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 $O(d)$ 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

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

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

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