The Application of the Moment Function in the Study of Distribution Laws in Statistics

abstract The moment function of an explosion is introduced, using the equivalence of an explosive point source and three mutually perpendicular linear dipoles. The seismic moment of an explosion is the final value, for large times, of the moment function. Its relation to source parameters is similar to that of the moment of an earthquake: M1 = (λ + 2μ)S1D1 (λ, μ = Lamé's parameters, S1 = surface area of a sphere surrounding the explosion in the elastic zone, D1 = static radial displacement on this sphere). From strain observations of other authors (Romig et al., 1969; Smith et al., 1969), the moment of the underground nuclear explosion BENHAM is estimated to be about 1024 dyne cm. This moment value supports the assumption that the source-time function for the long-period radiation from large nuclear explosions (periods greater than about 10 sec) is essentially a step-function. On the other hand, a quantitative estimate of the long-period P-wave spectrum of the explosions JORUM, HANDLEY and MILROW and a comparison with observed spectra of Molnar (1971) for JORUM and HANDLEY and Wyss et al. (1971) for MILROW support the assumption of an impulsive source-time function. This discrepancy, which is typical of current opinions among seismologists, is not resolved. It is concluded that an explosive point source is possibly not a sufficient model for the long-time radiation and the static displacement field of a nuclear underground explosion whose elastic radius is about equal to its depth and which is detonated in a prestressed medium.

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Regularized Orthogonal Machine Learning for Nonlinear Semiparametric Models

Econometrics Journal ◽

10.1093/ectj/utab022 ◽

2021 ◽

Author(s):

Nekipelov Denis ◽

Semenova Vira ◽

Syrgkanis Vasilis

Keyword(s):

Machine Learning ◽

Loss Function ◽

Moment Function ◽

Conditional Moment ◽

Parametric Problem ◽

Welfare Participation ◽

Single Index ◽

Participation Decision ◽

The Moment ◽

Nuisance Function

Abstract This paper proposes a Lasso-type estimator for a high-dimensional sparse parameter identified by a single index conditional moment restriction (CMR). In addition to this parameter, the moment function can also depend on a nuisance function, such as the propensity score or the conditional choice probability, which we estimate by modern machine learning tools. We first adjust the moment function so that the gradient of the future loss function is insensitive (formally, Neyman-orthogonal) with respect to the first-stage regularization bias, preserving the single index property. We then take the loss function to be an indefinite integral of the adjusted moment function with respect to the single index. The proposed Lasso estimator converges at the oracle rate, where the oracle knows the nuisance function and solves only the parametric problem. We demonstrate our method by estimating the short-term heterogeneous impact of Connecticut’s Jobs First welfare reform experiment on women’s welfare participation decision.

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The moment function for the ratio of correlated generalized gamma variables

Statistics & Probability Letters ◽

10.1016/j.spl.2013.06.026 ◽

2013 ◽

Vol 83 (10) ◽

pp. 2353-2356 ◽

Cited By ~ 3

Author(s):

Çağatay Candan ◽

Umut Orguner

Keyword(s):

Moment Function ◽

Generalized Gamma ◽

The Moment

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The High Resolution Scanning Transmission Electron Microscope

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100051591 ◽

1974 ◽

Vol 32 ◽

pp. 316-317

Author(s):

A. V. Crewe

Keyword(s):

Electron Microscope ◽

High Resolution ◽

High Vacuum ◽

Scanning Transmission Electron Microscope ◽

Ultra High Vacuum ◽

Resolving Power ◽

Imaging Characteristics ◽

Transmission Electron ◽

Scanning Transmission ◽

The Moment

The high resolution STEM is now a fact of life. I think that we have, in the last few years, demonstrated that this instrument is capable of the same resolving power as a CEM but is sufficiently different in its imaging characteristics to offer some real advantages.It seems possible to prove in a quite general way that only a field emission source can give adequate intensity for the highest resolution^ and at the moment this means operating at ultra high vacuum levels. Our experience, however, is that neither the source nor the vacuum are difficult to manage and indeed are simpler than many other systems and substantially trouble-free.

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Pinocytotic-Like Forms of Mitochondria From Rat Anterior Pituitary

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100100470 ◽

1968 ◽

Vol 26 ◽

pp. 146-147

Author(s):

Burton B. Silver

Keyword(s):

Electron Micrographs ◽

Conformational Changes ◽

Anterior Pituitary ◽

Dynamic State ◽

Surrounding Cell ◽

The Matrix ◽

The Moment ◽

Cell Medium ◽

Sectioned Tissue ◽

State Of Activity

Sectioned tissue rarely indicates evidence of what is probably a highly dynamic state of activity in mitochondria which have been reported to undergo a variety of movements such as streaming, divisions and coalescence. Recently, mitochondria from the rat anterior pituitary have been fixed in a variety of configurations which suggest that conformational changes were occurring at the moment of fixation. Pinocytotic-like vacuoles which may be taking in or expelling materials from the surrounding cell medium, appear to be forming in some of the mitochondria. In some cases, pores extend into the matrix of the mitochondria. In other forms, the remains of what seems to be pinched off vacuoles are evident in the mitochondrial interior. Dense materials, resembling secretory droplets, appear at the junction of the pores and the cytoplasm. The droplets are similar to the secretory materials commonly identified in electron micrographs of the anterior pituitary.

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Advances in Stem Instrumentation for Biology

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100180562 ◽

1990 ◽

Vol 48 (1) ◽

pp. 362-363

Author(s):

J. S. Wall

Keyword(s):

Scanning Transmission Electron Microscope ◽

Carbon Films ◽

Specimen Preparation ◽

Material Deposition ◽

Active User ◽

Percent Improvement ◽

Scanning Transmission ◽

The Moment ◽

Film Substrate ◽

High Level

The forte of the Scanning transmission Electron Microscope (STEM) is high resolution imaging with high contrast on thin specimens, as demonstrated by visualization of single heavy atoms. of equal importance for biology is the efficient utilization of all available signals, permitting low dose imaging of unstained single molecules such as DNA.Our work at Brookhaven has concentrated on: 1) design and construction of instruments optimized for a narrow range of biological applications and 2) use of such instruments in a very active user/collaborator program. Therefore our program is highly interactive with a strong emphasis on producing results which are interpretable with a high level of confidence.The major challenge we face at the moment is specimen preparation. The resolution of the STEM is better than 2.5 A, but measurements of resolution vs. dose level off at a resolution of 20 A at a dose of 10 el/A2 on a well-behaved biological specimen such as TMV (tobacco mosaic virus). To track down this problem we are examining all aspects of specimen preparation: purification of biological material, deposition on the thin film substrate, washing, fast freezing and freeze drying. As we attempt to improve our equipment/technique, we use image analysis of TMV internal controls included in all STEM samples as a monitor sensitive enough to detect even a few percent improvement. For delicate specimens, carbon films can be very harsh-leading to disruption of the sample. Therefore we are developing conducting polymer films as alternative substrates, as described elsewhere in these Proceedings. For specimen preparation studies, we have identified (from our user/collaborator program ) a variety of “canary” specimens, each uniquely sensitive to one particular aspect of sample preparation, so we can attempt to separate the variables involved.

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Traumatic Brain Injury: A Trauma Surgeon's Perspective

Perspectives on Neurophysiology and Neurogenic Speech and Language Disorders ◽

10.1044/nnsld22.3.82 ◽

2012 ◽

Vol 22 (3) ◽

pp. 82-89

Author(s):

Oscar D. Guillamondegui

Keyword(s):

Traumatic Brain Injury ◽

Brain Injury ◽

Multidisciplinary Approach ◽

Trauma Team ◽

The United States ◽

Long Term Outcomes ◽

Term Care ◽

Injured Brain ◽

The Moment

Traumatic brain injury (TBI) is a serious epidemic in the United States. It affects patients of all ages, race, and socioeconomic status (SES). The current care of these patients typically manifests after sequelae have been identified after discharge from the hospital, long after the inciting event. The purpose of this article is to introduce the concept of identification and management of the TBI patient from the moment of injury through long-term care as a multidisciplinary approach. By promoting an awareness of the issues that develop around the acutely injured brain and linking them to long-term outcomes, the trauma team can initiate care early to alter the effect on the patient, family, and community. Hopefully, by describing the care afforded at a trauma center and by a multidisciplinary team, we can bring a better understanding to the armamentarium of methods utilized to treat the difficult population of TBI patients.

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