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Search Results: 1 - 10 of 25 matches for " Krumm "
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Thermodynamics and the Structure of Quantum Theory as a Generalized Probabilistic Theory
Marius Krumm
Physics , 2015,
Abstract: This thesis investigates the connection between quantum theory, thermodynamics and information theory. Theories with structure similar to that of quantum theory are considered, mathematically described by the framework of "Generalized Probabilistic Theories". For these theories, a thought experiment by von Neumann is adapted to obtain a natural thermodynamic entropy definition, following a proposal by J. Barrett. Mathematical properties of this entropy are compared to physical consequences of the thought experiment. The validity of the second law of thermodynamics is investigated. In that context, observables and projective measurements are generalized to prove an entropy increase for projective measurements of ensembles. Information-theoretically motivated definitions of the entropy are compared to the entropy from the thermodynamic thought experiment. The conditions for the thermodynamic entropy to be well-defined are considered in greater detail. Several further properties of the theories under consideration (e.g. whether there is higher order interference, Pfister's state discrimination principle) and their relation to entropy are investigated.
Squarefree parts of polynomial values
David Krumm
Mathematics , 2014,
Abstract: Given a separable nonconstant polynomial $f(x)$ with integer coefficients, we consider the set $S$ consisting of the squarefree parts of all the rational values of $f(x)$, and study its behavior modulo primes. Fixing a prime $p$, we determine necessary and sufficient conditions for $S$ to contain an element divisible by $p$. Furthermore, we conjecture that if $p$ is large enough, then $S$ contains infinitely many representatives from every nonzero residue class modulo $p$. The conjecture is proved by elementary means assuming $f(x)$ has degree 1 or 2. If $f(x)$ has degree 3, or if it has degree 4 and has a rational root, the conjecture is shown to follow from the Parity Conjecture for elliptic curves. For polynomials of arbitrary degree, a local analogue of the conjecture is proved using standard results from class field theory, and empirical evidence is given to support the global version of the conjecture.
Computing points of bounded height in projective space over a number field
David Krumm
Mathematics , 2014,
Abstract: We construct an algorithm for solving the following problem: given a number field $K$, a positive integer $N$, and a positive real number $B$, determine all points in $\mathbb P^N(K)$ having relative height at most $B$. A theoretical analysis of the efficiency of the algorithm is provided, as well as sample computations showing how the algorithm performs in practice. Two variants of the method are described, and examples are given to compare their running times. In the case $N=1$ we compare our method to an earlier algorithm for enumerating elements of bounded height in number fields.
A local-global principle in the dynamics of quadratic polynomials
David Krumm
Mathematics , 2015,
Abstract: Let $K$ be a number field, $f\in K[x]$ a quadratic polynomial, and $n\in\{1,2,3\}$. We show that if $f$ has a point of period $n$ in every non-archimedean completion of $K$, then $f$ has a point of period $n$ in $K$. For $n\in\{4,5\}$ we show that there exist at most finitely many linear conjugacy classes of quadratic polynomials over $K$ for which this local-global principle fails. By considering a stronger form of this principle, we strengthen global results obtained by Morton and Flynn-Poonen-Schaefer in the case $K=\mathbf Q$. More precisely, we show that for every quadratic polynomial $f\in\mathbf Q[x]$ there exist infinitely many primes $p$ such that $f$ does not have a point of period 4 in the $p$-adic field $\mathbf Q_p$. Conditional on knowing all rational points on a particular curve of genus 11, the same result is proved for points of period 5.
Estudio exploratorio de las propiedades psicométricas de la Escala de Personalidad Creadora (EPC) en su versión Heteroevaluación
Gabriela Krumm,Viviana Lemos
Revista Interamericana de Psicología , 2011,
Abstract: El objetivo de esta investigación fue evaluar de modo exploratorio el funcionamiento en nuestro medio, de la Escala de Personalidad Creadora (EPC) de Garaigordobil (2004) en su versión heteroevaluación. La muestra estuvo constituida por 160 padres, con hijos de 9 a 12 a os, seleccionados de manera intencional de la provincia de Entre Ríos (Argentina). Se analizó el poder discriminativo de los ítems y la consistencia interna por medio del coeficiente Alpha de Cronbach. Tanto el índice de Kaiser-Meyer y Olkin (KMO) y el Test de Esfericidad de Bartlett, indicaron la viabilidad de factorizar la escala por lo que la estructura del instrumento fue estudiada a través de un Análisis Factorial de componentes principales con rotación oblicua. El instrumento presentó una adecuada consistencia interna y todos sus ítems resultaron discriminativos. Por otra parte, al comparar la estructura factorial de la versión autoevaluación presentada por la autora, con la versión heteroevaluación, obtenida en este estudio, se observó que si bien se mantuvo el número de factores en cinco, tal como propone la autora, los ítems se redistribuyeron, generando una nueva clasificación de los mismos.
Evidence of an upper ordovician thermo-metamorphic event in the SW-Corner of the Cantabrian Mountains (N-Spain)
Keller, M.,Krumm, S.
Estudios Geologicos , 1992, DOI: 10.3989/egeol.92485-6395
Abstract: According to Illite crystallinity (IC) data, the metamorphic evolution of the SW Cantabrian Mountains took place in several steps. After a Precambrian deformation with accompanying low-grade metamorphism a thermal event during the Upper Ordovician affected the Cambro-Ordovician sediments. This event is marked by anchizonal IC values in the Pre-Silurian sequence contrasting the diagenetic data obtained from Siluro-Devonian rocks. Apparently, the metamorphic history in that part of the Cantabrian Mountains ended during the Late Ordovician, a Hercynian metamorphism cannot be proven conclusively. Segun la cristalinidad de Illita (IC) la evolución metamórfica de la zona sudoeste de la Cordillera Cantábrica tuvo lugar en varias etapas. Siguiendo una deformación precámbrica con un metamorfismo de bajo grado, un evento térmico durante el Ordovícico Superior afecto a la secuencia Cambro-Ordovícica. Este evento esta marcado en las rocas pre-Silúricas por valores de IC indicando la anchizona. Estos datos contrastan con valores obtenidos de la secuencia Siluro-Devónica, que son característicos de la diagénesis. Aparentemente, la evolución metamórfica del sudoeste de la Cordillera Cantábrica termino durante el Ordovícico, un metamorfismo Hercínico no pudo ser comprobado.
Targeted Deletion of Multiple CTCF-Binding Elements in the Human C-MYC Gene Reveals a Requirement for CTCF in C-MYC Expression
Wendy M. Gombert, Anton Krumm
PLOS ONE , 2009, DOI: 10.1371/journal.pone.0006109
Abstract: Background Insulators and domain boundaries both shield genes from adjacent enhancers and inhibit intrusion of heterochromatin into transgenes. Previous studies examined the functional mechanism of the MYC insulator element MINE and its CTCF binding sites in the context of transgenes that were randomly inserted into the genome by transfection. However, the contribution of CTCF binding sites to both gene regulation and maintenance of chromatin has not been tested at the endogenous MYC gene. Methodology/Principal Findings To determine the impact of CTCF binding on MYC expression, a series of mutant human chromosomal alleles was prepared in homologous recombination-efficient DT40 cells and individually transferred by microcell fusion into murine cells. Functional tests reported here reveal that deletion of CTCF binding elements within the MINE does not impact the capacity of this locus to correctly organize an ‘accessible’ open chromatin domain, suggesting that these sites are not essential for the formation of a competent, transcriptionally active locus. Moreover, deletion of the CTCF site at the MYC P2 promoter reduces transcription but does not affect promoter acetylation or serum-inducible transcription. Importantly, removal of either CTCF site leads to DNA methylation of flanking sequences, thereby contributing to progressive loss of transcriptional activity. Conclusions These findings collectively demonstrate that CTCF-binding at the human MYC locus does not repress transcriptional activity but is required for protection from DNA methylation.
Heterogeneity: multilingualism and democracy
Hans-Jürgen Krumm
Utbildning & Demokrati : Tidsskrift f?r Didaktik och Utbildningspolitik , 2004,
Abstract: Linguistic diversity and multilingualism on the part of individuals are aprerequisite and a constitutive condition of enabling people to live togetherin a world of growing heterogeneity. Foreign language teaching plays animportant part in democratic education because it can be seen as a trainingin respecting otherness and developing an intercultural, non-ethnocentricperception and attitude. This is all the more important because of the neces-sity of integrating children from migrant families into school life.My article argues that language education policy has to take this per-spective into account, i.e., of establishing a planned diversification so thatpupils (and their parents) will not feel satisfied with learning English only,but also become motivated to learn languages of their own neighbourhood,such as migrant and minority languages. However, in order to make use ofthe linguistic resources in the classroom, relating it to the democratic impetusof foreign language education, it is necessary to revise existing languagepolicies and to develop a multilingual perspective for all educational institutions.
Computing algebraic numbers of bounded height
John R. Doyle,David Krumm
Mathematics , 2011,
Abstract: We describe an algorithm for listing all elements of bounded height in a given number field.
Preperiodic points for quadratic polynomials over quadratic fields
John R. Doyle,Xander Faber,David Krumm
Mathematics , 2013,
Abstract: To each quadratic number field $K$ and each quadratic polynomial $f$ with $K$-coefficients, one can associate a finite directed graph $G(f,K)$ whose vertices are the $K$-rational preperiodic points for $f$, and whose edges reflect the action of $f$ on these points. This paper has two main goals. (1) For an abstract directed graph $G$, classify the pairs $(K,f)$ such that the isomorphism class of $G$ is realized by $G(f,K)$. We succeed completely for many graphs $G$ by applying a variety of dynamical and Diophantine techniques. (2) Give a complete description of the set of isomorphism classes of graphs that can be realized by some $G(f,K)$. A conjecture of Morton and Silverman implies that this set is finite. Based on our theoretical considerations and a wealth of empirical evidence derived from an algorithm that is developed in this paper, we speculate on a complete list of isomorphism classes of graphs that arise from quadratic polynomials over quadratic fields.
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