scholarly journals Critical Brownian multiplicative chaos

2021 ◽  
Author(s):  
Antoine Jego
Keyword(s):  
A Priori ◽  
Stochastic Calculus ◽  
Local Times ◽  
Square Root ◽  
Borel Measures ◽  
Planar Brownian Motion ◽  
Critical Measure ◽  
The One ◽  
Non Gaussian ◽  
Universal Measure

AbstractBrownian multiplicative chaos measures, introduced in Jego (Ann Probab 48:1597–1643, 2020), Aïdékon et al. (Ann Probab 48(4):1785–1825, 2020) and Bass et al. (Ann Probab 22:566–625, 1994), are random Borel measures that can be formally defined by exponentiating $$\gamma $$ γ times the square root of the local times of planar Brownian motion. So far, only the subcritical measures where the parameter $$\gamma $$ γ is less than 2 were studied. This article considers the critical case where $$\gamma =2$$ γ = 2 , using three different approximation procedures which all lead to the same universal measure. On the one hand, we exponentiate the square root of the local times of small circles and show convergence in the Seneta–Heyde normalisation as well as in the derivative martingale normalisation. On the other hand, we construct the critical measure as a limit of subcritical measures. This is the first example of a non-Gaussian critical multiplicative chaos. We are inspired by methods coming from critical Gaussian multiplicative chaos, but there are essential differences, the main one being the lack of Gaussianity which prevents the use of Kahane’s inequality and hence a priori controls. Instead, a continuity lemma is proved which makes it possible to use tools from stochastic calculus as an effective substitute.

Consideration of the objections raised against the geometrical repre­sentation of the square roots of negative quantities

1833 ◽  
Vol 2 ◽  
pp. 371-372
Keyword(s):  
A Priori ◽  
The Other ◽  
Square Root ◽  
Square Roots ◽  
Negative Direction ◽  
The Third ◽  
Oblique Direction ◽  
Positive Quantity ◽  
Algebraic Operations ◽  
The One

It has always appeared a paradox in mathematics, that by em­ploying what are called imaginary or impossible quantities, and sub­jecting them to the same algebraic operations as those which are performed on quantities that are real and possible, the results ob­tained should always prove perfectly correct. The author inferring from this fact, that the operations of algebra are of a more compre­hensive nature than its definitions and fundamental principles, was led to inquire what extension might be given to these definitions and principles, so as to render them strictly applicable to quantities of every description, whether real or imaginary. This deficiency, he conceives, may be supplied by having recourse to certain geometrical considerations. By taking into account the directions as well as the lengths of lines drawn in a given plane, from a given point, the ad­dition of such lines may admit of being performed in the same man­ner as the composition of motions in dynamics; and four such lines may be regarded as proportional, both in length and direction, when they are proportionals in length, and, when also the fourth is inclined to the third at the same angle that the second is to the first. From this principle he deduces, that if a line drawn in any given di­rection be assumed as a positive quantity, and consequently its op­posite a negative quantity, a line drawn at right angles to the posi­tive or negative direction will be represented by the square root of a negative quantity ; and a line drawn in an oblique direction will be represented by the sum of two quantities, the one either positive or negative, and the other the square root of a negative quantity. On this subject, the author published a treatise in April 1828; since which period several objections have been made to this hypothesis. The purpose of the present paper is to answer these objections. The first of these is, that impossible roots should be considered merely as the indications of some impossible condition, which the pro­position that has given rise to them involves; and that they have in fact no real or absolute existence. To this it is replied by the author, that although such a statement may be true in some cases, it is by no means necessarily so in all; and that these quantities re­semble in this respect fractional and negative roots, which, whenever they are excluded by the nature of the question, are indeed signs of impossibility, but yet in other cases are admitted to be real and significant quantities. We have therefore no stronger reasons, à priori , for denying the real existence of what are called impossible roots, because they are in some cases the signs of impossibility, than we should have for refusing that character to fractional or negative roots on similar grounds.

scholarly journals Minkowski box from Yangian bootstrap

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Luke Corcoran ◽  
Florian Loebbert ◽  
Julian Miczajka ◽  
Matthias Staudacher
Keyword(s):  
Minkowski Space ◽  
Wigner Function ◽  
Functional Form ◽  
A Priori ◽  
Alternative Methods ◽  
Feynman Integrals ◽  
The One

Abstract We extend the recently developed Yangian bootstrap for Feynman integrals to Minkowski space, focusing on the case of the one-loop box integral. The space of Yangian invariants is spanned by the Bloch-Wigner function and its discontinuities. Using only input from symmetries, we constrain the functional form of the box integral in all 64 kinematic regions up to twelve (out of a priori 256) undetermined constants. These need to be fixed by other means. We do this explicitly, employing two alternative methods. This results in a novel compact formula for the box integral valid in all kinematic regions of Minkowski space.

scholarly journals Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
B. S. Merzlikin ◽  
K. V. Stepanyantz
Keyword(s):  
Effective Action ◽  
A Priori ◽  
Coupling Constant ◽  
Harmonic Superspace ◽  
Classical Action ◽  
Higher Derivative ◽  
Component Approach ◽  
Dimensionless Coupling ◽  
The One ◽  
Dimensionless Coupling Constant

Abstract We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6D, $$ \mathcal{N} $$ N = (1, 0) supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and $$ \mathcal{N} $$ N = (1, 0) supersymmetric way. We exploit the regularization by dimensional reduction, in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant β-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed a priori. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations.

Three Kantian Routes to the Synthetic A Priori

2021 ◽  
pp. 1-28
Author(s):  
Robert Audi
Keyword(s):  
A Priori ◽  
Pure Reason ◽  
Critique Of Pure Reason ◽  
Insufficient Attention ◽  
Synthetic A Priori ◽  
The One ◽  
Philosophical Importance

Abstract Kant influentially distinguished analytic from synthetic a priori propositions, and he took certain propositions in the latter category to be of immense philosophical importance. His distinction between the analytic and the synthetic has been accepted by many and attacked by others; but despite its importance, a number of discussions of it since at least W. V. Quine’s have paid insufficient attention to some of the passages in which Kant draws the distinction. This paper seeks to clarify what appear to be three distinct conceptions of the analytic (and implicitly of the synthetic) that are presented in Kant’s Critique of Pure Reason and in some other Kantian texts. The conceptions are important in themselves, and their differences are significant even if they are extensionally equivalent. The paper is also aimed at showing how the proposed understanding of these conceptions—and especially the one that has received insufficient attention from philosophers—may bear on how we should conceive the synthetic a priori, in and beyond Kant’s own writings.

WTLS-Bayes Filter-based Relative Pose Estimation for Space Non-cooperative Unknown Target Without a Priori Knowledge

2021 ◽  
Author(s):  
CHENGGUANG ZHU ◽  
zhongpai Gao ◽  
Jiankang Zhao ◽  
Haihui Long ◽  
Chuanqi Liu
Keyword(s):  
Pose Estimation ◽  
A Priori ◽  
Convergence Time ◽  
Estimation Accuracy ◽  
A Priori Knowledge ◽  
One Step ◽  
Relative Pose ◽  
The One ◽  
Negative Factors ◽  
Priori Knowledge

Abstract The relative pose estimation of a space noncooperative target is an attractive yet challenging task due to the complexity of the target background and illumination, and the lack of a priori knowledge. Unfortunately, these negative factors have a grave impact on the estimation accuracy and the robustness of filter algorithms. In response, this paper proposes a novel filter algorithm to estimate the relative pose to improve the robustness based on a stereovision system. First, to obtain a coarse relative pose, the weighted total least squares (WTLS) algorithm is adopted to estimate the relative pose based on several feature points. The resulting relative pose is fed into the subsequent filter scheme as observation quantities. Second, the classic Bayes filter is exploited to estimate the relative state except for moment-of-inertia ratios. Additionally, the one-step prediction results are used as feedback for WTLS initialization. The proposed algorithm successfully eliminates the dependency on continuous tracking of several fixed points. Finally, comparison experiments demonstrate that the proposed algorithm presents a better performance in terms of robustness and convergence time.

scholarly journals Tracking Algorithm of Multiple Pedestrians Based on Particle Filters in Video Sequences

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Hui Li ◽  
Yun Liu ◽  
Chuanxu Wang ◽  
Shujun Zhang ◽  
Xuehong Cui
Keyword(s):  
Particle Filters ◽  
A Priori ◽  
Texture Features ◽  
Tracking Algorithm ◽  
Video Sequences ◽  
Particle State ◽  
Pedestrian Tracking ◽  
Estimation Problems ◽  
Non Gaussian ◽  
Gaussian Estimation

Pedestrian tracking is a critical problem in the field of computer vision. Particle filters have been proven to be very useful in pedestrian tracking for nonlinear and non-Gaussian estimation problems. However, pedestrian tracking in complex environment is still facing many problems due to changes of pedestrian postures and scale, moving background, mutual occlusion, and presence of pedestrian. To surmount these difficulties, this paper presents tracking algorithm of multiple pedestrians based on particle filters in video sequences. The algorithm acquires confidence value of the object and the background through extracting a priori knowledge thus to achieve multipedestrian detection; it adopts color and texture features into particle filter to get better observation results and then automatically adjusts weight value of each feature according to current tracking environment. During the process of tracking, the algorithm processes severe occlusion condition to prevent drift and loss phenomena caused by object occlusion and associates detection results with particle state to propose discriminated method for object disappearance and emergence thus to achieve robust tracking of multiple pedestrians. Experimental verification and analysis in video sequences demonstrate that proposed algorithm improves the tracking performance and has better tracking results.

scholarly journals Word meaning access: The one-to-many mapping from form to meaning

2019 ◽  
Author(s):  
Jennifer M Rodd
Keyword(s):  
A Priori ◽  
Word Meaning ◽  
Semantic Features ◽  
Contextual Cues ◽  
Word Meanings ◽  
Wide Range ◽  
Core Feature ◽  
Distributional Information ◽  
Current Context ◽  
The One

This chapter focuses on the process by which stored knowledge about a word’s form (orthographic or phonological) maps onto stored knowledge about its meaning. This mapping is made challenging by the ambiguity that is ubiquitous in natural language: most familiar words can refer to multiple different concepts. This one-to-many mapping from form to meaning within the lexicon is a core feature of word-meaning access. Fluent, accurate word-meaning access requires that comprehenders integrate multiple cues in order to determine which of a word’s possible semantic features are relevant in the current context. Specifically, word-meaning access is guided by (i) distributional information about the a priori relative likelihoods of different word meanings and (ii) a wide range of contextual cues that indicate which meanings are most likely in the current context.

scholarly journals Testing Economic Theory

2018 ◽  
pp. 303-313
Author(s):  
Christopher P. Guzelian
Keyword(s):  
A Priori ◽  
Number System ◽  
Physical Reality ◽  
Economic Research ◽  
Economic Knowledge ◽  
Fractional Reserve Banking ◽  
Physical Universe ◽  
And Mathematics ◽  
Reserve Banking ◽  
The One

Two years ago, Bob Mulligan and I empirically tested whether the Bank of Amsterdam, a prototypical central bank, had caused a boom-bust cycle in the Amsterdam commodities markets in the 1780s owing to the bank’s sudden initiation of low-fractional-re-serve banking (Guzelian & Mulligan 2015).1 Widespread criticism came quickly after we presented our data findings at that year’s Austrian Economic Research Conference. Walter Block representa-tively responded: «as an Austrian, I maintain you cannot «test» apodictic theories, you can only illustrate them».2 Non-Austrian, so-called «empirical» economists typically have no problem with data-driven, inductive research. But Austrians have always objected strenuously on ontological and epistemolog-ical grounds that such studies do not produce real knowledge (Mises 1998, 113-115; Mises 2007). Camps of economists are talking past each other in respective uses of the words «testing» and «eco-nomic theory». There is a vital distinction between «testing» (1) an economic proposition, praxeologically derived, and (2) the rele-vance of an economic proposition, praxeologically derived. The former is nonsensical; the latter may be necessary to acquire eco-nomic theory and knowledge. Clearing up this confusion is this note’s goal. Rothbard (1951) represents praxeology as the indispensible method for gaining economic knowledge. Starting with a Aristote-lian/Misesian axiom «humans act» or a Hayekian axiom of «humans think», a voluminous collection of logico-deductive eco-nomic propositions («theorems») follows, including theorems as sophisticated and perhaps unintuitive as the one Mulligan and I examined: low-fractional-reserve banking causes economic cycles. There is an ontological and epistemological analog between Austrian praxeology and mathematics. Much like praxeology, we «know» mathematics to be «true» because it is axiomatic and deductive. By starting with Peano Axioms, mathematicians are able by a long process of creative deduction, to establish the real number system, or that for the equation an + bn = cn, there are no integers a, b, c that satisfy the equation for any integer value of n greater than 2 (Fermat’s Last Theorem). But what do mathematicians mean when they then say they have mathematical knowledge, or that they have proven some-thing «true»? Is there an infinite set of rational numbers floating somewhere in the physical universe? Naturally no. Mathemati-cians mean that they have discovered an apodictic truth — some-thing unchangeably true without reference to physical reality because that truth is a priori.

scholarly journals Papernomics. Sciences as Games and Means of Censorship / Papernomics. Ciencias y juegos como medios de censura

2017 ◽  
pp. 110
Author(s):  
José Carlos Bermejo
Keyword(s):  
A Priori ◽  
Scientific Field ◽  
Hierarchical System ◽  
Scientific Journals ◽  
Double Blind ◽  
The One

The journals are basically the only channel through the scientists can make the result of their research known to their colleagues. Scientific journals select the information they publish and guarantee its quality by means of a double blind procedure of censorship by peers. If on the one hand this procedure seems logical as a method for including a study within a consolidated scientific field, it is also true that it can function as a mechanism for censorship. The idea that the works not included in a standard publication lack a priori of practically any value is the basis of the career of academic scholars. Starting with this principle, a hierarchical system of scientific ranking has been built among researchers. The basis of his scientific curriculum is the metric of vanity.Key WordsScientific journals, curriculum, censorshipResumenLas revistas son básicamente el único canal a través del cual los científicos pueden dar a conocer el resultado de su investigación a sus colegas. Las revistas científicas seleccionan la información que publican y garantizan su calidad por medio de un procedimiento de censura por pares de doble ciego. Si, por un lado, este procedimiento parece lógico como método para incluir un estudio en un campo científico consolidado, también es verdad que puede funcionar como mecanismo de censura. La idea de que los trabajos no incluidos en una publicación estándar carecen a priori de prácticamente ningún valor es la base de la carrera académica. Partiendo de este principio se ha construido entre los investigadores un sistema jerárquico de clasificación. La base de este currículum científico es la métrica de la vanidad.Palabras claveRevistas científicas, currículum, censura.

Sign in / Sign up

Export Citation Format

Share Document