5,728 research outputs found
Intra-tumour signalling entropy determines clinical outcome in breast and lung cancer.
The cancer stem cell hypothesis, that a small population of tumour cells are responsible for tumorigenesis and cancer progression, is becoming widely accepted and recent evidence has suggested a prognostic and predictive role for such cells. Intra-tumour heterogeneity, the diversity of the cancer cell population within the tumour of an individual patient, is related to cancer stem cells and is also considered a potential prognostic indicator in oncology. The measurement of cancer stem cell abundance and intra-tumour heterogeneity in a clinically relevant manner however, currently presents a challenge. Here we propose signalling entropy, a measure of signalling pathway promiscuity derived from a sample's genome-wide gene expression profile, as an estimate of the stemness of a tumour sample. By considering over 500 mixtures of diverse cellular expression profiles, we reveal that signalling entropy also associates with intra-tumour heterogeneity. By analysing 3668 breast cancer and 1692 lung adenocarcinoma samples, we further demonstrate that signalling entropy correlates negatively with survival, outperforming leading clinical gene expression based prognostic tools. Signalling entropy is found to be a general prognostic measure, valid in different breast cancer clinical subgroups, as well as within stage I lung adenocarcinoma. We find that its prognostic power is driven by genes involved in cancer stem cells and treatment resistance. In summary, by approximating both stemness and intra-tumour heterogeneity, signalling entropy provides a powerful prognostic measure across different epithelial cancers
A matrix representation of graphs and its spectrum as a graph invariant
We use the line digraph construction to associate an orthogonal matrix with
each graph. From this orthogonal matrix, we derive two further matrices. The
spectrum of each of these three matrices is considered as a graph invariant.
For the first two cases, we compute the spectrum explicitly and show that it is
determined by the spectrum of the adjacency matrix of the original graph. We
then show by computation that the isomorphism classes of many known families of
strongly regular graphs (up to 64 vertices) are characterized by the spectrum
of this matrix. We conjecture that this is always the case for strongly regular
graphs and we show that the conjecture is not valid for general graphs. We
verify that the smallest regular graphs which are not distinguished with our
method are on 14 vertices.Comment: 14 page
Lorentz Beams
A new kind of tridimensional scalar optical beams is introduced. These beams
are called Lorentz beams because the form of their transverse pattern in the
source plane is the product of two independent Lorentz functions. Closed-form
expression of free-space propagation under paraxial limit is derived and pseudo
non-diffracting features pointed out. Moreover, as the slowly varying part of
these fields fulfils the scalar paraxial wave equation, it follows that there
exist also Lorentz-Gauss beams, i.e. beams obtained by multipying the original
Lorentz beam to a Gaussian apodization function. Although the existence of
Lorentz-Gauss beams can be shown by using two different and independent ways
obtained recently from Kiselev [Opt. Spectr. 96, 4 (2004)] and Gutierrez-Vega
et al. [JOSA A 22, 289-298, (2005)], here we have followed a third different
approach, which makes use of Lie's group theory, and which possesses the merit
to put into evidence the symmetries present in paraxial Optics.Comment: 11 pages, 1 figure, submitted to Journal of Optics
Mass Transfer Mechanisms during Dehydration of Vegetable Food: Traditional and Innovative Approaches
Lettera di accettazione in dat
Longitudinal LASSO: Jointly Learning Features and Temporal Contingency for Outcome Prediction
Longitudinal analysis is important in many disciplines, such as the study of
behavioral transitions in social science. Only very recently, feature selection
has drawn adequate attention in the context of longitudinal modeling. Standard
techniques, such as generalized estimating equations, have been modified to
select features by imposing sparsity-inducing regularizers. However, they do
not explicitly model how a dependent variable relies on features measured at
proximal time points. Recent graphical Granger modeling can select features in
lagged time points but ignores the temporal correlations within an individual's
repeated measurements. We propose an approach to automatically and
simultaneously determine both the relevant features and the relevant temporal
points that impact the current outcome of the dependent variable. Meanwhile,
the proposed model takes into account the non-{\em i.i.d} nature of the data by
estimating the within-individual correlations. This approach decomposes model
parameters into a summation of two components and imposes separate block-wise
LASSO penalties to each component when building a linear model in terms of the
past measurements of features. One component is used to select features
whereas the other is used to select temporal contingent points. An accelerated
gradient descent algorithm is developed to efficiently solve the related
optimization problem with detailed convergence analysis and asymptotic
analysis. Computational results on both synthetic and real world problems
demonstrate the superior performance of the proposed approach over existing
techniques.Comment: Proceedings of the 21th ACM SIGKDD International Conference on
Knowledge Discovery and Data Mining. ACM, 201
Pretty good state transfer in qubit chains-The Heisenberg Hamiltonian
Pretty good state transfer in networks of qubits occurs when a continuous-time quantum walk allows the transmission of a qubit state from one node of the network to another, with fidelity arbitrarily close to 1. We prove that in a Heisenberg chain with n qubits, there is pretty good state transfer between the nodes at the jth and (n − j + 1)th positions if n is a power of 2. Moreover, this condition is also necessary for j = 1. We obtain this result by applying a theorem due to Kronecker about Diophantine approximations, together with techniques from algebraic graph theory
Universal quantum computation with unlabeled qubits
We show that an n-th root of the Walsh-Hadamard transform (obtained from the
Hadamard gate and a cyclic permutation of the qubits), together with two
diagonal matrices, namely a local qubit-flip (for a fixed but arbitrary qubit)
and a non-local phase-flip (for a fixed but arbitrary coefficient), can do
universal quantum computation on n qubits. A quantum computation, making use of
n qubits and based on these operations, is then a word of variable length, but
whose letters are always taken from an alphabet of cardinality three.
Therefore, in contrast with other universal sets, no choice of qubit lines is
needed for the application of the operations described here. A quantum
algorithm based on this set can be interpreted as a discrete diffusion of a
quantum particle on a de Bruijn graph, corrected on-the-fly by auxiliary
modifications of the phases associated to the arcs.Comment: 6 page
Some families of density matrices for which separability is easily tested
We reconsider density matrices of graphs as defined in [quant-ph/0406165].
The density matrix of a graph is the combinatorial laplacian of the graph
normalized to have unit trace. We describe a simple combinatorial condition
(the "degree condition") to test separability of density matrices of graphs.
The condition is directly related to the PPT-criterion. We prove that the
degree condition is necessary for separability and we conjecture that it is
also sufficient. We prove special cases of the conjecture involving nearest
point graphs and perfect matchings. We observe that the degree condition
appears to have value beyond density matrices of graphs. In fact, we point out
that circulant density matrices and other matrices constructed from groups
always satisfy the condition and indeed are separable with respect to any
split. The paper isolates a number of problems and delineates further
generalizations.Comment: 14 pages, 4 figure
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