70,736 research outputs found
Natural process – Natural selection
Life is supported by a myriad of chemical reactions. To describe the overall process we have formulated entropy for an open system undergoing chemical reactions. The entropy formula allows us to recognize various ways for the system to move towards more probable states. These correspond to the basic processes of life i.e. proliferation, differentiation, expansion, energy intake, adaptation and maturation. We propose that the rate of entropy production by various mechanisms is the fitness criterion of natural selection. The quest for more probable states results in organization of matter in functional hierarchies
Modularity and Delayed Product Differentiation in Assemble-to-order Systems: Analysis and Extensions from a Complexity Perspective
The paper assumes a product design around modular architectures and discusses the suitability of the principle of delayed product differentiation in assemble-to-order environments. We demonstrate that this principle does not enable one to make optimal decisions concerning how variety should proliferate in the assembly process. Therefore, we propose to complement this principle in that we additionally consider the variety induced complexity throughout the assembly process. The weighted Shannon entropy is proposed as a measure for the evaluation of this complexity. Our results show that the delayed product differentiation principle is reliable when the selection probabilities of module variants at each assembly stage are equal and the pace at which value is added in the whole assembly process is constant. Otherwise, the proposed measure provides different results. Furthermore, the entropy measure provides interesting clues concerning eventual reversals of assembly sequences and supports decisions regarding what modules in an assembly stage could be substituted by a common module.modularity; complexity; ATO; delayed product differentiation
Hessian and concavity of mutual information, differential entropy, and entropy power in linear vector Gaussian channels
Within the framework of linear vector Gaussian channels with arbitrary
signaling, closed-form expressions for the Jacobian of the minimum mean square
error and Fisher information matrices with respect to arbitrary parameters of
the system are calculated in this paper. Capitalizing on prior research where
the minimum mean square error and Fisher information matrices were linked to
information-theoretic quantities through differentiation, closed-form
expressions for the Hessian of the mutual information and the differential
entropy are derived. These expressions are then used to assess the concavity
properties of mutual information and differential entropy under different
channel conditions and also to derive a multivariate version of the entropy
power inequality due to Costa.Comment: 33 pages, 2 figures. A shorter version of this paper is to appear in
IEEE Transactions on Information Theor
Entanglement Availability Differentiation Service for the Quantum Internet
A fundamental concept of the quantum Internet is quantum entanglement. In a
quantum Internet scenario where the legal users of the network have different
priority levels or where a differentiation of entanglement availability between
the users is a necessity, an entanglement availability service is essential.
Here we define the entanglement availability differentiation (EAD) service for
the quantum Internet. In the proposed EAD framework, the differentiation is
either made in the amount of entanglement with respect to the relative entropy
of entanglement associated with the legal users, or in the time domain with
respect to the amount of time that is required to establish a maximally
entangled system between the legal parties. The framework provides an efficient
and easily-implementable solution for the differentiation of entanglement
availability in experimental quantum networking scenarios.Comment: 18 pages, Journal-ref: Scientific Report
Single-cell entropy for accurate estimation of differentiation potency from a cell's transcriptome
The ability to quantify differentiation potential of single cells is a task of critical importance. Here we demonstrate, using over 7,000 single-cell RNA-Seq profiles, that differentiation potency of a single cell can be approximated by computing the signalling promiscuity, or entropy, of a cell's transcriptome in the context of an interaction network, without the need for feature selection. We show that signalling entropy provides a more accurate and robust potency estimate than other entropy-based measures, driven in part by a subtle positive correlation between the transcriptome and connectome. Signalling entropy identifies known cell subpopulations of varying potency and drug resistant cancer stem-cell phenotypes, including those derived from circulating tumour cells. It further reveals that expression heterogeneity within single-cell populations is regulated. In summary, signalling entropy allows in silico estimation of the differentiation potency and plasticity of single cells and bulk samples, providing a means to identify normal and cancer stem-cell phenotypes
Differentiation and Replication of Spots in a Reaction Diffusion System with Many Chemicals
The replication and differentiation of spots in reaction diffusion equations
are studied by extending the Gray-Scott model with self-replicating spots to
include many degrees of freedom needed to model systems with many chemicals. By
examining many possible reaction networks, the behavior of this model is
categorized into three types: replication of homogeneous fixed spots,
replication of oscillatory spots, and differentiation from `m ultipotent
spots'. These multipotent spots either replicate or differentiate into other
types of spots with different fixed-point dynamics, and as a result, an
inhomogeneous pattern of spots is formed. This differentiation process of spots
is analyzed in terms of the loss of chemical diversity and decrease of the
local Kolmogorov-Sinai entropy. The relevance of the results to developmental
cell biology and stem cells is also discussed.Comment: 8 pages, 12 figures, Submitted to EP
State entropy and differentiation phenomenon
In the formalism of quantum theory, a state of a system is represented by a density operator . Mathematically, a density operator can be decomposed into a weighted sum of (projection) operators representing an ensemble of pure states (a state distribution), but such decomposition is not unique. Various pure states distributions are mathematically described by the same density operator. These distributions are categorized into classical ones obtained from the Schatten decomposition and other, non-classical, ones. In this paper, we define the quantity called the state entropy . It can be considered as a generalization of the von Neumann entropy evaluating the diversity of states constituting a distribution. Further, we apply the state entropy to the analysis of non-classical states created at the intermediate stages in the process of quantum measurement . To do this, we employ the model of differentiation , where a system experiences step by step state transitions under the influence of environmental factors. This approach can be used for modeling various natural and mental phenomena: cell’s differentiation, evolution of biological populations, and decision makin
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