17,851 research outputs found
Veitch diagram plotter simplifies Boolean functions
This device for simplifying the plotting of a Veitch diagram consists of several overlays for blocking out the unwanted squares. This method of plotting the various input combinations to a computer is used in conjunction with the Boolean functions
Stationary Points of Scalar Fields Coupled to Gravity
We investigate the dynamics of gravity coupled to a scalar field using a
non-canonical form of the kinetic term. It is shown that its singular point
represents an attractor for classical solutions and the stationary value of the
field may occur distant from the minimum of the potential. In this paper
properties of universes with such stationary states are considered. We reveal
that such state can be responsible for modern dark energy density.Comment: H. Kroger, invited talk, FFP6, Udine (2004), revised version with
corrected author lis
Open Questions in Classical Gravity
We discuss some outstanding open questions regarding the validity and
uniqueness of the standard second order Newton-Einstein classical gravitational
theory. On the observational side we discuss the degree to which the realm of
validity of Newton's Law of Gravity can actually be extended to distances much
larger than the solar system distance scales on which the law was originally
established. On the theoretical side we identify some commonly accepted but
actually still open to question assumptions which go into the formulating of
the standard second order Einstein theory in the first place. In particular, we
show that while the familiar second order Poisson gravitational equation (and
accordingly its second order covariant Einstein generalization) may be
sufficient to yield Newton's Law of Gravity they are not in fact necessary. The
standard theory thus still awaits the identification of some principle which
would then make it necessary too. We show that current observational
information does not exclusively mandate the standard theory, and that the
conformal invariant fourth order theory of gravity considered recently by
Mannheim and Kazanas is also able to meet the constraints of data, and in fact
to do so without the need for any so far unobserved non-luminous or dark
matter.Comment: UCONN-93-1, plain TeX format, 22 pages (plus 7 figures - send
requests to [email protected]). To appear in a special issue of
Foundations of Physics honoring Professor Fritz Rohrlich on the occasion of
his retirement, L. P. Horwitz and A. van der Merwe Editors, Plenum Publishing
Company, N.Y., Fall 199
Self-stabilization of extra dimensions
We show that the problem of stabilization of extra dimensions in Kaluza-Klein
type cosmology may be solved in a theory of gravity involving high-order
curvature invariants. The method suggested (employing a slow-change
approximation) can work with rather a general form of the gravitational action.
As examples, we consider pure gravity with Lagrangians quadratic and cubic in
the scalar curvature and some more complex ones in a simple Kaluza-Klein
framework. After a transition to the 4D Einstein conformal frame, this results
in effective scalar field theories with certain effective potentials, which in
many cases possess positive minima providing stable small-size extra
dimensions. Estimates made in the original (Jordan) conformal frame show that
the problem of a small value of the cosmological constant in the present
Universe is softened in this framework but is not solved completely.}Comment: 10 pages, 4 figures, revtex4. Version with additions and corrections,
accepted at Phys. Rev.
Multidimensional world, inflation and modern acceleration
Starting from pure multidimensional gravity with curvature-nonlinear terms
but no matter fields in the initial action, we obtain a cosmological model with
two effective scalar fields related to the size of two extra factor spaces. The
model includes both an early inflationary stage and that of modern accelerated
expansion and satisfies the observational data. There are no small parameters;
the effective inflaton mass depends on the initial conditions which explain its
small value as compared to the Planck mass. At the modern stage, the size of
extra dimensions slowly increases, therefore this model predicts drastic
changes in the physical laws of our Universe in the remote future.Comment: 7 two-column revtex pages, 2 figure
Spatial Degrees of Freedom in Everett Quantum Mechanics
Stapp claims that, when spatial degrees of freedom are taken into account,
Everett quantum mechanics is ambiguous due to a "core basis problem." To
examine an aspect of this claim I generalize the ideal measurement model to
include translational degrees of freedom for both the measured system and the
measuring apparatus. Analysis of this generalized model using the Everett
interpretation in the Heisenberg picture shows that it makes unambiguous
predictions for the possible results of measurements and their respective
probabilities. The presence of translational degrees of freedom for the
measuring apparatus affects the probabilities of measurement outcomes in the
same way that a mixed state for the measured system would. Examination of a
measurement scenario involving several observers illustrates the consistency of
the model with perceived spatial localization of the measuring apparatus.Comment: 34 pp., no figs. Introduction, discussion revised. Material
tangential to main point remove
Differentially Private Model Selection with Penalized and Constrained Likelihood
In statistical disclosure control, the goal of data analysis is twofold: The
released information must provide accurate and useful statistics about the
underlying population of interest, while minimizing the potential for an
individual record to be identified. In recent years, the notion of differential
privacy has received much attention in theoretical computer science, machine
learning, and statistics. It provides a rigorous and strong notion of
protection for individuals' sensitive information. A fundamental question is
how to incorporate differential privacy into traditional statistical inference
procedures. In this paper we study model selection in multivariate linear
regression under the constraint of differential privacy. We show that model
selection procedures based on penalized least squares or likelihood can be made
differentially private by a combination of regularization and randomization,
and propose two algorithms to do so. We show that our private procedures are
consistent under essentially the same conditions as the corresponding
non-private procedures. We also find that under differential privacy, the
procedure becomes more sensitive to the tuning parameters. We illustrate and
evaluate our method using simulation studies and two real data examples
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