Inequalities for Propability Contents of Convex Sets via Geometric Average.

1985 ◽  
Author(s):  
Moshe Shaked ◽  
Y. L. Tong
Keyword(s):  
Convex Sets ◽  
Geometric Average

scholarly journals Inequalities for probability contents of convex sets via geometric average

1988 ◽  
Vol 24 (2) ◽  
pp. 330-340 ◽  
Author(s):  
Moshe Shaked ◽  
Y.L Tong
Keyword(s):  
Convex Sets ◽  
Geometric Average

On the Use of POCS for Restoring the “Missing Wedge” in Electron Tomography

1990 ◽  
Vol 48 (1) ◽  
pp. 520-521
Author(s):  
Neng-Yu Zhang ◽  
Bruce F. McEwen ◽  
Joachim Frank
Keyword(s):  
Function Space ◽  
Convex Sets ◽  
Electron Tomography ◽  
Spinal Ganglion ◽  
Fourier Space ◽  
Missing Information ◽  
Voltage Electron ◽  
High Voltage Electron Microscope ◽  
Energy Bound ◽  
Spatial Boundedness

Reconstructions of asymmetric objects computed by electron tomography are distorted due to the absence of information, usually in an angular range from 60 to 90°, which produces a “missing wedge” in Fourier space. These distortions often interfere with the interpretation of results and thus limit biological ultrastructural information which can be obtained. We have attempted to use the Method of Projections Onto Convex Sets (POCS) for restoring the missing information. In POCS, use is made of the fact that known constraints such as positivity, spatial boundedness or an upper energy bound define convex sets in function space. Enforcement of such constraints takes place by iterating a sequence of function-space projections, starting from the original reconstruction, onto the convex sets, until a function in the intersection of all sets is found. First applications of this technique in the field of electron microscopy have been promising.To test POCS on experimental data, we have artificially reduced the range of an existing projection set of a selectively stained Golgi apparatus from ±60° to ±50°, and computed the reconstruction from the reduced set (51 projections). The specimen was prepared from a bull frog spinal ganglion as described by Lindsey and Ellisman and imaged in the high-voltage electron microscope.

The Standard Metric

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Affine Transformation ◽  
Convex Sets ◽  
Finite Dimension ◽  
Affine Subspace ◽  
Affine Transformations ◽  
Real Vector ◽  
Euclidean Metric ◽  
Affine Hyperplane ◽  
Tits Building ◽  
Convex Closure

This chapter presents some results about groups generated by reflections and the standard metric on a Bruhat-Tits building. It begins with definitions relating to an affine subspace, an affine hyperplane, an affine span, an affine map, and an affine transformation. It then considers a notation stating that the convex closure of a subset a of X is the intersection of all convex sets containing a and another notation that denotes by AGL(X) the group of all affine transformations of X and by Trans(X) the set of all translations of X. It also describes Euclidean spaces and assumes that the real vector space X is of finite dimension n and that d is a Euclidean metric on X. Finally, it discusses Euclidean representations and the standard metric.

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

Pyruvate as an Indicator of Quality in Grading Nonfat Dry Milk1

1982 ◽  
Vol 45 (6) ◽  
pp. 561-565 ◽  
Author(s):  
R. T. MARSHALL ◽  
Y. H. LEE ◽  
B. L. O'BRIEN ◽  
W. A. MOATS
Keyword(s):  
Geometric Mean ◽  
Regression Line ◽  
Skim Milk ◽  
Plate Count ◽  
Department Of Agriculture ◽  
Standard Plate Count ◽  
Geometric Average ◽  
Dry Milk ◽  
Standard Plate ◽  
Microscopic Count

Samples of skim milk and nonfat dry milk (NDM) made from it were collected, paired and tested for pyruvate concentration, [P], and Direct Microscopic count (DMC). The skim milk was tested for Standard Plate Count (SPC) and Psychrotrophic Plate Count (PPC). The geometric average DMC of skim milk was more than three times higher than that of the paired NDM samples. However, [P] of NDM was not significantly different from that of the skim milk. Although [P] of skim milk was poorly correlated with SPC and PPC, r = .31 and .26, respectively, it was relatively well correlated with DMC, r = .64. Data were widely dispersed around the regression line when [P] was ≤ 4.0 mg/L. However, [P] increased rapidly when DMCs were > 106/ml. A limit of 10 mg/L of [P] in NDM reconstituted 1:9 was chosen to represent the current U.S. Department of Agriculture Standard for DMC in NDM. This limit failed to classify about 10% of the samples correctly, assuming that each geometric mean DMC was correct. However, the probability that samples meeting the DMC standard would be rejected by the pyruvate test was quite low and the probability was moderate that samples which would be acceptable by the pyruvate test would be rejected by the DMC. For the latter, 28% of the samples having DMCs of ≥ 107/ml contained < 10 mg/L of pyruvate. No sample having ≥ 10 mg/L of pyruvate had a DMC of ≤ 107/ml. Pyruvate concentration in NDM did not change during storage at 5 or 32°C for 90 days.

scholarly journals Further steps on the reconstruction of convex polyominoes from orthogonal projections

2021 ◽  
Author(s):  
Paolo Dulio ◽  
Andrea Frosini ◽  
Simone Rinaldi ◽  
Lama Tarsissi ◽  
Laurent Vuillon
Keyword(s):  
Discrete Geometry ◽  
Convex Subset ◽  
Convex Sets ◽  
A Priori ◽  
Orthogonal Projections ◽  
Reconstruction Process ◽  
Combinatorial Properties ◽  
The Family ◽  
Discrete Counterpart ◽  
Interior Part

AbstractA remarkable family of discrete sets which has recently attracted the attention of the discrete geometry community is the family of convex polyominoes, that are the discrete counterpart of Euclidean convex sets, and combine the constraints of convexity and connectedness. In this paper we study the problem of their reconstruction from orthogonal projections, relying on the approach defined by Barcucci et al. (Theor Comput Sci 155(2):321–347, 1996). In particular, during the reconstruction process it may be necessary to expand a convex subset of the interior part of the polyomino, say the polyomino kernel, by adding points at specific positions of its contour, without losing its convexity. To reach this goal we consider convexity in terms of certain combinatorial properties of the boundary word encoding the polyomino. So, we first show some conditions that allow us to extend the kernel maintaining the convexity. Then, we provide examples where the addition of one or two points causes a loss of convexity, which can be restored by adding other points, whose number and positions cannot be determined a priori.

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