120 research outputs found
Brownian motion meets Riemann curvature
The general covariance of the diffusion equation is exploited in order to
explore the curvature effects appearing on brownian motion over a d-dimensional
curved manifold. We use the local frame defined by the so called Riemann normal
coordinates to derive a general formula for the mean-square geodesic distance
(MSD) at the short-time regime. This formula is written in terms of
invariants that depend on the Riemann curvature tensor. We study the
n-dimensional sphere case to validate these results. We also show that the
diffusion for positive constant curvature is slower than the diffusion in a
plane space, while the diffusion for negative constant curvature turns out to
be faster. Finally the two-dimensional case is emphasized, as it is relevant
for the single particle diffusion on biomembranes.Comment: 16 pages and 3 figure
Notes on noncommutative supersymmetric gauge theory on the fuzzy supersphere
In these notes we review Klimcik's construction of noncommutative gauge
theory on the fuzzy supersphere. This theory has an exact SUSY gauge symmetry
with a finite number of degrees of freedom and thus in principle it is amenable
to the methods of matrix models and Monte Carlo numerical simulations. We also
write down in this article a novel fuzzy supersymmetric scalar action on the
fuzzy supersphere
Axially symmetric membranes with polar tethers
Axially symmetric equilibrium configurations of the conformally invariant
Willmore energy are shown to satisfy an equation that is two orders lower in
derivatives of the embedding functions than the equilibrium shape equation, not
one as would be expected on the basis of axial symmetry. Modulo a translation
along the axis, this equation involves a single free parameter c.If c\ne 0, a
geometry with spherical topology will possess curvature singularities at its
poles. The physical origin of the singularity is identified by examining the
Noether charge associated with the translational invariance of the energy; it
is consistent with an external axial force acting at the poles. A one-parameter
family of exact solutions displaying a discocyte to stomatocyte transition is
described.Comment: 13 pages, extended and revised version of Non-local sine-Gordon
equation for the shape of axi-symmetric membrane
Bases and foundations of the treatment of peritoneal carcinomatosis: Review article
Peritoneal carcinomatosis refers to a shedding or tumor that spreads to the peritoneal serosa and structures of the abdominal cavity. It is an entity with a poor prognosis. Several conditions can cause this, the most common being colon, rectum, ovary, stomach or appendix
cancers, including peritoneal pseudomyxoma, among others. The abdominal cavity invasion is considered a clinical stage IV. For a long time life expectancy of this entity was very short. With the advent of meticulous techniques in cytoreductive surgery (CRS) and hyperthermic intraperitoneal chemotherapy (HIPEC) the prognosis of patients has changed. In some conditions, these
procedures are standard treatments. CRS is a very important prognostic factor; leaving a less residual disease in the patient, the evolution will be better. The HIPEC starts immediately after the surgical event. The hyperthermia increases the cytotoxic effect of antineoplastic drugs. Numerous studies have appeared in medical literature wherein the clear improvement in survival of the affected population is demonstrated. It is essential that a multidisciplinary team participates in the decision for the best treatment option and the maximum clinical benefit of the patients
Generally covariant state-dependent diffusion
Statistical invariance of Wiener increments under SO(n) rotations provides a
notion of gauge transformation of state-dependent Brownian motion. We show that
the stochastic dynamics of non gauge-invariant systems is not unambiguously
defined. They typically do not relax to equilibrium steady states even in the
absence of extenal forces. Assuming both coordinate covariance and gauge
invariance, we derive a second-order Langevin equation with state-dependent
diffusion matrix and vanishing environmental forces. It differs from previous
proposals but nevertheless entails the Einstein relation, a Maxwellian
conditional steady state for the velocities, and the equipartition theorem. The
over-damping limit leads to a stochastic differential equation in state space
that cannot be interpreted as a pure differential (Ito, Stratonovich or else).
At odds with the latter interpretations, the corresponding Fokker-Planck
equation admits an equilibrium steady state; a detailed comparison with other
theories of state-dependent diffusion is carried out. We propose this as a
theory of diffusion in a heat bath with varying temperature. Besides
equilibrium, a crucial experimental signature is the non-uniform steady spatial
distribution.Comment: 24 page
Artificial intelligence assisted Mid-infrared laser spectroscopy in situ detection of petroleum in soils
A simple, remote-sensed method of detection of traces of petroleum in soil combining
artificial intelligence (AI) with mid-infrared (MIR) laser spectroscopy is presented. A portable MIR
quantum cascade laser (QCL) was used as an excitation source, making the technique amenable to
field applications. The MIR spectral region is more informative and useful than the near IR region for
the detection of pollutants in soil. Remote sensing, coupled with a support vector machine (SVM)
algorithm, was used to accurately identify the presence/absence of traces of petroleum in soil mixtures.
Chemometrics tools such as principal component analysis (PCA), partial least square-discriminant
analysis (PLS-DA), and SVM demonstrated the e ectiveness of rapidly di erentiating between
di erent soil types and detecting the presence of petroleum traces in di erent soil matrices such as
sea sand, red soil, and brown soil. Comparisons between results of PLS-DA and SVM were based
on sensitivity, selectivity, and areas under receiver-operator curves (ROC). An innovative statistical
analysis method of calculating limits of detection (LOD) and limits of decision (LD) from fits of the
probability of detection was developed. Results for QCL/PLS-DA models achieved LOD and LD
of 0.2% and 0.01% for petroleum/soil, respectively. The superior performance of QCL/SVM models
improved these values to 0.04% and 0.003%, respectively, providing better identification probability
of soils contaminated with petroleum
Matrix geometries and Matrix Models
We study a two parameter single trace 3-matrix model with SO(3) global
symmetry. The model has two phases, a fuzzy sphere phase and a matrix phase.
Configurations in the matrix phase are consistent with fluctuations around a
background of commuting matrices whose eigenvalues are confined to the interior
of a ball of radius R=2.0. We study the co-existence curve of the model and
find evidence that it has two distinct portions one with a discontinuous
internal energy yet critical fluctuations of the specific heat but only on the
low temperature side of the transition and the other portion has a continuous
internal energy with a discontinuous specific heat of finite jump. We study in
detail the eigenvalue distributions of different observables.Comment: 20 page
Mid-Infrared laser spectroscopy detection and quantification of explosives in soils using multivariate analysis and artificial intelligence
A tunable quantum cascade laser (QCL) spectrometer was used to develop methods for
detecting and quantifying high explosives (HE) in soil based on multivariate analysis (MVA) and
artificial intelligence (AI). For quantification, mixes of 2,4-dinitrotoluene (DNT) of concentrations
from 0% to 20% w/w with soil samples were investigated. Three types of soils, bentonite, synthetic
soil, and natural soil, were used. A partial least squares (PLS) regression model was generated for
predicting DNT concentrations. To increase the selectivity, the model was trained and evaluated using
additional analytes as interferences, including other HEs such as pentaerythritol tetranitrate (PETN),
trinitrotoluene (TNT), cyclotrimethylenetrinitramine (RDX), and non-explosives such as benzoic acid
and ibuprofen. For the detection experiments, mixes of different explosives with soils were used to
implement two AI strategies. In the first strategy, the spectra of the samples were compared with
spectra of soils stored in a database to identify the most similar soils based on QCL spectroscopy.
Next, a preprocessing based on classical least squares (Pre-CLS) was applied to the spectra of soils
selected from the database. The parameter obtained based on the sum of the weights of Pre-CLS was
used to generate a simple binary discrimination model for distinguishing between contaminated and
uncontaminated soils, achieving an accuracy of 0.877. In the second AI strategy, the same parameter
was added to a principal component matrix obtained from spectral data of samples and used to
generate multi-classification models based on different machine learning algorithms. A random forest
model worked best with 0.996 accuracy and allowing to distinguish between soils contaminated with
DNT, TNT, or RDX and uncontaminated soils
Heat kernel expansion and induced action for matrix models
In this proceeding note, I review some recent results concerning the quantum
effective action of certain matrix models, i.e. the supersymmetric IKKT model,
in the context of emergent gravity. The absence of pathological UV/IR mixing is
discussed, as well as dynamical SUSY breaking and some relations with string
theory and supergravity.Comment: 11 pages, 1 figure; talk given at the 7th International Conference on
Quantum Theory and Symmetries, August 7-13, 2011, Prague/Czech Republi
Localization for Yang-Mills Theory on the Fuzzy Sphere
We present a new model for Yang-Mills theory on the fuzzy sphere in which the
configuration space of gauge fields is given by a coadjoint orbit. In the
classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find
all classical solutions of the gauge theory and use nonabelian localization
techniques to write the partition function entirely as a sum over local
contributions from critical points of the action, which are evaluated
explicitly. The partition function of ordinary Yang-Mills theory on the sphere
is recovered in the classical limit as a sum over instantons. We also apply
abelian localization techniques and the geometry of symmetric spaces to derive
an explicit combinatorial expression for the partition function, and compare
the two approaches. These extend the standard techniques for solving gauge
theory on the sphere to the fuzzy case in a rigorous framework.Comment: 55 pages. V2: references added; V3: minor corrections, reference
added; Final version to be published in Communications in Mathematical
Physic
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