133,467 research outputs found
Machine-learning the Sato-Tate conjecture
No full textWe apply some of the latest techniques from machine-learning to the arithmetic of hyperelliptic curves. More precisely we show that, with impressive accuracy and confidence (between 99 and 100 percent precision), and in very short time (matter of seconds on an ordinary laptop), a Bayesian classifier can distinguish between Sato–Tate groups given a small number of Euler factors for the L-function. Our observations are in keeping with the Sato-Tate conjecture for curves of low genus. For elliptic curves, this amounts to distinguishing generic curves (with Sato–Tate group SU(2)) from those with complex multiplication. In genus 2, a principal component analysis is observed to separate the generic Sato–Tate group USp(4) from the non-generic groups. Furthermore in this case, for which there are many more non-generic possibilities than in the case of elliptic curves, we demonstrate an accurate characterisation of several Sato–Tate groups with the same identity component. Throughout, our observations are verified using known results from the literature and the data available in the LMFDB. The results in this paper suggest that a machine can be trained to learn the Sato–Tate distributions and may be able to classify curves efficiently
Preprint: Machine-Learning the Sato-Tate Conjecture
No full textWe apply some of the latest techniques from machine-learning to the arithmetic of hyperelliptic curves. More precisely we show that, with impressive accuracy and confidence (between 99 and 100 percent precision), and in very short time (matter of seconds on an ordinary laptop), a Bayesian classifier can distinguish between Sato-Tate groups given a small number of Euler factors for the L-function. Our observations are in keeping with the Sato-Tate conjecture for curves of low genus. For elliptic curves, this amounts to distinguishing generic curves (with Sato-Tate group SU(2)) from those with complex multiplication. In genus 2, a principal component analysis is observed to separate the generic Sato-Tate group USp(4) from the non-generic groups. Furthermore in this case, for which there are many more non-generic possibilities than in the case of elliptic curves, we demonstrate an accurate characterisation of several Sato-Tate groups with the same identity component. Throughout, our observations are verified using known results from the literature and the data available in the LMFDB. The results in this paper suggest that a machine can be trained to learn the Sato-Tate distributions and may be able to classify curves much more efficiently than the methods available in the literature
Joseph Masahiro Sato: interviews on May 9 and 16, 1984
No full textTranscript (typescript, 26 pages) of two interviews with Joseph Masahiro Sato, a Japanese-American living in Utah in 1984. Mr. Sato (b. 1900) recalls his childhood in Japan, working in Tokyo, and getting a job on an ocean liner, then leaving ship in Texas to work there and in Denver, Colorad
"Robustness of the Separating Information Maximum Likelihood Estimation of Realized Volatility with Micro-Market Noise"
No full textFor estimating the realized volatility and covariance by using high frequency data, Kunitomo and Sato (2008a,b) have proposed the Separating Information Maximum Likelihood (SIML) method when there are micro-market noises. The SIML estimator has reasonable asymptotic properties; it is consistent and it has the asymptotic normality (or the stable convergence in the general case) when the sample size is large under general conditions including non-Gaussian processes and volatility models. We also show that the SIML estimator has the asymptotic robustness in the sense that it is consistent and it has the asymptotic normality when there are autocorrelations in the market noise terms and there are endogenous correlations between the signal and noise terms.
Valsiner, J., Marsico, G., Chaudhary, N., Sato, T. & Dazzani, V. (2015). What is changing in psychology? In J., Valsiner, G., Marsico, N. Chaudhary, T., Sato, V., Dazzani, (Eds). (2016). Psychology as a Science of Human Being: The Yokohama Manifesto, Annals of Theoretical Psychology, 13, (p. v-vii), Geneve, Switzerland: Springer
No full textWe think that psychology as science is – once again—at a crossroads. As it has happened recurrently in the past it is about to lose its appropriate focus—that of the subjective domain of the human being (the Psyche) that is an immediate component in the arena of living—involving all the activities of being human. Being ourselves—as human beings—involves happiness and sorrow, hopes and their failures, endless searches of “who am I” and developing sellable tools for helping others as well as destroying them. Both construction and destruction have been parts of being human—poetry and cruelty go hand in hand in our lives.
The human Psyche is complex, subjective, meaningful, and mysterious. As such it cannot be reduced to explanations that consider it accounted for by causal mechanisms of lower levels of organization. Thus, the efforts to reduce higher level psychological functions to physiological or genetic “causes” violates the hierarchical systemic structure of the totality of human beings. That system is organized at multiple levels—all of which are related, yet in ways that is functionally non-causal. Each level is simultaneously participating in the organization of adjacent levels as well as buffering against the potential malfunctions of these levels. The result is a highly resilient open system that deends on the relations with the environment—yet it is not in any way “caused” by direct environmental “influences”. In a similar vein, all higher levels of organization of the psychological phenomena are related with physiological and genetic levels—but not determined by them
Elements of Wonder: The Public Art of Norie Sato
No full textCreating over 45 site-integrated public art installations since 1982, Norie Sato (Japanese-American, b. 1949) strives to add meaning and human touch to the built environment and considers edges, transitions, and connections as important as the center. Her public art installations are located around the United States, with five site-specific installations in Iowa. Sato has created three major installations at Iowa State University - One, Now, All (1999-2000) in the Palmer Building, e+l+e+m+e+n+t+a+l (2010-2012) in Hach Hall, and most recently, The Fifth Muse (2015-2016) in Marston Hall. This exhibition of selected conceptual drawings, models and sculptural elements invites the viewer to explore Sato’s public art projects from conceptualization to fabrication and final installation.</p
Microstructures and mechanical properties of aluminum alloys processed by equal-channel Aagular pressing
No full text"Quantity or Quality: The Impact of Labor-Saving Innovation on US and Japanese Growth Rates, 1960-2004"
No full textThis article deals with both theoretical and empirical analyses of the post-war period (1960-2004) for the United States and Japan. We investigated three factors contributing to growth: the growth rates of capital, labor, and labor-saving innovation. It is shown that in Japan, the growth rate of the labor force has been much less important than its quality improvement-i.e., labor-saving technical change-while in the US, the growth rate of labor and population has contributed more than their quality improvement. The policy implication here is Japan's declining population can be compensated for by additional quality improvement of the existing labor force.
Refinements on vertical Sato-Tate
No full textVertical Sato-Tate states that the Frobenius trace of a randomly chosen
elliptic curve over tends to a semicircular distribution as
. We go beyond this statement by considering the number of
elliptic curves with a given trace over and
characterizing the 2-dimensional distribution of . In particular,
this gives the distribution of the size of isogeny classes of elliptic curves
over . Furthermore, we show a notion of stronger convergence for
vertical Sato-Tate which states that the number of elliptic curves with
Frobenius trace in an interval of length converges to the expected
amount. The key step in the proof is to truncate Gekeler's infinite product
formula, which relies crucially on an effective Chebotarev's density theorem
that was recently developed by Pierce, Turnage-Butterbaugh and Wood.Comment: 27 pages, 4 figures. Minor edits for clarit
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