and analysis. Uncertainty in estimating mean asbestos fiber concentrations given only a single count is derived. Decision limits (limits of detection) and detection limits are considered for controlling false-positive and false-negative detection assertions and are compared to traditional limits computed assuming normal distributions. Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.
Weak Approximation of SDEs by Discrete-Time Processes
Directory of Open Access Journals (Sweden)
Henryk Zähle
2008-01-01
Full Text Available We consider the martingale problem related to the solution of an SDE on the line. It is shown that the solution of this martingale problem can be approximated by solutions of the corresponding time-discrete martingale problems under some conditions. This criterion is especially expedient for establishing the convergence of population processes to SDEs. We also show that the criterion yields a weak Euler scheme approximation of SDEs under fairly weak assumptions on the driving force of the approximating processes.
Approximation for a Coulomb-Volkov solution in strong fields
Reiss, H. R.; Krainov, V. P.
1994-08-01
A simple analytical approximation is found for the wave function of an electron simultaneously exposed to a strong, circularly polarized plane-wave field and an atomic Coulomb potential. The approximation is valid when α0>>1, where α0 is the classical radius of motion of a free electron in the plane-wave field. This constraint is sufficiently mild at low frequencies that it makes possible a major extension of the lower bound of laser intensities for which Volkov-solution-based approximations are useful.
Pade approximants and efficient analytic continuation of a power series
International Nuclear Information System (INIS)
Suetin, S P
2002-01-01
This survey reflects the current state of the theory of Pade approximants, that is, best rational approximations of power series. The main focus is on the so-called inverse problems of this theory, in which one must make deductions about analytic continuation of a given power series on the basis of the known asymptotic behaviour of the poles of some sequence of Pade approximants of this series. Row and diagonal sequences are studied from this point of view. Gonchar's and Rakhmanov's fundamental results of inverse nature are presented along with results of the author
Good and Bad Neighborhood Approximations for Outlier Detection Ensembles
DEFF Research Database (Denmark)
Kirner, Evelyn; Schubert, Erich; Zimek, Arthur
2017-01-01
Outlier detection methods have used approximate neighborhoods in filter-refinement approaches. Outlier detection ensembles have used artificially obfuscated neighborhoods to achieve diverse ensemble members. Here we argue that outlier detection models could be based on approximate neighborhoods...... in the first place, thus gaining in both efficiency and effectiveness. It depends, however, on the type of approximation, as only some seem beneficial for the task of outlier detection, while no (large) benefit can be seen for others. In particular, we argue that space-filling curves are beneficial...
Approximate Quantum Adders with Genetic Algorithms: An IBM Quantum Experience
Directory of Open Access Journals (Sweden)
Li Rui
2017-07-01
Full Text Available It has been proven that quantum adders are forbidden by the laws of quantum mechanics. We analyze theoretical proposals for the implementation of approximate quantum adders and optimize them by means of genetic algorithms, improving previous protocols in terms of efficiency and fidelity. Furthermore, we experimentally realize a suitable approximate quantum adder with the cloud quantum computing facilities provided by IBM Quantum Experience. The development of approximate quantum adders enhances the toolbox of quantum information protocols, paving the way for novel applications in quantum technologies.
Error bounds for approximations with deep ReLU networks.
Yarotsky, Dmitry
2017-10-01
We study expressive power of shallow and deep neural networks with piece-wise linear activation functions. We establish new rigorous upper and lower bounds for the network complexity in the setting of approximations in Sobolev spaces. In particular, we prove that deep ReLU networks more efficiently approximate smooth functions than shallow networks. In the case of approximations of 1D Lipschitz functions we describe adaptive depth-6 network architectures more efficient than the standard shallow architecture. Copyright © 2017 Elsevier Ltd. All rights reserved.
An approximation to the interference term using Frobenius Method
Energy Technology Data Exchange (ETDEWEB)
Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C. da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear; E-mail: aquilino@lmp.ufrj.br
2007-07-01
An analytical approximation of the interference term {chi}(x,{xi}) is proposed. The approximation is based on the differential equation to {chi}(x,{xi}) using the Frobenius method and the parameter variation. The analytical expression of the {chi}(x,{xi}) obtained in terms of the elementary functions is very simple and precise. In this work one applies the approximations to the Doppler broadening functions and to the interference term in determining the neutron cross sections. Results were validated for the resonances of the U{sup 238} isotope for different energies and temperature ranges. (author)
An approximation to the interference term using Frobenius Method
International Nuclear Information System (INIS)
Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C. da
2007-01-01
An analytical approximation of the interference term χ(x,ξ) is proposed. The approximation is based on the differential equation to χ(x,ξ) using the Frobenius method and the parameter variation. The analytical expression of the χ(x,ξ) obtained in terms of the elementary functions is very simple and precise. In this work one applies the approximations to the Doppler broadening functions and to the interference term in determining the neutron cross sections. Results were validated for the resonances of the U 238 isotope for different energies and temperature ranges. (author)
Approximating the ground state of gapped quantum spin systems
Energy Technology Data Exchange (ETDEWEB)
Michalakis, Spyridon [Los Alamos National Laboratory; Hamza, Eman [NON LANL; Nachtergaele, Bruno [NON LANL; Sims, Robert [NON LANL
2009-01-01
We consider quantum spin systems defined on finite sets V equipped with a metric. In typical examples, V is a large, but finite subset of Z{sup d}. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset {chi} {contained_in} V the ground state projector can be approximated by the product of two projections, one supported on {chi} and one supported on {chi}{sup c}, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. Such an approximation was useful in proving an area law in one dimension, and this result corresponds to a multi-dimensional analogue.
Kullback-Leibler divergence and the Pareto-Exponential approximation.
Weinberg, G V
2016-01-01
Recent radar research interests in the Pareto distribution as a model for X-band maritime surveillance radar clutter returns have resulted in analysis of the asymptotic behaviour of this clutter model. In particular, it is of interest to understand when the Pareto distribution is well approximated by an Exponential distribution. The justification for this is that under the latter clutter model assumption, simpler radar detection schemes can be applied. An information theory approach is introduced to investigate the Pareto-Exponential approximation. By analysing the Kullback-Leibler divergence between the two distributions it is possible to not only assess when the approximation is valid, but to determine, for a given Pareto model, the optimal Exponential approximation.
The degenerate-internal-states approximation for cold collisions
Maan, A.C.; Tiesinga, E.; Stoof, H.T.C.; Verhaar, B.J.
1990-01-01
The Degenerate-Internal-States approximation as well as its first-order correction are shown to provide a convenient method for calculating elastic and inelastic collision amplitudes for low temperature atomic scattering.
High-order finite element approximations of the Maxwell equations
Sarmany, D.
2010-01-01
This thesis discusses numerical approximations of electromagnetic wave propagation, which is mathematically described by the Maxwell equations. These equations are typically either formulated as integral equations or as (partial) differential equations. Throughout this thesis, the numerical
Comparison of different caries detectors for approximal caries detection
Directory of Open Access Journals (Sweden)
Esin Bozdemir
2016-09-01
Conclusion: The ability of bitewing radiography to identify sound surfaces was better than that of the other methods. The LF device was the most sensitive tool for detecting approximal surfaces with caries, followed by the LED device.
Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems
Energy Technology Data Exchange (ETDEWEB)
Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)
1996-12-31
A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.
Embedding relations connected with strong approximation of Fourier ...
Indian Academy of Sciences (India)
. © Indian Academy of Sciences. Embedding relations connected with strong approximation of Fourier series. BOGDAN SZAL. Faculty of Mathematics, Computer Science and Econometrics,. University of Zielona Góra, 65-516 Zielona Góra, ul.
Approximating one class of finitely differentiable functions by another
Kudryavtsev, S. N.
1997-04-01
Necessary and sufficient conditions are found for approximating (with preassigned accuracy in an integral metric) a class of functions with a given majorant for the moduli of continuity of the highest derivatives by another class.
Rotational and Helical Surface Approximation for Reverse Engineering
DEFF Research Database (Denmark)
Randrup, Thomas; Pottmann, Helmut
1997-01-01
to basic shapes used in computer aided design. The algorithms apply methods of line geometry to the set of surface normals in combination with techniques of numerical approximation. The presented results possess applications in reverse engineering and computer aided manufacturing....
Interpolation function for approximating knee joint behavior in human gait
Toth-Taşcǎu, Mirela; Pater, Flavius; Stoia, Dan Ioan
2013-10-01
Starting from the importance of analyzing the kinematic data of the lower limb in gait movement, especially the angular variation of the knee joint, the paper propose an approximation function that can be used for processing the correlation among a multitude of knee cycles. The approximation of the raw knee data was done by Lagrange polynomial interpolation on a signal acquired using Zebris Gait Analysis System. The signal used in approximation belongs to a typical subject extracted from a lot of ten investigated subjects, but the function domain of definition belongs to the entire group. The study of the knee joint kinematics plays an important role in understanding the kinematics of the gait, this articulation having the largest range of motion in whole joints, in gait. The study does not propose to find an approximation function for the adduction-abduction movement of the knee, this being considered a residual movement comparing to the flexion-extension.
A weighted random walk approximation to fractional Brownian motion
Lindstrøm, Tom
2007-01-01
We present a random walk approximation to fractional Brownian motion where the increments of the fractional random walk are defined as a weighted sum of the past increments of a Bernoulli random walk.
A random walk approximation to fractional Brownian motion
Lindstrøm, Tom
2007-01-01
We present a random walk approximation to fractional Brownian motion where the increments of the fractional random walk are defined as a weighted sum of the past increments of a Bernoulli random walk.
Technical notes. Spherical harmonics approximations of neutron transport
Energy Technology Data Exchange (ETDEWEB)
Demeny, A.; Dede, K.M.; Erdei, K.
1976-12-01
A double-range spherical harmonics approximation obtained by expanding the angular flux separately in the two regions combined with the conventional single-range spherical harmonics is found to give superior description of neutron transport.
Approximate equations at breaking for nearshore wave transformation coefficients
Digital Repository Service at National Institute of Oceanography (India)
Chandramohan, P.; Nayak, B.U.; SanilKumar, V.
Based on small amplitude wave theory approximate equations are evaluated for determining the coefficients of shoaling, refraction, bottom friction, bottom percolation and viscous dissipation at breaking. The results obtainEd. by these equations...
Real-time creased approximate subdivision surfaces with displacements.
Kovacs, Denis; Mitchell, Jason; Drone, Shanon; Zorin, Denis
2010-01-01
We present an extension of Loop and Schaefer's approximation of Catmull-Clark surfaces (ACC) for surfaces with creases and corners. We discuss the integration of ACC into Valve's Source game engine and analyze performance of our implementation.
APPECT: An Approximate Backbone-Based Clustering Algorithm for Tags
DEFF Research Database (Denmark)
Zong, Yu; Xu, Guandong; Jin, Pin
2011-01-01
resulting from the severe difficulty of ambiguity, redundancy and less semantic nature of tags. Clustering method is a useful tool to address the aforementioned difficulties. Most of the researches on tag clustering are directly using traditional clustering algorithms such as K-means or Hierarchical...... algorithm for Tags (APPECT). The main steps of APPECT are: (1) we execute the K-means algorithm on a tag similarity matrix for M times and collect a set of tag clustering results Z={C1,C2,…,Cm}; (2) we form the approximate backbone of Z by executing a greedy search; (3) we fix the approximate backbone...... Agglomerative Clustering on tagging data, which possess the inherent drawbacks, such as the sensitivity of initialization. In this paper, we instead make use of the approximate backbone of tag clustering results to find out better tag clusters. In particular, we propose an APProximate backbonE-based Clustering...
Approximation with positive linear operators and linear combinations
Gupta, Vijay
2017-01-01
This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian–Ivanov for linear combinations of Bernstein and Bernstein–Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as we...
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Mickael D. Chekroun
2017-07-01
Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.
Approximate eigensolutions of Dirac equation for the superposition ...
Indian Academy of Sciences (India)
2014-07-02
Uvarov (NU) method is used to examine the approximate analytical energy eigenvalues and two-component wave function of the Dirac equation with the Hellmann potential for arbitrary spin-orbit quantum number κ in the ...
Numerical approximation of random periodic solutions of stochastic differential equations
Feng, Chunrong; Liu, Yu; Zhao, Huaizhong
2017-10-01
In this paper, we discuss the numerical approximation of random periodic solutions of stochastic differential equations (SDEs) with multiplicative noise. We prove the existence of the random periodic solution as the limit of the pull-back flow when the starting time tends to -∞ along the multiple integrals of the period. As the random periodic solution is not explicitly constructible, it is useful to study the numerical approximation. We discretise the SDE using the Euler-Maruyama scheme and modified Milstein scheme. Subsequently, we obtain the existence of the random periodic solution as the limit of the pull-back of the discretised SDE. We prove that the latter is an approximated random periodic solution with an error to the exact one at the rate of √{Δ t} in the mean square sense in Euler-Maruyama method and Δ t in the Milstein method. We also obtain the weak convergence result for the approximation of the periodic measure.
Approximate relationship between frequency-dependent skin depth ...
Indian Academy of Sciences (India)
Home; Journals; Journal of Earth System Science; Volume 125; Issue 7. Approximate relationship between frequency-dependent skin depth resolved from geoelectromagnetic pedotransfer function and depth of investigation resolved from geoelectrical measurements: A case study of coastal formation, southern Nigeria.
The Space Complexity of 2-Dimensional Approximate Range Counting
DEFF Research Database (Denmark)
Wei, Zhewei; Yi, Ke
2013-01-01
with respect to orthogonal ranges, and the best lower bound is . The ε-approximation is a rather restricted data structure, as we are not allowed to store any information other than the coordinates of a subset of points in P. In this paper, we explore what can be achieved without any restriction on the data...... with additive error εn. A well-known solution for this problem is the ε-approximation. Informally speaking, an ε-approximation of P is a subset A ⊆ P that allows us to estimate the number of points in P ∩ R by counting the number of points in A ∩ R. It is known that an ε-approximation of size exists for any P...
Approximation generation for correlations in thermal-hydraulic analysis codes
International Nuclear Information System (INIS)
Pereira, Luiz C.M.; Carmo, Eduardo G.D. do
1997-01-01
A fast and precise evaluation of fluid thermodynamic and transport properties is needed for the efficient mass, energy and momentum transport phenomena simulation related to nuclear plant power generation. A fully automatic code capable to generate suitable approximation for correlations with one or two independent variables is presented. Comparison in terms of access speed and precision with original correlations currently used shows the adequacy of the approximation obtained. (author). 4 refs., 8 figs., 1 tab