Precision-recall operating characteristic (P-ROC) curves in imprecise environments

Traditionally, machine learning algorithms have been evaluated in applications where assumptions can be reliably made about class priors and/or misclassification costs. In this paper, we consider the case of imprecise environments, where little may be known about these factors and they may well vary significantly when the system is applied. Specifically, the use of precision-recall analysis is investigated and compared to the more well known performance measures such as error-rate and the receiver operating characteristic (ROC). We argue that while ROC analysis is invariant to variations in class priors, this invariance in fact hides an important factor of the evaluation in imprecise environments. Therefore, we develop a generalised precision-recall analysis methodology in which variation due to prior class probabilities is incorporated into a multi-way analysis of variance (ANOVA). The increased sensitivity and reliability of this approach is demonstrated in a remote sensing application.

Generators of supersymmetric polynomials in positive characteristic

In Kantor and Trishin (1997) [3], Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m vertical bar n) and a related algebra A, of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A(s) was investigated earlier by Stembridge (1985) who in [9] called the elements of A(s) supersymmetric polynomials and determined generators of A(s). The case of positive characteristic p of the ground field K has been recently investigated by La Scala and Zubkov (in press) in [6]. We extend their work and give a complete description of generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m vertical bar n) and generators of A(s).

Lie properties of symmetric elements in group rings

Let * be an involution of a group G extended linearly to the group algebra KG. We prove that if G contains no 2-elements and K is a field of characteristic p, 0 2, then the *-symmetric elements of KG are Lie nilpotent (Lie n-Engel) if and only if KG is Lie nilpotent (Lie n-Engel). (C) 2008 Elsevier Inc. All rights reserved.

Filtered Multiplicative Bases of Restricted Enveloping Algebras

We study the problem of the existence of filtered multiplicative bases of a restricted enveloping algebra u(L), where L is a finite-dimensional and p-nilpotent restricted Lie algebra over a field of positive characteristic p.

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

delta-Superderivations of Semisimple Finite-Dimensional Jordan Superalgebras

In the paper, a complete description of the delta-derivations and the delta-superderivations of semisimple finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic p not equal 2 is given. In particular, new examples of nontrivial (1/2)-derivations and odd (1/2)-superderivations are given that are not operators of right multiplication by an element of the superalgebra.

Über die Linearität der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen

Über die Liniarität der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen. In meiner Arbeit beschäftige ich mich mit Darstellungen der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen. Mein Ansatz hierbei ist, die Teichmüllersche Modulgruppe in eine p-adische Liegruppe einzubetten. Sei nun F die von zwei Elementen erzeugte freie Gruppe und Aut(F) die Automorphismengruppe von F. Inhalt des ersten Kapitels ist es nun zu zeigen, daß folgende Aussagen äquivalent sind: - Die Teichmüllersche Modulgruppe des Torus mit zwei Punktierungen ist linear, - Aut(F)ist linear, - F besitzt eine p-Kongruenzstruktur, deren Folgen- glieder von Aut(F) festgehalten werden, also charak- teristisch sind. Im zweiten Kapitel wird unter anderem gezeigt, daß es eine Einbettung einer Untergruppe endlichen Indexes der Aut(F) in die Automorphismengruppe einer einfachen p-adischen Liegruppe gibt. Bisher ist unbekannt, ob die Buraudarstellung treu ist.In dieser Arbeit wird ein unendliches, lineares Gleichungssystem, dessen Lösungen gerade die Koeffizienten der Wörter des Kernes der Buraudarstellung sind, vorgestellt.Im dritten Kapitel wird mit den Methoden des 1.Kapitels gezeigt, daß der Torus mit zwei Punktierungen genau dann linear ist, wenn die Teichmüllersche Modulgruppe der Sphäre mit 5 Punktierungen es auch ist. Bekanntlich ist die 4. Braidgruppe linear. Nun ist aber die 4. Braidgruppe letztlich die Teichmüllersche Modulgruppe der abgeschlossenen Kreisscheibe mit 5 Punktierungen. Wenn man nun deren Randpunkte miteinander identifiziert und anschließend wegläßt, erhält man die 5-fach punktiereSphäre.Mit der eben beschriebenen Abbildung kann man zeigen, daß die Teichmüllersche Modulgruppe der fünffach punktierten Sphäre linear ist.

Isomorphism of Commutative Modular Group Algebras

∗ The work was supported by the National Fund “Scientific researches” and by the Ministry of Education and Science in Bulgaria under contract MM 70/91.

Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group

2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.

Motivic Decomposition of Projective Pseudo-Homogeneous Varieties

Let G be a semi-simple algebraic group over a field k. Projective G-homogeneous varieties are projective varieties over which G acts transitively. The stabilizer or the isotropy subgroup at a point on such a variety is a parabolic subgroup which is always smooth when the characteristic of k is zero. However, when k has positive characteristic, we encounter projective varieties with transitive G-action where the isotropy subgroup need not be smooth. We call these varieties projective pseudo-homogeneous varieties. To every such variety, we can associate a corresponding projective homogeneous variety. In this thesis, we extensively study the Chow motives (with coefficients from a finite connected ring) of projective pseudo-homogeneous varieties for G inner type over k and compare them to the Chow motives of the corresponding projective homogeneous varieties. This is done by proving a generic criterion for the motive of a variety to be isomorphic to the motive of a projective homogeneous variety which works for any characteristic of k. As a corollary, we give some applications and examples of Chow motives that exhibit an interesting phenomenon. We also show that the motives of projective pseudo-homogeneous varieties satisfy properties such as Rost Nilpotence and Krull-Schmidt.

Characteristic study of maximum modal gain of p-doped 1.3 mu m InAs/GaAs quantum dot lasers

We report an experimental and theoretical study of maximum modal gain of p-doped 1.3 mu m InAs/GaAs quantum dot (QD) lasers. The maximum modal gain of the QD laser with five stacks of QDs is as high as 17.5 cm(-1) which is the same as that of the undoped laser with identical structures. The expression of the maximum modal gain is derived and it is indicated that p-doping has no effect to the maximum modal gain. We theoretically calculated the maximum modal gain of the QD lasers and the result is in a good agreement with the experimental data. Furthermore, QDs with lower height or smaller aspect ratio are beneficial to achieving a greater maximum modal gain that leads to lower threshold current density and higher differential modal gain, which is good for the application of p-doped 1.3 mu m InAs/GaAs QD lasers in optical communications systems.

1.5 mu m luminescence characteristic of erbium in B, P doped a-SiO : H films

Hydrogenated amorphous silicon films co-doped with oxygen (O), boron (B) and phosphorus (P) were fabricated using PECVD technique. The erbium (Er) implanted samples were annealed in a N-2 ambient by rapid thermal annealing. Strong photoluminescence (PL) spectra of these samples were observed at room temperature. The incorporation of O, B and P could not only enhance the PL intensity but also the thermal annealing temperature of the strongest PL intensity. It seems that the incorporation of B or P can decrease the grain boundary potential barriers thus leading to an easier movement of carriers and a stronger PL intensity. Temperature dependence of PL indicated the thermal quenching of Er-doped hydrogenated amorphous silicon is very weak.

Electroless nickel composite (Ni-P/SiC) coating - A study on interface and corrosion characteristic

Surface behaviour is of paramount importance as failure and degradation tend to initiate from the surface. Electroless composite coating (NiP/SiC) was developed using SiC as reinforcing particles. As heat treatment plays a vital role in electroless nickel coating owing to the changes in microstructure, phase structure and mechanical properties, an insight at the interface changes in chemistry and micromechanical behaviour was investigated using scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) and microindentation techniques. Corrosion performance was analysed using electrochemical impedance spectroscopy (EIS). Absence of zinc and migration of copper at the interface was detected. Brittleness and microcracks was seen long the interface when indenting at load of 500 gf (Vickers). Corrosion performance is weaker than particles free coating. However, a thin blanket of NiP could enhance the resistance to corrosive medium.

An experimental based assessment of the deviation of the bearing characteristic frequencies

Slippage in the contact roller-races has always played a central role in the field of diagnostics of rolling element bearings. Due to this phenomenon, vibrations triggered by a localized damage are not strictly periodic and therefore not detectable by means of common spectral functions as power spectral density or discrete Fourier transform. Due to the strong second order cyclostationary component, characterizing these signals, techniques such as cyclic coherence, its integrated form and square envelope spectrum have proven to be effective in a wide range of applications. An expert user can easily identify a damage and its location within the bearing components by looking for particular patterns of peaks in the output of the selected cyclostationary tool. These peaks will be found in the neighborhood of specific frequencies, that can be calculated in advance as functions of the geometrical features of the bearing itself. Unfortunately the non-periodicity of the vibration signal is not the only consequence of the slippage: often it also involves a displacement of the damage characteristic peaks from the theoretically expected frequencies. This issue becomes particularly important in the attempt to develop highly automated algorithms for bearing damage recognition, and, in order to correctly set thresholds and tolerances, a quantitative description of the magnitude of the above mentioned deviations is needed. This paper is aimed at identifying the dependency of the deviations on the different operating conditions. This has been possible thanks to an extended experimental activity performed on a full scale bearing test rig, able to reproduce realistically the operating and environmental conditions typical of an industrial high power electric motor and gearbox. The importance of load will be investigated in detail for different bearing damages. Finally some guidelines on how to cope with such deviations will be given, accordingly to the expertise obtained in the experimental activity.

Om naturens förvandlingar : Vetenskap, kunskap och frihet i Rudolf Steiners tidiga tänkande. Idéhistoriska perspektiv på Waldorfpedagogiken

TRANSFORMATIONS OF NATURE Science, Knowledge and Freedom in the Early Thinking of Rudolf Steiner. Perspectives on Waldorf Education in the light of the History of Ideas Waldorf Education is based on the worldview that Rudolf Steiner (1861-1925) developed to a wide-ranging anthroposophical movement in the first decades of the 20th century. This thesis takes as its departure the early thinking of Rudolf Steiner that precedes anthroposophy, and its main purpose is to uncover the tradition of ideas represented in Steiner´s early life and which, in different ways, have emerged in the practice of Waldorf Education. Through systematic analysis I attempt to bring to light different aspects of Steiner’s early thinking: his concept of science, his epistemological startingpoints and his philosophy of freedom. By departing from J. W. Goethe’s qualitative concept of science, Steiner strove in his early works to formulate a monistic worldview which appears to be closely related to the Romantic Movement and its philosophy of nature. Characteristic traits of his thinking are, on the one hand, a critique of a one-sided enlightenment and, on the other hand, an aspiration to see the world as a living organic unity. Human beings can, by developing our intuitive faculties, get a deeper understanding of the indissoluble relationship between man and nature. Against this background Steiner´s early thinking can be read as a special kind of romantic development narrative. Steiner’s early thinking also opens the way for romantic perspectives on Waldorf Education. It appears that many central aims and conceptions in Waldorf Education can be illuminated by the epistemological perspective upon which Steiner elaborated early in his life. An organic curriculum, phenomenological didactics and high ideal of freedom can be considered seen as educational applications of conceptions that played an important role in Goethe and his age. Thus, Waldorf Education provides in our contemporary society an exceptional set of educational values: a holistic education with romantic undertones.