scholarly journals Functional Imaging with Higher-Dimensional Electrical Data Sets

2018 ◽  
Vol 26 (6) ◽  
pp. 18-27 ◽  
Author(s):  
P. De Wolf ◽  
Z. Huang ◽  
B. Pittenger ◽  
A. Dujardin ◽  
M. Febvre ◽  
...  
Keyword(s):  
Functional Imaging ◽  
Data Sets ◽  
Higher Dimensional ◽  
Image Position ◽  
Electrical Data

Abstract

On Certain Functional Identities in EN

1971 ◽  
Vol 23 (2) ◽  
pp. 315-324 ◽  
Author(s):  
A. McD. Mercer
Keyword(s):  
Euclidean Space ◽  
Taylor Series ◽  
Dimensional Space ◽  
The Real ◽  
Higher Dimensional ◽  
Isolated Points ◽  
Functional Identities ◽  
Image Position ◽  
Special Case ◽  
Real Euclidean Space

1. If f is a real-valued function possessing a Taylor series convergent in (a — R, a + R), then it satisfies the following operational identity1.1in which D2 = d2/du2. Furthermore, when g is a solution of y″ + λ2y = 0 in (a – R, a + R), then g is such a function and (1.1) specializes to1.2In this note we generalize these results to the real Euclidean space EN, our conclusions being Theorems 1 and 2 below. Clearly, (1.2) is a special case of (1.1) but in higher-dimensional space it is of interest to allow g, now a solution of1.3to possess singularities at isolated points away from the origin. It is then necessary to consider not only a neighbourhood of the origin but annular regions also.

Directionally Independent Failure Prediction of End-Milling Tools by Tracking Increasing Chaotic Noise at the Machining Frequencies Due to Wear

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Christopher A. Suprock ◽  
John T. Roth
Keyword(s):  
Discrete Cosine Transform ◽  
End Milling ◽  
Dimensional Space ◽  
Data Sets ◽  
Cosine Transform ◽  
Modal Reduction ◽  
Milling Operations ◽  
Higher Dimensional ◽  
System Energy ◽  
Fourier Type

Accurate on-line forecasting of a tool’s condition during end-milling operations is advantageous to the functionality and reliability of automated industrial processes. The ability to disengage the tool prior to catastrophic failure reduces manufacturing costs, excessive machine deterioration, and personnel hazards. Rapid computational feedback describing the system’s state is critical for realizing a practical failure forecasting model. To this end, spectral analysis by fast Fourier type algorithms allows a rapid computational response. The research described herein explores the development of nontraditional real fast Fourier transform (discrete cosine transform) based algorithms performed in unique higher-dimensional states of observed data sets. Moreover, the developed Fourier algorithm quantifies chaotic noise rather than relying on the more traditional observation of system energy. By increasing the vector dimensionality of the discrete cosine transform, the respective linear transform basis more effectively cross correlates the transform data into fewer (more significant) transform coefficients. Thus, a single vector in orthogonally higher-dimensional space is observed instead of multiple orthogonal vectors in single-dimensional space. More specifically, a novel modal reduction technique is utilized to track trends measured from triaxial force dynamometer signals. This transformation effectively achieves both modal reduction and directional independence by observing the chaotic noise instead of system energy. Algorithm output trends from six end-milling life tests are tracked from both linear and pocketing maneuvers in order to demonstrate the technique’s capabilities. In all six tests, the algorithm predicts impending tool failure with sufficient time for tool removal.

scholarly journals The thermal conductivity of seasonal snow

1997 ◽  
Vol 43 (143) ◽  
pp. 26-41 ◽  
Author(s):  
Matthew Sturm ◽  
Jon Holmgren ◽  
Max König ◽  
Kim Morris
Keyword(s):  
Thermal Conductivity ◽  
Quadratic Equation ◽  
Mean Value ◽  
Data Sets ◽  
Data Set ◽  
Seasonal Snow ◽  
Kinetic Growth ◽  
Image Position ◽  
Snow Microstructure ◽  
Independent Behavior

AbstractTwenty-seven studies on the thermal conductivity of snow (Keff) have been published since 1886. Combined, they comprise 354 values ofKeff, and have been used to derive over 13 regression equation and predictingKeffvs density. Due to large (and largely undocumented) differences in measurement methods and accuracy, sample temperature and snow type, it is not possible to know what part of the variability in this data set is the result of snow microstructure. We present a new data set containing 488 measurements for which the temperature, type and measurement accuracy are known. A quadratic equation,whereρis in g cm−3, andKeffis in W m−1K−1, can be fit to the new data (R2= 0.79). A logarithmic expression,can also be used. The first regression is better when estimating values beyond the limits of the data; the second when estimating values for low-density snow. Within the data set, snow types resulting from kinetic growth show density-independent behavior. Rounded-grain and wind-blown snow show strong density dependence. The new data set has a higher mean value of density but a lower mean value of thermal conductivity than the old set. This shift is attributed to differences in snow types and sample temperatures in the sets. Using both data sets, we show that there are well-defined limits to the geometric configurations that natural seasonal snow can take.

Families of Triangular Norm-Based Kernel Functions and Their Application to Kernel k-Means

2017 ◽  
Vol 21 (3) ◽  
pp. 534-542
Author(s):  
Kazushi Okamoto ◽  
Keyword(s):  
Feature Space ◽  
Kernel Functions ◽  
Rand Index ◽  
Adjusted Rand Index ◽  
Data Sets ◽  
Linear Kernel ◽  
Triangular Norm ◽  
Higher Dimensional ◽  
Rbf Kernel ◽  
Map Data

This study proposes the concept of families of triangular norm (t-norm)-based kernel functions, and discusses their positive-definite property and the conditions for applicable t-norms. A clustering experiment with kernel k-means is performed in order to analyze the characteristics of the proposed concept, as well as the effects of the t-norm and parameter selections. It is evaluated that the clusters obtained in terms of the adjusted rand index and the experimental results suggested the following : (1) the adjusted rand index values obtained by the proposed method were almost the same or higher than those produced using the linear kernel for all of the data sets; (2) the proposed method slightly improved the adjusted rand index values for some data sets compared with the radial basis function (RBF) kernel; (3) the proposed method tended to map data to a higher dimensional feature space than the linear kernel but the dimension was lower than that using the RBF kernel.

scholarly journals Robustifying the multivariate chain-ladder method: A comparison of two methods

2016 ◽  
Vol 5 (1) ◽  
pp. 70-77
Author(s):  
Martine Van Wouwe ◽  
Nattakorn Phewchean
Keyword(s):  
Life Insurance ◽  
Higher Dimensions ◽  
Data Sets ◽  
Multiple Constraints ◽  
Insurance Company ◽  
Life Insurance Company ◽  
Robust Solutions ◽  
Higher Dimensional ◽  
Chain Ladder Method ◽  
Chain Ladder

The expected result of a non-life insurance company is usually determined for its activity in different business lines as a whole. This implies that the claims reserving problem for a portfolio of several (perhaps correlated) subportfolios is to be solved. A popular technique for studying such a portfolio is the chain-ladder method. However, it is well known that the chain-ladder method is very sensitive to outlying data. For the bivariate situation, we have already developed robust solutions for the chain-ladder method by introducing two techniques for detecting and correcting outliers. In this article we focus on higher dimensions. Being subjected to multiple constraints (no graphical plots available), the goal of our research is to find solutions to detect and smooth the influence of outlying data on the outstanding claims reserve in higher dimensional data sets. The methodologies are illustrated and computed for real examples from the insurance practice.

Radiocarbon calibration beyond 20,000 14C yr B.P. by means of planktonic foraminifera of the Iberian Margin

2004 ◽  
Vol 61 (2) ◽  
pp. 204-214 ◽  
Author(s):  
Edouard Bard ◽  
Frauke Rostek ◽  
Guillemette Ménot-Combes
Keyword(s):  
Planktonic Foraminifera ◽  
Data Sets ◽  
Last Glacial Period ◽  
Polynomial Curve ◽  
Abrupt Changes ◽  
Image Position ◽  
Reservoir Age ◽  
Iberian Margin ◽  
Good Agreement ◽  
The Last Glacial

We present a new set of 14C ages obtained by accelerator mass spectrometry (AMS) on planktonic foraminifera from a deep-sea core collected off the Iberian Margin (MD952042). This site, at 37°N, is distant from the high-latitude zones where 14C reservoir age is large and variable. Many independent proxies — alkenones, magnetic susceptibility, ice-rafted debris, foraminifera stable isotopes, abundances of foraminifera, pollen, and dinoflagellates — show abrupt changes correlative with Dansgaard-Oeschger and Heinrich events of the last glacial period. The good stratigraphic agreement of all proxies — from the fine to the coarse-size fractions — indicates that the foraminifera 14C ages are representative of the different sediment fractions. To obtain reliable 14C ages of foraminifera beyond 20,000 14C yr B.P. we leached the shells prior to carbonate hydrolysis and subsequent analysis. For a calendar age scale, we matched the Iberian Margin profile with that of Greenland Summit δ18O. Both are proxies for temperature, which in models varies synchronously in the two areas. The match creates no spurious jumps in sedimentation rate and requires only a limited number of tie points. Except for ages older than 40,000 14C yr B.P. Greenland's GISP2 and GRIP records yield similar calendars. The 14C and imported calendar ages of the Iberian Margin record are then compared to data — from lacustrine annual varves and from corals and speleothems dated by U–Th — previously used to extend the calibration beyond 20,000 14C yr B.P. The new record follows a smooth pattern between 23,000 and 50,000 cal yr B.P. We find good agreement with the previous data sets between 23,000 and 31,000 cal yr B.P. In the interval between 33,000 and 41,000 cal yr B.P. for which previous records disagree by up to 5000 cal yr, the Iberian Margin record closely follows the polynomial curve that was previously defined by an interpolation of the coral ages and runs between the Lake Suigetsu and the Bahamian speleothem data sets.

scholarly journals ESTIMATES FOR MARCINKIEWICZ INTEGRALS IN BMO AND CAMPANATO SPACES

2007 ◽  
Vol 49 (2) ◽  
pp. 167-187 ◽  
Author(s):  
GUOEN HU ◽  
YAN MENG ◽  
DACHUN YANG
Keyword(s):  
Regularity Condition ◽  
Mean Value ◽  
Marcinkiewicz Integral ◽  
Degree Zero ◽  
Marcinkiewicz Integrals ◽  
Almost Everywhere ◽  
Higher Dimensional ◽  
Lusin Area Integral ◽  
Image Position ◽  
Marcinkiewicz Integral Operator

AbstractIn this paper, the authors consider the behavior on BMO($\mathbb R^n$) and Campanato spaces for the higher-dimensional Marcinkiewicz integral operator which is defined by where Ω is homogeneous of degree zero, has mean value zero and is integrable on the unit sphere. Under certain weak regularity condition on Ω, the authors prove that if f belongs to BMO($\mathbb R^n$) or to a certain Campanato space, then [μΩ(f)]2 is either infinite everywhere or finite almost everywhere, and in the latter case, some kind of boundedness is also obtained. The corresponding Lusin area integral is also considered.

scholarly journals Forbidden Hypermatrices Imply General Bounds on Induced Forbidden Subposet Problems

2017 ◽  
Vol 26 (4) ◽  
pp. 593-602 ◽  
Author(s):  
ABHISHEK METHUKU ◽  
DÖMÖTÖR PÁLVÖLGYI
Keyword(s):  
Higher Dimensional ◽  
Image Position

We prove that for every posetP, there is a constantCPsuch that the size of any family of subsets of {1, 2, . . .,n} that does not containPas an induced subposet is at most$$C_P{\binom{n}{\lfloor\gfrac{n}{2}\rfloor}},$$settling a conjecture of Katona, and Lu and Milans. We obtain this bound by establishing a connection to the theory of forbidden submatrices and then applying a higher-dimensional variant of the Marcus–Tardos theorem, proved by Klazar and Marcus. We also give a new proof of their result.

Sign in / Sign up

Export Citation Format

Share Document