Lecture 11: High Dimensional Geometry, Curse of Dimensionality, Dimension Reduction
... In machine learning and statistics sometimes the term refers to the fact that available data is too sparse in high dimensions; different take on the same underlying phenomenon. I hereby coin a new term: Blessing of dimensionality. This refers to the fact that many phenomena become much clearer and e ...
... In machine learning and statistics sometimes the term refers to the fact that available data is too sparse in high dimensions; different take on the same underlying phenomenon. I hereby coin a new term: Blessing of dimensionality. This refers to the fact that many phenomena become much clearer and e ...
Topological Casimir effect in nanotubes and nanoloops
... Feature that the VEV of the current density is finite on the brane could be argued on the base of general arguments In quantum field theory the ultraviolet divergences in the VEVs of physical observables bilinear in the field are determined by the local geometrical characteristics of the bulk and bo ...
... Feature that the VEV of the current density is finite on the brane could be argued on the base of general arguments In quantum field theory the ultraviolet divergences in the VEVs of physical observables bilinear in the field are determined by the local geometrical characteristics of the bulk and bo ...
Cumulants and partition lattices.
... This is the first paper to appear in the statistical literature pointing out the importance of the partition lattice in the theory of statistical moments and their close cousins, the cumulants. The paper was first brought to my attention by Susan Wilson, shotly after I had given a talk at Imperial C ...
... This is the first paper to appear in the statistical literature pointing out the importance of the partition lattice in the theory of statistical moments and their close cousins, the cumulants. The paper was first brought to my attention by Susan Wilson, shotly after I had given a talk at Imperial C ...
another essay - u.arizona.edu
... fundamental non-gravitational interactions are quantum theories, and since the 1970's these have been to a large extent unified in the so-called Standard Model. Contrary to Einstein’s conviction, and despite his scruples, there is a widespread belief today that any plausible candidate for a unified ...
... fundamental non-gravitational interactions are quantum theories, and since the 1970's these have been to a large extent unified in the so-called Standard Model. Contrary to Einstein’s conviction, and despite his scruples, there is a widespread belief today that any plausible candidate for a unified ...
Quantum Contributions to Cosmological Correlations
... over internal wave numbers, and how these problems may be circumvented. In Section VI we return to the theories introduced in Section III, and we show that the conditions of the theorem proved in Section IV are satisfied for these theories. This means that, to all orders of perturbation theory, if u ...
... over internal wave numbers, and how these problems may be circumvented. In Section VI we return to the theories introduced in Section III, and we show that the conditions of the theorem proved in Section IV are satisfied for these theories. This means that, to all orders of perturbation theory, if u ...
Talk1_Nardi
... typical scale: • These considerations make sense if • therefore • We are dealing with a weakly coupled and non-perturbative system. • Effective theory : small-x gluons are described as the classical colour fields radiated by colour sources at higher rapidity. • This effective theory describes the sa ...
... typical scale: • These considerations make sense if • therefore • We are dealing with a weakly coupled and non-perturbative system. • Effective theory : small-x gluons are described as the classical colour fields radiated by colour sources at higher rapidity. • This effective theory describes the sa ...
Non-Abelian String-Net Ladders Marc Daniel Schulz, S´ebastien Dusuel, and Julien Vidal
... plaquette p. Explicit form of this operator in the edge basis is given in Ref. [19]. The second term is diagonal in the link (edge) basis since δl(r),0 is the projector onto the state 0, acting on the rung r. Without loss of generality, we set Jp = cos θ and Jr = sin θ. For any modular theory, H has ...
... plaquette p. Explicit form of this operator in the edge basis is given in Ref. [19]. The second term is diagonal in the link (edge) basis since δl(r),0 is the projector onto the state 0, acting on the rung r. Without loss of generality, we set Jp = cos θ and Jr = sin θ. For any modular theory, H has ...
A summary on Solitons in Quantum field theory
... Finite energy solutions are crucial to understand the interplay between the topology of space-time and physical phenomena. It is very important to deepen our understanding of these kind of solutions because they might be useful in the discovery of new physical phenomena. The study of one (1+1)-dimen ...
... Finite energy solutions are crucial to understand the interplay between the topology of space-time and physical phenomena. It is very important to deepen our understanding of these kind of solutions because they might be useful in the discovery of new physical phenomena. The study of one (1+1)-dimen ...
Y-Bias and Angularity
... these interactions to be robust, it must not only accommodate phenomena which are known to occur and all rigorously documented phenomena, predict phenomena which are as-yet undiscovered, and allow for the inclusion of all rigorously observed, impeccably documented, accurately reported data derived f ...
... these interactions to be robust, it must not only accommodate phenomena which are known to occur and all rigorously documented phenomena, predict phenomena which are as-yet undiscovered, and allow for the inclusion of all rigorously observed, impeccably documented, accurately reported data derived f ...
Scale invariance
In physics, mathematics, statistics, and economics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor. The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry.In mathematics, scale invariance usually refers to an invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilatations. It is also possible for the probability distributions of random processes to display this kind of scale invariance or self-similarity.In classical field theory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically describe classical physical processes with no characteristic length scale.In quantum field theory, scale invariance has an interpretation in terms of particle physics. In a scale-invariant theory, the strength of particle interactions does not depend on the energy of the particles involved.In statistical mechanics, scale invariance is a feature of phase transitions. The key observation is that near a phase transition or critical point, fluctuations occur at all length scales, and thus one should look for an explicitly scale-invariant theory to describe the phenomena. Such theories are scale-invariant statistical field theories, and are formally very similar to scale-invariant quantum field theories.Universality is the observation that widely different microscopic systems can display the same behaviour at a phase transition. Thus phase transitions in many different systems may be described by the same underlying scale-invariant theory.In general, dimensionless quantities are scale invariant. The analogous concept in statistics are standardized moments, which are scale invariant statistics of a variable, while the unstandardized moments are not.