Surface Comparison with Mass Transportation

We use mass-transportation as a tool to compare surfaces (2-manifolds). In particular, we determine the "similarity" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation problem differs from the standard case in that we require the solution to be invariant under global M\"obius transformations. Our approach provides a constructive way of defining a metric in the abstract space of simply-connected smooth surfaces with boundary (i.e. surfaces of disk-type); this metric can also be used to define meaningful intrinsic distances between pairs of "patches" in the two surfaces, which allows automatic alignment of the surfaces. We provide numerical experiments on "real-life" surfaces to demonstrate possible applications in natural sciences

A topological approach for protein classification

Protein function and dynamics are closely related to its sequence and structure. However prediction of protein function and dynamics from its sequence and structure is still a fundamental challenge in molecular biology. Protein classification, which is typically done through measuring the similarity be- tween proteins based on protein sequence or physical information, serves as a crucial step toward the understanding of protein function and dynamics. Persistent homology is a new branch of algebraic topology that has found its success in the topological data analysis in a variety of disciplines, including molecular biology. The present work explores the potential of using persistent homology as an indepen- dent tool for protein classification. To this end, we propose a molecular topological fingerprint based support vector machine (MTF-SVM) classifier. Specifically, we construct machine learning feature vectors solely from protein topological fingerprints, which are topological invariants generated during the filtration process. To validate the present MTF-SVM approach, we consider four types of problems. First, we study protein-drug binding by using the M2 channel protein of influenza A virus. We achieve 96% accuracy in discriminating drug bound and unbound M2 channels. Additionally, we examine the use of MTF-SVM for the classification of hemoglobin molecules in their relaxed and taut forms and obtain about 80% accuracy. The identification of all alpha, all beta, and alpha-beta protein domains is carried out in our next study using 900 proteins. We have found a 85% success in this identifica- tion. Finally, we apply the present technique to 55 classification tasks of protein superfamilies over 1357 samples. An average accuracy of 82% is attained. The present study establishes computational topology as an independent and effective alternative for protein classification

Complexity, rate, and scale in sliding friction dynamics between a finger and textured surface.

Sliding friction between the skin and a touched surface is highly complex, but lies at the heart of our ability to discriminate surface texture through touch. Prior research has elucidated neural mechanisms of tactile texture perception, but our understanding of the nonlinear dynamics of frictional sliding between the finger and textured surfaces, with which the neural signals that encode texture originate, is incomplete. To address this, we compared measurements from human fingertips sliding against textured counter surfaces with predictions of numerical simulations of a model finger that resembled a real finger, with similar geometry, tissue heterogeneity, hyperelasticity, and interfacial adhesion. Modeled and measured forces exhibited similar complex, nonlinear sliding friction dynamics, force fluctuations, and prominent regularities related to the surface geometry. We comparatively analysed measured and simulated forces patterns in matched conditions using linear and nonlinear methods, including recurrence analysis. The model had greatest predictive power for faster sliding and for surface textures with length scales greater than about one millimeter. This could be attributed to the the tendency of sliding at slower speeds, or on finer surfaces, to complexly engage fine features of skin or surface, such as fingerprints or surface asperities. The results elucidate the dynamical forces felt during tactile exploration and highlight the challenges involved in the biological perception of surface texture via touch

``Sum over Surfaces'' form of Loop Quantum Gravity

We derive a spacetime formulation of quantum general relativity from (hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the 3-geometry in proper time. We show that the perturbation expansion of this operator is finite and computable order by order. By giving a graphical representation a' la Feynman of this expansion, we find that the theory can be expressed as a sum over topologically inequivalent (branched, colored) 2d surfaces in 4d. The contribution of one surface to the sum is given by the product of one factor per branching point of the surface. Therefore branching points play the role of elementary vertices of the theory. Their value is determined by the matrix elements of the hamiltonian constraint, which are known. The formulation we obtain can be viewed as a continuum version of Reisenberger's simplicial quantum gravity. Also, it has the same structure as the Ooguri-Crane-Yetter 4d topological field theory, with a few key differences that illuminate the relation between quantum gravity and TQFT. Finally, we suggests that certain new terms should be added to the hamiltonian constraint in order to implement a ``crossing'' symmetry related to 4d diffeomorphism invariance.Comment: Seriously revised version. LaTeX, with revtex and epsfi

Cascade Freezing of Supercooled Water Droplet Collectives

Surface icing affects the safety and performance of numerous processes in technology. Previous studies mostly investigated freezing of individual droplets. The interaction among multiple droplets during freezing is investigated less, especially on nanotextured icephobic surfaces, despite its practical importance as water droplets never appear in isolation, but in groups. Here we show that freezing of a supercooled droplet leads to spontaneous self-heating and induces strong vaporization. The resulting, rapidly propagating vapor front causes immediate cascading freezing of neighboring supercooled droplets upon reaching them. We put forth the explanation that, as the vapor approaches cold neighboring droplets, it can lead to local supersaturation and formation of airborne microscopic ice crystals, which act as freezing nucleation sites. The sequential triggering and propagation of this mechanism results in the rapid freezing of an entire droplet ensemble resulting in ice coverage of the nanotextured surface. Although cascade freezing is observed in a low-pressure environment, it introduces an unexpected pathway of freezing propagation that can be crucial for the performance of rationally designed icephobic surfaces

The pertinence of Jet Emitting Discs physics to Microquasars: Application to Cygnus X-1

The interpretation of the X-ray spectra of X-ray binaries during their hard states requires a hot, optically thin medium. There are several accretion disc models in the literature that account for this aspect. However, none is designed to simultaneously explain the presence of powerful jets detected during these states. A new quasi-keplerian hot accretion disc solution, a Jet Emitting disc (JED hereafter), which is part of a global disc-jet MHD structure producing stationary super-alfv\'enic ejection, is investigated here. Its radiative and energetic properties are then compared to the observational constraints found in Cygnus X-1. We solve the disc energy equation by balancing the local heating term with advection and cooling by synchrotron, bremsstrahlung and Comptonization processes. The heating term, disc density, accretion velocity and magnetic field amplitude were taken from published self-similar models of accretion-ejection structures. Both optically thin and thick regimes are considered in a one temperature gas supported disc. Three branches of solutions are found possible at a given radius but we investigate only the hot, optically thin and geometrically slim solutions. These solutions give simultaneously, and in a consistent way, the radiative and energetics properties of the disc-jet system. They are able to very well reproduce the accretion-ejection properties of Cygnus X-1, namely its X-ray spectral emission, jet power and jet velocity. About half of the released accretion power is used to produce two mildly relativistic (v/c~0.5) jets and for a luminosity of the order of 1\% of the Eddington luminosity, the JED temperature and optical depth are close to that observed in the hard state Cygnus X-1. The JEDs properties are in agreement with the observations of the prototypical black hole binary Cygnus X-1. and are likely to be relevant to the whole class of microquasars.Comment: 12 pages, 9 figures. Accepted in Astronomy and Astrophysic

Complex Systems Science: Dreams of Universality, Reality of Interdisciplinarity

Using a large database (~ 215 000 records) of relevant articles, we empirically study the "complex systems" field and its claims to find universal principles applying to systems in general. The study of references shared by the papers allows us to obtain a global point of view on the structure of this highly interdisciplinary field. We show that its overall coherence does not arise from a universal theory but instead from computational techniques and fruitful adaptations of the idea of self-organization to specific systems. We also find that communication between different disciplines goes through specific "trading zones", ie sub-communities that create an interface around specific tools (a DNA microchip) or concepts (a network).Comment: Journal of the American Society for Information Science and Technology (2012) 10.1002/asi.2264