1,721,136 research outputs found
Ben Lee With Deer
No full textBen Lee of Salt Lake takes this deer on Dutch Charlie Flat on Brush Creek Mountain
Determinants vs. Algebraic Branching Programs
Full text linkWe show that for every homogeneous polynomial of degree d, if it has determinantal complexity at most s, then it can be computed by a homogeneous algebraic branching program (ABP) of size at most O(d⁵s). Moreover, we show that for most homogeneous polynomials, the width of the resulting homogeneous ABP is just s-1 and the size is at most O(ds).
Thus, for constant degree homogeneous polynomials, their determinantal complexity and ABP complexity are within a constant factor of each other and hence, a super-linear lower bound for ABPs for any constant degree polynomial implies a super-linear lower bound on determinantal complexity; this relates two open problems of great interest in algebraic complexity. As of now, super-linear lower bounds for ABPs are known only for polynomials of growing degree [Mrinal Kumar, 2019; Prerona Chatterjee et al., 2022], and for determinantal complexity the best lower bounds are larger than the number of variables only by a constant factor [Mrinal Kumar and Ben Lee Volk, 2022].
While determinantal complexity and ABP complexity are classically known to be polynomially equivalent [Meena Mahajan and V. Vinay, 1997], the standard transformation from the former to the latter incurs a polynomial blow up in size in the process, and thus, it was unclear if a super-linear lower bound for ABPs implies a super-linear lower bound on determinantal complexity. In particular, a size preserving transformation from determinantal complexity to ABPs does not appear to have been known prior to this work, even for constant degree polynomials
"Die Mischung macht den Unterschied". Selektive Wirksamkeitsstudie zur Förderung emotionaler und sozialer Kompetenzen mit dem Ben & Lee Programm
Full text linkBei der Umsetzung präventiver Maßnahmen in der Schule bestehen einige Herausforderungen. Viele Grundschulen haben u.a. Probleme, die zeitlichen Resscourcen für Förderprogramme aufzubringen und die Maßnahmen mit dem Lehrplan in Einklang zu bringen. Ein Lösungsansatz für diese Herausforderung könnte die Integration Sozial-Emotionalen-Lernens (SEL) in das reguläre Curriculum sein, so wie es von Ben & Lee umgesetzt wird. Die Wirkung von SEL-Programmen fällt in der Primarstufe stark heterogen aus. Die Zielstellung der vorliegenden Studie ist daher einerseits, die Wirksamkeit von Ben & Lee zu überprüfen und andererseits, mögliche Einflussfaktoren auf die Effekte zu identifizieren. Ben & Lee wurde mittels quasi-experimentellem Kontrollgruppen-Design in 36 Klassen aus 3. und 4. Jahrgangsstufen umgesetzt. Das sozial-emotionale Wissen, das Verhalten und das Erleben von 405 Kindern mit auffälligem Verhalten im Lehrerurteil wurde vor, direkt nach und drei Monaten nach Beendigung der Förderung mittels standardisierter Verfahren (Test, Fremd- und Selbstbeurteilung) erhoben. Die Datenanalyse erfolgte mit Hilfe linearer Mehrebenenwachstumsmodelle. Kinder mit Schwierigkeiten im Verhalten zeigten nach dem Einsatz von Ben & Lee im Vergleich zur Kontrollgruppe ein signifikant erhöhtes sozialemotinales Wissen (d = 0.5). Dieses führt jedoch nicht unmittelbar zu Veränderungem im Verhalten und im Erleben der Schülerinnen und Schüler. Für eine Verbesserungen in diesen Bereichen kommt es auf die Klassenzusammensetzung sowie das Feedbackverhalten der Lehrperson an. Der Beitrag diskutiert Handlungsschritte sowohl auf Ebene der Lehrpersonen als auch auf schulorganisatorischer Ebene. (DIPF/Orig.
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
A Lower Bound on Determinantal Complexity
Full text linkThe determinantal complexity of a polynomial P ∈ [x₁, …, x_n] over a field is the dimension of the smallest matrix M whose entries are affine functions in [x₁, …, x_n] such that P = Det(M). We prove that the determinantal complexity of the polynomial ∑_{i = 1}^n x_i^n is at least 1.5n - 3.
For every n-variate polynomial of degree d, the determinantal complexity is trivially at least d, and it is a long standing open problem to prove a lower bound which is super linear in max{n,d}. Our result is the first lower bound for any explicit polynomial which is bigger by a constant factor than max{n,d}, and improves upon the prior best bound of n + 1, proved by Alper, Bogart and Velasco [Jarod Alper et al., 2017] for the same polynomial
Lower Bounds for Matrix Factorization
Full text linkWe study the problem of constructing explicit families of matrices which cannot be expressed as a product of a few sparse matrices. In addition to being a natural mathematical question on its own, this problem appears in various incarnations in computer science; the most significant being in the context of lower bounds for algebraic circuits which compute linear transformations, matrix rigidity and data structure lower bounds.
We first show, for every constant d, a deterministic construction in time exp(n^(1-Ω(1/d))) of a family {M_n} of n × n matrices which cannot be expressed as a product M_n = A_1 ⋯ A_d where the total sparsity of A_1,…,A_d is less than n^(1+1/(2d)). In other words, any depth-d linear circuit computing the linear transformation M_n⋅ has size at least n^(1+Ω(1/d)). This improves upon the prior best lower bounds for this problem, which are barely super-linear, and were obtained by a long line of research based on the study of super-concentrators (albeit at the cost of a blow up in the time required to construct these matrices).
We then outline an approach for proving improved lower bounds through a certain derandomization problem, and use this approach to prove asymptotically optimal quadratic lower bounds for natural special cases, which generalize many of the common matrix decompositions
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
A Polynomial Degree Bound on Equations for Non-Rigid Matrices and Small Linear Circuits
Full text linkWe show that there is an equation of degree at most poly(n) for the (Zariski closure of the) set of the non-rigid matrices: that is, we show that for every large enough field , there is a non-zero n²-variate polynomial P ∈ [x_{1, 1}, …, x_{n, n}] of degree at most poly(n) such that every matrix M which can be written as a sum of a matrix of rank at most n/100 and a matrix of sparsity at most n²/100 satisfies P(M) = 0. This confirms a conjecture of Gesmundo, Hauenstein, Ikenmeyer and Landsberg [Fulvio Gesmundo et al., 2016] and improves the best upper bound known for this problem down from exp(n²) [Abhinav Kumar et al., 2014; Fulvio Gesmundo et al., 2016] to poly(n).
We also show a similar polynomial degree bound for the (Zariski closure of the) set of all matrices M such that the linear transformation represented by M can be computed by an algebraic circuit with at most n²/200 edges (without any restriction on the depth). As far as we are aware, no such bound was known prior to this work when the depth of the circuits is unbounded.
Our methods are elementary and short and rely on a polynomial map of Shpilka and Volkovich [Amir Shpilka and Ilya Volkovich, 2015] to construct low degree "universal" maps for non-rigid matrices and small linear circuits. Combining this construction with a simple dimension counting argument to show that any such polynomial map has a low degree annihilating polynomial completes the proof.
As a corollary, we show that any derandomization of the polynomial identity testing problem will imply new circuit lower bounds. A similar (but incomparable) theorem was proved by Kabanets and Impagliazzo [Valentine Kabanets and Russell Impagliazzo, 2004]
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