Universal Constant Rebalanced Portfolios with Switching

This note provides a neat and enjoyable expansion and application of the magnificent Ordentlich-Cover theory of “universal portfolios”. I generalize Cover’s benchmark of the best constant-rebalanced portfolio (or 1-linear trading strategy) in hindsight by considering the best bilinear trading strategy determined in hindsight for the realized sequence of asset prices. A bilinear trading strategy is a mini two-period active strategy whose final capital growth factor is linear separately in each period’s gross return vector for the asset market. I apply Thomas Cover’s ingenious performance-weighted averaging technique to construct a universal bilinear portfolio that is guaranteed (uniformly for all possible market behavior) to compound its money at the same asymptotic rate as the best bilinear trading strategy in hindsight. Thus, the universal bilinear portfolio asymptotically dominates the original (1-linear) universal portfolio in the same technical sense that Cover’s universal portfolios asymptotically dominate all constant-rebalanced portfolios and all buy-and-hold strategies. In fact, like so many Russian dolls, one can get carried away and use these ideas to construct an endless hierarchy of ever more dominant H-linear universal portfolios.

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A universal constant in temporal segmentation of human speech

The Science of Nature ◽

10.1007/bf01139205 ◽

1992 ◽

Vol 79 (10) ◽

pp. 479-480 ◽

Cited By ~ 33

Author(s):

M. Vollrath ◽

J. Kazenwadel ◽

H.-P. Kr�ger

Keyword(s):

Universal Constant ◽

Temporal Segmentation ◽

Human Speech

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The Effect of Froude Number on Entrainment in Two-Dimensional Line Plumes

Journal of Fluids Engineering ◽

10.1115/1.3240818 ◽

1981 ◽

Vol 103 (3) ◽

pp. 471-477 ◽

Cited By ~ 3

Author(s):

W. F. Phillips

Keyword(s):

Froude Number ◽

Large Distance ◽

Universal Constant ◽

Temperature Profiles ◽

Two Dimensional ◽

Development Length ◽

High Discharge ◽

Entrainment Coefficient ◽

Theoretical Results

Theoretical results are presented which predict the entrainment coefficient in a forced plume as a function of the local Froude number. The model does not require any external specification of the velocity and temperature profiles. The Froude number for any plume, in a motionless isothermal ambient, approaches a universal constant, at a large distance above the source. However, it is shown here that the development length for the Froude number, in plumes with high discharge Froude number, is of the order of a few hundred times the discharge width.

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Low degree connectivity of ad-hoc networks via percolation

Advances in Applied Probability ◽

10.1017/s0001867800004195 ◽

2010 ◽

Vol 42 (02) ◽

pp. 559-576

Author(s):

Emilio De Santis ◽

Fabrizio Grandoni ◽

Alessandro Panconesi

Keyword(s):

Ad Hoc Networks ◽

Maximum Degree ◽

High Probability ◽

Ad Hoc ◽

Classical Problem ◽

Universal Constant ◽

Giant Component ◽

Second Phase ◽

Connected Network ◽

Hoc Networks

Consider the following classical problem in ad-hoc networks. Suppose that n devices are distributed uniformly at random in a given region. Each device is allowed to choose its own transmission radius, and two devices can communicate if and only if they are within the transmission radius of each other. The aim is to (quickly) establish a connected network of low average and maximum degree. In this paper we present the first efficient distributed protocols that, in poly-logarithmically many rounds and with high probability, set up a connected network with O(1) average degree and O(log n) maximum degree. Our algorithms are based on the following result, which is a nontrivial consequence of classical percolation theory. Suppose that each device sets up its transmission radius in order to reach the K closest devices. There exists a universal constant K (independent of n) such that, with high probability, there will be a unique giant component (i.e. a connected component of size Θ(n)). Furthermore, all remaining components will be of size O(log2 n). This leads to an efficient distributed probabilistic test for membership in the giant component, which can be used in a second phase to achieve full connectivity.

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Bekenstein‐Hawking black hole entropy, Hawking temperature, and the Unruh effect: Insight from the laws of thermodynamics

Physics Essays ◽

10.4006/0836-1398-33.2.143 ◽

2020 ◽

Vol 33 (2) ◽

pp. 143-148

Author(s):

Stephen J. Crothers ◽

Pierre-Marie Robitaille

Keyword(s):

Black Hole ◽

Scientific Inquiry ◽

Black Hole Entropy ◽

Universal Constant ◽

Unruh Effect ◽

Physical Sciences ◽

Laws Of Thermodynamics ◽

Large Systems ◽

Definition Of ◽

Schwarzschild Radius

The laws of thermodynamics play a central role in scientific inquiry, guiding physics as to the validity of hypothesized claims. It is for this reason that quantities of thermodynamic relevance must retain their character wherever they appear. Temperature, for example, must always be intensive, a requirement set by the 0th law. Otherwise, the very definition of temperature is compromised. Similarly, entropy must remain extensive, in order to conform to the second law. These rules must be observed whenever a system is large enough to be characterized by macroscopic quantities, such as volume or area. This explains why ensembles comprised of just a few atoms cannot be considered thermodynamic systems. In this regard, black holes are hypothesized to be large systems, characterized by the Schwarzschild radius (rs = 2GM/c 2) and its associated “horizon” area (A = 4πrs 2), where G, M, and c represent the universal constant of gravitation, the mass of the black hole, and the speed of light in vacuum, respectively. It can be readily demonstrated that Bekenstein‐Hawking black hole entropy is nonextensive, while the Hawking and the Unruh temperatures are nonintensive. As a result, the associated equations violate the laws of thermodynamics and can hold no place in the physical sciences.

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Globular Clusters as Extragalactic Distance Indicators: Maximum Likelihood Methods

Symposium - International Astronomical Union ◽

10.1017/s0074180900043321 ◽

1988 ◽

Vol 126 ◽

pp. 617-618

Author(s):

David A. Hanes ◽

Donna G. Whittaker

Keyword(s):

Maximum Likelihood ◽

Globular Cluster ◽

Globular Clusters ◽

Likelihood Estimation ◽

Absolute Magnitude ◽

Universal Constant ◽

Precise Determination ◽

Good Precision ◽

Distance Information ◽

Distance Indicators

We have explored the use of maximum likelihood estimation techniques in the use of globular cluster luminosity functions (LFs) as distance indicators. In particular, we have tested size-of-sample effects through the analysis of Monte Carlo simulations of LFs drawn from an assumed universal population like that characterizing the globular clusters in the Local Group. Our working assumption, following others before us, is that the underlying LF is adequately well described by a Gaussian normal in a number vs. absolute magnitude representation.For typically observable sample sizes in studies which are limited to the bright half of the LF, statistical limitations preclude a precise determination of the attributes which fully describe the LF, even in the absence of field object contamination. In particular, the intrinsic dispersion (the shape parameter of the LF) must be taken to be a universal constant, independent of galaxy type; only then may the turnover magnitude (which contains the distance information) be derived with good precision. Some data exist for nearby galaxies (including ellipticals) which permit an assessment of the universality of the intrinsic dispersion: they are not inconsistent with the hypothesis. However, it will be important to test this point in future as more data are secured.Real globular clusters in remote galaxies are unresolved, and the samples are contaminated with foreground field stars and remote background objects. This contamination necessitates corrections which are statistical in nature, applicable to binned LFs. Through numerical simulations, we have tested the limitations imposed by realistic numbers of field objects in globular cluster LFs in remote galaxies, testing for systematic biases and assessing the attainable precision in derived distance as a function of the sample size and the limiting magnitude.

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LA STRUTTURA DEL TEMPO FISICO *

Nuncius ◽

10.1163/182539178x00349 ◽

1988 ◽

Vol 3 (2) ◽

pp. 101-147 ◽

Cited By ~ 2

Author(s):

GIUSEPPE BRUZZANITI

Keyword(s):

Quantum Electrodynamics ◽

Universal Constant ◽

Physical Structure ◽

Quantum Fields ◽

Scientific Theories ◽

Typical Problem ◽

The Third ◽

Space And Time ◽

Historical Dynamics

Abstract<title> SUMMARY </title>The foundamental problems related to the physical structure of space and time are today motivated by problems that arise from other scientific theories, for instance: relativistic theories, quantum electrodynamics, elementary particles.One of principal purposes of this historical-critical paper is to examine a typical problem related to the structure of time i.e. its continuity. This problem arises from all attempts to discretize space and time through the introduction of a new universal constant besides h and c.The three sections of this paper reflect the different problems considerated: in the first are ana.yzed same attempts, arisen in the quantum fields theory between 1940 and 1960, directed to the introduction of a universal constant with the dimension of a lenght. In the second, the historical dynamics of problems that conducted to the introduction of a universal constant with the dimension of a time is examinated. In the third, finally, the most important epistemological implications of this problems are considerated.

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