213,279 research outputs found

    Asymptotic properties of the Bernstein density copula for dependent data

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    Copulas are extensively used for dependence modeling. In many cases the data does not reveal how the dependence can be modeled using a particular parametric copula. Nonparametric copulas do not share this problem since they are entirely data based. This paper proposes nonparametric estimation of the density copula for α-mixing data using Bernstein polynomials. We study the asymptotic properties of the Bernstein density copula, i.e., we provide the exact asymptotic bias and variance, we establish the uniform strong consistency and the asymptotic normality.nonparametric estimation, copula, Bernstein polynomial, α-mixing, asymptotic properties, boundary bias

    Letter: Ida M. Tarbell to Herman Bernstein, June 23, 1923

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    Writes of Jews in America and Lincoln and Germans, Jews and Catholics in the Civil Wa

    Structured matrix methods for computations on Bernstein basis polynomials

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    This thesis considers structure preserving matrix methods for computations on Bernstein polynomials whose coefficients are corrupted by noise. The ill-posed operations of greatest common divisor computations and polynomial division are considered, and it is shown that structure preserving matrix methods yield excellent results. With respect to greatest common divisor computations, the most difficult part is the computation of its degree, and several methods for its determination are presented. These are based on the Sylvester resultant matrix, and it is shown that a new form of the Sylvester resultant matrix in the modified Bernstein basis yields the best results. The B´ezout resultant matrix in the modified Bernstein basis is also considered, and it is shown that the results from it are inferior to those from the Sylvester resultant matrix in the modified Bernstein basis

    Motion along the mental number line reveals shared representations for numerosity and space

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    <p>Single subject data from six experiments in "Motion along the mental number line reveals shared representations for numerosity and space" by Caspar M. Schwiedrzik, Benjamin Bernstein, and Lucia Melloni. </p

    Herman Bernstein 1897-1935

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    Correspondence, clippings, manuscripts, notes, reports, relating to Bernstein's journalistic, literary and diplomatic careers. Correspondence with well-known literary, political and communal, society personalities, 1908-1935. Includes Cyrus Adler, Viscount Allenby, Joseph Barondess, Bernard Baruch, Henri Bergson, Hayyim Nahman Bialik, Jacob Billikopf, Vladimir Bourtzeff, Louis Brandeis, Robert Cecil, Fyodor Chaliapin, Jacob de Haas, Albert Einstein, Henry Ford, Felix Frankfurter, Herbert Hoover, Vladimir Jabotinsky, Horace M. Kallen, Peretz Hirschbein, Peter Kropotkin, Herbert Lehman, Louis Lipsky, Judah L. Magnes, Louis Marshall, Henry Morgenthau, Max Nordau, Adolph Simon Ochs, David de Sola Pool, Bernard G. Richards, Theodore Roosevelt, Julius Rosenwald, Jacob Schiff, Harry Schneiderman, Maurice Schwartz, George Bernard Shaw, Sholem Aleichem, Nathan Straus, Henrietta Szold, Chaim Tchernowitz, Leo Tolstoy, Samuel Untermyer, Henry Van Dyke, Lillian Wald, Felix Warburg, Chaim Weizman n, Jefferson Williams, Stephen Wise, Israel Zangwill. Correspondence and other materials relating to Bernstein's post as U.S. ambassador to Albania. Materials pertaining to Bernstein's editorial work at *The Day*, *Jewish Tribune*, *New York Herald*, *Jewish Daily Bulletin*. Materials pertaining to Bernstein's involvement with the American Jewish Committee. Correspondence with organizations including American Jewish Congress, *American Hebrew*, HIAS, *Jewish Chronicle* (London), Jewish Community of New York, *Menorah Journal*, *New York American*, *New York Times*, ORT, U.S. Dept. of State, Yiddish Art Theater, Zionist Organization of America. Articles, clippings, correspondence and court materials relating to the Ford libel suit. Miscellaneous documents and reports relating to the Paris Peace Conference, the Jewish situation in Russia, 1917-1920, Russian revolutionary events of 1917. News dispatches from Russia, 1917-1920s. Translations by Bernstein of Russian wri Andre yev,Chekhov, Maksim Gorkii, Leo Tolstoy, Ivan Turgenev. Plays adapted by Bernstein from various languages. Interviews with celebrities including Ahad Ha'am, Henri Barbusse, Pope Benedict XV, I.V. Chicherin, Henry Ford, Amin al Husayni, Ignacy Paderewski, Marshal Jozef Pilsudski, Walther Rathenau, Edmond de Rothschild, Hjalmar Schacht, Leo Tolstoy, Menahem Ussishkin, Chaim Weizmann, Count Sergey Yulyevich Witte. Articles by Bernstein about Russian history, Jewish contemporary problems. Manuscripts, notes, outlines of books relating to the *Protocols of the Elders of Zion*. Biographies of American Jews. Clippings: articles and translations by Bernstein and articles about Bernstein. Personal papers of Bernstein.Index: English, 126 pp.; Inventory, 48 pp., typedAuthor, journalist, translator, playwright. Active in Jewish communal organizations. Secretary of the American Jewish Committee. Founder in 1914 and editor of *Der tog*, editor of the Jewish Daily Bulletin. Correspondent for the *New York Herald* in Russia, 1917-1920 and at the Paris Peace Conference, 1919. Instituted a libel suit in the 1920s against Henry Ford and the *Dearborn Independent* for publishing the *Protocols of the Elders of Zion*. U.S. envoy to Albania, 1931-1933. Born in Vladislavov, Lithuania. Lived in Russia and the U.S

    A survey of results on the q-Bernstein polynomials

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    It is now nearly a century since S. N. Bernstein introduced his well-known polynomials. This paper is concerned with generalizations of the Bernstein polynomials, mainly with the so called q-Bernstein polynomials. These are due to the author of this paper and are based on the q integers. They reduce to the Bernstein polynomials when we put q = 1 and share the shape-preserving properties of the Bernstein polynomials when q is an element of (0, 1). This paper also describes another earlier generalization of the Bernstein polynomials, a sequence of rational functions that are also based on the q-integers, proposed by A. Lupas, and two even earlier generalizations due to D. D. Stancu. The present author summarizes various results, due to a number of authors, that are concerned with the q-Bernstein polynomials and with Stancu's two generalizations.</p

    Deterministic Partially Dynamic Single Source Shortest Paths in Weighted Graphs

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    In this paper we consider the decremental single-source shortest paths (SSSP) problem, where given a graph G and a source node s the goal is to maintain shortest distances between s and all other nodes in G under a sequence of online adversarial edge deletions. In their seminal work, Even and Shiloach [JACM 1981] presented an exact solution to the problem in unweighted graphs with only O(mn) total update time over all edge deletions. Their classic algorithm was the state of the art for the decremental SSSP problem for three decades, even when approximate shortest paths are allowed. The first improvement over the Even-Shiloach algorithm was given by Bernstein and Roditty [SODA 2011], who for the case of an unweighted and undirected graph presented a (1+epsilon)-approximate algorithm with constant query time and a total update time of O(n^{2+o(1)}). This work triggered a series of new results, culminating in a recent breakthrough of Henzinger, Krinninger and Nanongkai [FOCS 14], who presented a (1+epsilon)-approximate algorithm for undirected weighted graphs whose total update time is near linear: O(m^{1+o(1)} log(W)), where W is the ratio of the heaviest to the lightest edge weight in the graph. In this paper they posed as a major open problem the question of derandomizing their result. Until very recently, all known improvements over the Even-Shiloach algorithm were randomized and required the assumption of a non-adaptive adversary. In STOC 2016, Bernstein and Chechik showed the first deterministic algorithm to go beyond O(mn) total update time: the algorithm is also (1+\epsilon)-approximate, and has total update time \tilde{O}(n^2). In SODA 2017, the same authors presented an algorithm with total update time \tilde{O}(mn^{3/4}). However, both algorithms are restricted to undirected, unweighted graphs. We present the first deterministic algorithm for weighted undirected graphs to go beyond the O(mn) bound. The total update time is \tilde{O}(n^2 \log(W))

    Bernstein Spaces on Siegel CR Manifolds

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    In this paper we introduce and study Bernstein spaces on a class of quadratic CR manifolds, which we call Siegel CR manifolds. These are spaces of entire functions of exponential type whose restrictions to a given Siegel CR submanifold are L p- integrable with respect to a natural measure. For these spaces, among other results, we prove the Plancherel–Pólya inequality, a Bernstein inequality and a sufficient condition for a sequence to be sampling
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