21,057 research outputs found
Calculation of Relaxation Spectra from Stress Relaxation Measurements
Application of stress on materials increases the energy of the system. After removal of stress,
macromolecules comprising the material shift towards equilibrium to minimize the total
energy of the system. This process occurs through molecular rearrangements or “relaxation”
during which macromolecules attain conformations of a lower energetic state. The time,
however, that is required for these rearrangements can be short or long depending on the
interactions between the macromolecular species that consist the material. When
rearrangements occur faster than the time of observation (experimental timescale) then
molecular motion is observed (flow) and the material is regarded as viscou
Direct and Inverse Computational Methods for Electromagnetic Scattering in Biological Diagnostics
Scattering theory has had a major roll in twentieth century mathematical
physics. Mathematical modeling and algorithms of direct,- and inverse
electromagnetic scattering formulation due to biological tissues are
investigated. The algorithms are used for a model based illustration technique
within the microwave range. A number of methods is given to solve the inverse
electromagnetic scattering problem in which the nonlinear and ill-posed nature
of the problem are acknowledged.Comment: 61 pages, 5 figure
Network estimation in State Space Model with L1-regularization constraint
Biological networks have arisen as an attractive paradigm of genomic science
ever since the introduction of large scale genomic technologies which carried
the promise of elucidating the relationship in functional genomics. Microarray
technologies coupled with appropriate mathematical or statistical models have
made it possible to identify dynamic regulatory networks or to measure time
course of the expression level of many genes simultaneously. However one of the
few limitations fall on the high-dimensional nature of such data coupled with
the fact that these gene expression data are known to include some hidden
process. In that regards, we are concerned with deriving a method for inferring
a sparse dynamic network in a high dimensional data setting. We assume that the
observations are noisy measurements of gene expression in the form of mRNAs,
whose dynamics can be described by some unknown or hidden process. We build an
input-dependent linear state space model from these hidden states and
demonstrate how an incorporated regularization constraint in an
Expectation-Maximization (EM) algorithm can be used to reverse engineer
transcriptional networks from gene expression profiling data. This corresponds
to estimating the model interaction parameters. The proposed method is
illustrated on time-course microarray data obtained from a well established
T-cell data. At the optimum tuning parameters we found genes TRAF5, JUND, CDK4,
CASP4, CD69, and C3X1 to have higher number of inwards directed connections and
FYB, CCNA2, AKT1 and CASP8 to be genes with higher number of outwards directed
connections. We recommend these genes to be object for further investigation.
Caspase 4 is also found to activate the expression of JunD which in turn
represses the cell cycle regulator CDC2.Comment: arXiv admin note: substantial text overlap with arXiv:1308.359
Anomalies in Ward Identities for Three-Point Functions Revisited
A general calculational method is applied to investigate symmetry relations
among divergent amplitudes in a free fermion model. A very traditional work on
this subject is revisited. A systematic study of one, two and three point
functions associated to scalar, pseudoscalar, vector and axial-vector densities
is performed. The divergent content of the amplitudes are left in terms of five
basic objects (external momentum independent). No specific assumptions about a
regulator is adopted in the calculations. All ambiguities and symmetry
violating terms are shown to be associated with only three combinations of the
basic divergent objects. Our final results can be mapped in the corresponding
Dimensional Regularization calculations (in cases where this technique could be
applied) or in those of Gertsein and Jackiw which we will show in detail. The
results emerging from our general approach allow us to extract, in a natural
way, a set of reasonable conditions (e.g. crucial for QED consistency) that
could lead us to obtain all Ward Identities satisfied. Consequently, we
conclude that the traditional approach used to justify the famous triangular
anomalies in perturbative calculations could be questionable. An alternative
point of view, dismissed of ambiguities, which lead to a correct description of
the associated phenomenology, is pointed out.Comment: 26 pages, Revtex, revised version, Refs. adde
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