4,208 research outputs found
Quantized chaotic dynamics and non-commutative KS entropy
We study the quantization of two examples of classically chaotic dynamics,
the Anosov dynamics of "cat maps" on a two dimensional torus, and the dynamics
of baker's maps. Each of these dynamics is implemented as a discrete group of
automorphisms of a von Neumann algebra of functions on a quantized torus. We
compute the non- commutative generalization of the Kolmogorov-Sinai entropy,
namely the Connes-Stormer entropy, of the generator of this group, and find
that its value is equal to the classical value. This can be interpreted as a
sign of persistence of chaotic behavior in a dynamical system under
quantization.Comment: a number of misprints corrected, new references and a new section
added. 21 pages, plain Te
Matrix Cartan superdomains, super Toeplitz operators, and quantization
We present a general theory of non-perturbative quantization of a class of
hermitian symmetric supermanifolds. The quantization scheme is based on the
notion of a super Toeplitz operator on a suitable Z_2 -graded Hilbert space of
superholomorphic functions. The quantized supermanifold arises as the C^*
-algebra generated by all such operators. We prove that our quantization
framework reproduces the invariant super Poisson structure on the classical
supermanifold as Planck's constant tends to zero.Comment: 52
Supersymmetry and Fredholm modules over quantized spaces
The purpose of this paper is to apply the framework of non- commutative
differential geometry to quantum deformations of a class of Kahler manifolds.
For the examples of the Cartan domains of type I and flat space, we construct
Fredholm modules over the quantized manifolds using the supercharges which
arise in the quantization of supersymmetric generalizations of the manifolds.
We compute the explicit formula for the Chern character on generators of the
Toeplitz C^* -algebra.Comment: 24
Parkinson's Law Quantified: Three Investigations on Bureaucratic Inefficiency
We formulate three famous, descriptive essays of C.N. Parkinson on
bureaucratic inefficiency in a quantifiable and dynamical socio-physical
framework. In the first model we show how the use of recent opinion formation
models for small groups can be used to understand Parkinson's observation that
decision making bodies such as cabinets or boards become highly inefficient
once their size exceeds a critical 'Coefficient of Inefficiency', typically
around 20. A second observation of Parkinson - which is sometimes referred to
as Parkinson's Law - is that the growth of bureaucratic or administrative
bodies usually goes hand in hand with a drastic decrease of its overall
efficiency. In our second model we view a bureaucratic body as a system of a
flow of workers, which enter, become promoted to various internal levels within
the system over time, and leave the system after having served for a certain
time. Promotion usually is associated with an increase of subordinates. Within
the proposed model it becomes possible to work out the phase diagram under
which conditions bureaucratic growth can be confined. In our last model we
assign individual efficiency curves to workers throughout their life in
administration, and compute the optimum time to send them to old age pension,
in order to ensure a maximum of efficiency within the body - in Parkinson's
words we compute the 'Pension Point'.Comment: 15 pages, 5 figure
Classical limit of the d-bar operators on quantum domains
We study one parameter families , of non-commutative analogs of
the d-bar operator D_0 = \frac{\d}{\d\bar{z}} on disks and annuli in complex
plane and show that, under suitable conditions, they converge in the classical
limit to their commutative counterpart. More precisely, we endow the
corresponding families of Hilbert spaces with the structures of continuous
fields over the interval and we show that the inverses of the operators
subject to APS boundary conditions form morphisms of those continuous
fields of Hilbert spaces
Disentangling genetic and environmental risk factors for individual diseases from multiplex comorbidity networks
Most disorders are caused by a combination of multiple genetic and/or environmental factors. If two diseases are caused by the same molecular mechanism, they tend to co-occur in patients. Here we provide a quantitative method to disentangle how much genetic or environmental risk factors contribute to the pathogenesis of 358 individual diseases, respectively. We pool data on genetic, pathway-based, and toxicogenomic disease-causing mechanisms with disease co-occurrence data obtained from almost two million patients. From this data we construct a multiplex network where nodes represent disorders that are connected by links that either represent phenotypic comorbidity of the patients or the involvement of a certain molecular mechanism. From the similarity of phenotypic and mechanism-based networks for each disorder we derive measure that allows us to quantify the relative importance of various molecular mechanisms for a given disease. We find that most diseases are dominated by genetic risk factors, while environmental influences prevail for disorders such as depressions, cancers, or dermatitis. Almost never we find that more than one type of mechanisms is involved in the pathogenesis of diseases
- …