The Experts below are selected from a list of 19878 Experts worldwide ranked by ideXlab platform
D. Juriev - One of the best experts on this subject based on the ideXlab platform.
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Infinite-Dimensional Geometry of the Universal Deformation of the Complex Disk
arXiv: Functional Analysis, 1994Co-Authors: D. JurievAbstract:The universal deformation of the complex disk is studied from the viewpoint of infinite-Dimensional Geometry. The structure of a subsymmetric space on the universal deformation is described. The foliation of the universal deformation by subsymmetry mirrors is shown to determine a real polarization. The subject of the paper maybe of interest to specialists in algebraic Geometry and representation theory as well as to researchers dealing with mathematical problems of modern quantum field theory. Contents. I. The infinite-Dimensional Geometry of the flag manifold of the Virasoro-Bott group (the base of the universal deformation of the complex disk). II. The infinite-Dimensional Geometry of the skeleton of the flag manifold of the Virasoro-Bott group. III. The infinite-Dimensional Geometry of the universal deformation of the complex disk.
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Infinite-Dimensional Geometry and closed string-field theory
Letters in Mathematical Physics, 1991Co-Authors: D. JurievAbstract:The Letter is deveted to the mathematical formulation of the closed string-field theory on a flat background.
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Infinite-Dimensional Geometry and generally covariant quantum closed string-field theory
Letters in Mathematical Physics, 1991Co-Authors: D. JurievAbstract:A version, based on infinite-Dimensional Geometry, of the generally covariant closed string-field theory is proposed.
G Dheeraj Kumar - One of the best experts on this subject based on the ideXlab platform.
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Dimensional QUANTIZATION OF TIME DILATION: Analysis of time dilation using Dimensional Geometry
International Journal of Research, 2014Co-Authors: G Dheeraj KumarAbstract:The term time dilation is somewhat seems to be a very difficult to understand whether the dilation is because of relative masses or relative velocities under same gravitational field. The thing interesting here is that, where the theory of relativity explains time dilation is due to gravity well which states that it occurs either because of the relative velocity of motion between two observers, or the difference in their distance from a gravitational mass. Now my contribution to this theory is that the time dilation not only due to because of theory of relativity but also due towave interaction loss of electromagnetic fields in gravitons because of the coordinate transformation in space which is explained by using Euclidean Dimensional Geometry. The theme of the paper is to produce the theoretical results using Dimensional Geometry to study the approximation of time dilation and time dimension.
Rocco A Servedio - One of the best experts on this subject based on the ideXlab platform.
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a robust khintchine inequality and algorithms for computing optimal constants in fourier analysis and high Dimensional Geometry
SIAM Journal on Discrete Mathematics, 2016Co-Authors: Ilias Diakonikolas, Rocco A ServedioAbstract:This paper makes two contributions towards determining some well-studied optimal constants in Fourier analysis of Boolean functions and high-Dimensional Geometry. It has been known since 1994 [C. Gotsman and N. Linial, Combinatorica, 14 (1994), pp. 35--50] that every linear threshold function (LTF) has a squared Fourier mass of at least $1/2$ on its degree-$0$ and degree-$1$ coefficients. Let the minimum such Fourier mass be ${\bf W}^{\leq 1}[{\bf LTF}]$, where the minimum is taken over all $n$-variable LTFs and all $n \ge 0$. Benjamini, Kalai, and Schramm [Publ. Math. Inst. Hautes Etudes Sci., 90 (1999), pp. 5--43] conjectured that the true value of ${\bf W}^{\leq 1}[{\bf LTF}]$ is $2/\pi$. We make progress on this conjecture by proving that ${\bf W}^{\leq 1}[{\bf LTF}] \geq 1/2 + c$ for some absolute constant $c>0$. The key ingredient in our proof is a “robust” version of the well-known Khintchine inequality in functional analysis, which we believe may be of independent interest. Let ${\bf W}^{\leq 1}[{...
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a robust khintchine inequality and algorithms for computing optimal constants in fourier analysis and high Dimensional Geometry
International Colloquium on Automata Languages and Programming, 2013Co-Authors: Ilias Diakonikolas, Rocco A ServedioAbstract:This paper makes two contributions towards determining some well-studied optimal constants in Fourier analysis of Boolean functions and high-Dimensional Geometry. 1 It has been known since 1994 [GL94] that every linear threshold function has squared Fourier mass at least 1/2 on its degree-0 and degree-1 coefficients. Denote the minimum such Fourier mass by W≤1[LTF], where the minimum is taken over all n-variable linear threshold functions and all n≥0. Benjamini, Kalai and Schramm [BKS99] have conjectured that the true value of W≤1[LTF] is 2/π. We make progress on this conjecture by proving that W≤1[LTF]≥1/2+c for some absolute constant c>0. The key ingredient in our proof is a "robust" version of the well-known Khintchine inequality in functional analysis, which we believe may be of independent interest. 2 We give an algorithm with the following property: given any η>0, the algorithm runs in time 2poly(1/η) and determines the value of W≤1[LTF] up to an additive error of ±η. We give a similar 2poly(1/η)-time algorithm to determine Tomaszewski's constant to within an additive error of ±η; this is the minimum (over all origin-centered hyperplanes H) fraction of points in {−1,1}n that lie within Euclidean distance 1 of H. Tomaszewski's constant is conjectured to be 1/2; lower bounds on it have been given by Holzman and Kleitman [HK92] and independently by Ben-Tal, Nemirovski and Roos [BTNR02]. Our algorithms combine tools from anti-concentration of sums of independent random variables, Fourier analysis, and Hermite analysis of linear threshold functions.
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a robust khintchine inequality and algorithms for computing optimal constants in fourier analysis and high Dimensional Geometry
arXiv: Computational Complexity, 2012Co-Authors: Ilias Diakonikolas, Rocco A ServedioAbstract:This paper makes two contributions towards determining some well-studied optimal constants in Fourier analysis \newa{of Boolean functions} and high-Dimensional Geometry. \begin{enumerate} \item It has been known since 1994 \cite{GL:94} that every linear threshold function has squared Fourier mass at least 1/2 on its degree-0 and degree-1 coefficients. Denote the minimum such Fourier mass by $\w^{\leq 1}[\ltf]$, where the minimum is taken over all $n$-variable linear threshold functions and all $n \ge 0$. Benjamini, Kalai and Schramm \cite{BKS:99} have conjectured that the true value of $\w^{\leq 1}[\ltf]$ is $2/\pi$. We make progress on this conjecture by proving that $\w^{\leq 1}[\ltf] \geq 1/2 + c$ for some absolute constant $c>0$. The key ingredient in our proof is a "robust" version of the well-known Khintchine inequality in functional analysis, which we believe may be of independent interest. \item We give an algorithm with the following property: given any $\eta > 0$, the algorithm runs in time $2^{\poly(1/\eta)}$ and determines the value of $\w^{\leq 1}[\ltf]$ up to an additive error of $\pm\eta$. We give a similar $2^{{\poly(1/\eta)}}$-time algorithm to determine \emph{Tomaszewski's constant} to within an additive error of $\pm \eta$; this is the minimum (over all origin-centered hyperplanes $H$) fraction of points in $\{-1,1\}^n$ that lie within Euclidean distance 1 of $H$. Tomaszewski's constant is conjectured to be 1/2; lower bounds on it have been given by Holzman and Kleitman \cite{HK92} and independently by Ben-Tal, Nemirovski and Roos \cite{BNR02}. Our algorithms combine tools from anti-concentration of sums of independent random variables, Fourier analysis, and Hermite analysis of linear threshold functions. \end{enumerate}
Remel Salmingo - One of the best experts on this subject based on the ideXlab platform.
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intraoperative implant rod three Dimensional Geometry measured by dual camera system during scoliosis surgery
Bio-medical Materials and Engineering, 2016Co-Authors: Remel Salmingo, Shigeru TadanoAbstract:Treatment for severe scoliosis is usually attained when the scoliotic spine is deformed and fixed by implant rods. In- vestigation of the intraoperative changes of implant rod shape in three-dimensions is necessary to understand the biomechanics of scoliosis correction, establish consensus of the treatment, and achieve the optimal outcome. The objective of this study was to measure the intraoperative three-Dimensional Geometry and deformation of implant rod during scoliosis corrective surgery. A pair of images was obtained intraoperatively by the dual camera system before rotation and after rotation of rods during scoliosis surgery. The three-Dimensional implant rod Geometry before implantation was measured directly by the surgeon and after surgery using a CT scanner. The images of rods were reconstructed in three-dimensions using quintic polynomial func- tions. The implant rod deformation was evaluated using the angle between the two three-Dimensional tangent vectors measured at the ends of the implant rod. The implant rods at the concave side were significantly deformed during surgery. The highest rod deformation was found after the rotation of rods. The implant curvature regained after the surgical treatment. Careful intraoperative rod maneuver is important to achieve a safe clinical outcome because the intraoperative forces could be higher than the postoperative forces. Continuous scoliosis correction was observed as indicated by the regain of the implant rod curvature after surgery.
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A Simple Method for In Vivo Measurement of Implant Rod Three-Dimensional Geometry During Scoliosis Surgery
Journal of biomechanical engineering, 2012Co-Authors: Remel Salmingo, Shigeru Tadano, Kazuhiro Fujisaki, Yuichiro Abe, Manabu ItoAbstract:Scoliosis is defined as a spinal pathology characterized as a three-Dimensional deformity of the spine combined with vertebral rotation. Treatment for severe scoliosis is achieved when the scoliotic spine is surgically corrected and fixed using implanted rods and screws. Several studies performed biomechanical modeling and corrective forces measurements of scoliosis correction. These studies were able to predict the clinical outcome and measured the corrective forces acting on screws, however, they were not able to measure the intraoperative three-Dimensional Geometry of the spinal rod. In effect, the results of biomechanical modeling might not be so realistic and the corrective forces during the surgical correction procedure were intra-operatively difficult to measure. Projective Geometry has been shown to be successful in the reconstruction of a three-Dimensional structure using a series of images obtained from different views. In this study, we propose a new method to measure the three-Dimensional Geometry of an implant rod using two cameras. The reconstruction method requires only a few parameters, the included angle θ between the two cameras, the actual length of the rod in mm, and the location of points for curve fitting. The implant rod utilized in spine surgery was used to evaluate the accuracy of the current method. The three-Dimensional Geometry of the rod was measured from the image obtained by a scanner and compared to the proposed method using two cameras. The mean error in the reconstruction measurements ranged from 0.32 to 0.45 mm. The method presented here demonstrated the possibility of intra-operatively measuring the three-Dimensional Geometry of spinal rod. The proposed method could be used in surgical procedures to better understand the biomechanics of scoliosis correction through real-time measurement of three-Dimensional implant rod Geometry in vivo.
Kenneth D M Harris - One of the best experts on this subject based on the ideXlab platform.
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high Dimensional Geometry of population responses in visual cortex
Nature, 2019Co-Authors: Carsen Stringer, Marius Pachitariu, Nicholas A Steinmetz, Matteo Carandini, Kenneth D M HarrisAbstract:A neuronal population encodes information most efficiently when its stimulus responses are high-Dimensional and uncorrelated, and most robustly when they are lower-Dimensional and correlated. Here we analysed the Dimensionality of the encoding of natural images by large populations of neurons in the visual cortex of awake mice. The evoked population activity was high-Dimensional, and correlations obeyed an unexpected power law: the nth principal component variance scaled as 1/n. This scaling was not inherited from the power law spectrum of natural images, because it persisted after stimulus whitening. We proved mathematically that if the variance spectrum was to decay more slowly then the population code could not be smooth, allowing small changes in input to dominate population activity. The theory also predicts larger power-law exponents for lower-Dimensional stimulus ensembles, which we validated experimentally. These results suggest that coding smoothness may represent a fundamental constraint that determines correlations in neural population codes.
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high Dimensional Geometry of population responses in visual cortex
bioRxiv, 2018Co-Authors: Carsen Stringer, Marius Pachitariu, Nicholas A Steinmetz, Matteo Carandini, Kenneth D M HarrisAbstract:A neuronal population encodes information most efficiently when its activity is uncorrelated and high-Dimensional, but correlated lower-Dimensional codes provide robustness against noise. Here, we analyzed the correlation structure of natural image coding, in large visual cortical populations recorded from awake mice. Evoked population activity was high Dimensional, with correlations obeying an unexpected power-law: the n-th principal component variance scaled as 1/n. This was not inherited from the 1/f spectrum of natural images, because it persisted after stimulus whitening. We proved mathematically that the variance spectrum must decay at least this fast if a population code is smooth, i.e. if small changes in input cannot dominate population activity. The theory also predicted larger power-law exponents for lower-Dimensional stimulus ensembles, which we validated experimentally. These results suggest that coding smoothness represents a fundamental constraint governing correlations in neural population codes.
