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Rai V.,Almende Research | Van Rossum A.,Almende Research | Van Rossum A.,University of Tilburg | Correll N.,CU Boulder
IEEE International Conference on Intelligent Robots and Systems | Year: 2011

We wish to design decentralized algorithms for self-assembly of robotic modules that have 100% yield even if the number of available building blocks is limited, and specifically when the number of available building blocks is identical to the number of blocks required by the structure. In contrast to self-assembly at the nano and micro scales where abundant building blocks are available, modular robotic systems need to self-assemble from a limited number of modules. In particular, when self-assembly is used for reconfiguration, it is desirable that the new conformation includes all of the available modules. We propose a suite of algorithms that (1) generate a reversible graph grammar, i.e., generates rules for a desired structure that allow the structure not only to assemble, but also to disassemble, and (2) have a set of structures that are growing in parallel converge to a single structure using broadcast communication. We show that by omitting a reversal rule for the last attached module, self-assembly eventually completes, and that communication can drastically speed up this process. © 2011 IEEE.


Rumanov I.,CU Boulder
Journal of Mathematical Physics | Year: 2015

Beta-ensembles of random matrices are naturally considered as quantum integrable systems, in particular, due to their relation with conformal field theory, and more recently appeared connection with quantized Painlevé Hamiltonians. Here, we demonstrate that, at least for even integer beta, these systems are classically integrable, e.g., there are Lax pairs associated with them, which we explicitly construct. To come to the result, we show that a solution of every Fokker-Planck equation in one space (and one time) dimensions can be considered as a component of an eigenvector of a Lax pair. The explicit finding of the Lax pair depends on finding a solution of a governing system-a closed system of two nonlinear partial differential equations (PDEs) of hydrodynamic type. This result suggests that there must be a solution for all values of beta. We find the solution of this system for even integer beta in the particular case of quantum Painlevé II related to the soft edge of the spectrum for beta-ensembles. The solution is given in terms of Calogero system of ?/2 particles in an additional time-dependent potential. Thus, we find another situation where quantum integrability is reduced to classical integrability. © 2015 AIP Publishing LLC.


Rumanov I.,CU Boulder
Communications in Mathematical Physics | Year: 2016

In Rumanov (J Math Phys 56:013508, 2015), we found explicit Lax pairs for the soft edge of beta ensembles with even integer values of (Formula presented.). Using this general result, the case (Formula presented.) is further considered here. This is the smallest even (Formula presented.) , when the corresponding Lax pair and its relation to Painlevé II (PII) have not been known before, unlike cases (Formula presented.) and 4. It turns out that again everything can be expressed in terms of the Hastings–McLeod solution of PII. In particular, a second order nonlinear ordinary differential equation (ODE) for the logarithmic derivative of Tracy–Widom distribution for (Formula presented.) involving the PII function in the coefficients is found, which allows one to compute asymptotics for the distribution function. The ODE is a consequence of a linear system of three ODEs for which the local singularity analysis yields series solutions with exponents in the set 4/3, 1/3 and −2/3. © 2015, Springer-Verlag Berlin Heidelberg.


This is all well and good - eventual cell death is as it should be. Without cell death, there is cell immortality and with cell immortality there is cancer. Cancer cells counteract the breakdown of telomeres by building them up as quickly as they are degraded. A cancer cell does this by spackling a telomere with the enzyme telomerase. Basically, when telomerase finds and attaches to a telomere, it adds a repeating DNA sequence to the repeating DNA sequences that are already in place, lengthening the telomere and adding to the chromosome's protective ends. Oncologists and cancer researchers wish that telomerase would not do this. Without this constant telomere repair, chromosomes would eventually degrade and cancer cells would die. Without the interaction of telomerase with telomeres, cancer cells would be mortal. A study led by University of Colorado Cancer Center investigator, Thomas Cech, PhD, CU Boulder Distinguished Professor, Nobel laureate, and director of CU's BioFrontiers Institute, uses CRISPR gene editing technology (shortlisted for the Nobel Prize) and live cell, single molecule microscopy (which led to the 2014 Nobel Prize in Chemistry for unaffiliated researchers Betzig, Hell and Moerner) to watch in real-time, for the first time, this essential interaction between telomerase and telomeres. Results are published in the journal Cell. What Cech and co-authors Jens Schmidt, PhD, Damon Runyon Cancer Foundation postdoctoral fellow and staff scientist Arthur Zaug saw is that telomerase diffuses throughout the cell nucleus, bumping into things. Neither telomerase nor telomeres are common in the nucleus but sometimes chance has it that the first hits the second. But it doesn't do any good for telomerase to attach at a telomere midpoint. To protect the chromosome, telomerase must attach at the very end of the rope. So if telomerase hits the middle of a telomere, it soon detaches and tries again. Cech and colleagues call this "probing". Only if probing results in a direct hit at the end of the telomere does telomerase attach and stay. "It's like looking through TripAdvisor for a place you want to stay," Cech says. "You probe different hotels and finally you find one that has all the features you want." Cech calls this mechanism "plausibly the simplest way that a rare little machine can find its very rare landing site within the complex landscape of the nucleus." Think about it: Telomerase diffuses evenly through the nucleus. When it happens to hit anywhere on a telomere, it sticks briefly, thus increasing the concentration of telomerase near telomeres and thus increasing the chance that telomerase will happen to hit a telomere end where it can attach securely. The group was able to make this process visible by using the CRISPR DNA editing technology to insert code into the gene that makes telomerase. This inserted code manufactured a fluorescent protein, which was attached to telomerase. The group then used what some call nanoscopy to see this fluorescent protein. "The amazing thing to me is that three years ago, you couldn't have done any of this. This is how fast things are moving in biology, just rocketing ahead," Cech says. Previously, looking close enough to see the fluorescence of a single protein would have required "fixing" the cell and visualizing it with a microscope. It would have been a snapshot. The ability to see the processes inside a live cell at this magnification is like shooting video. "With this fixed cell imaging, we didn't see the dynamics," Cech says. "And the rapidly diffusing telomerase is invisible, washed out or lost in the background." Cech points out that this technique of CRISPR-aided nanoscopy will likely be used by scientists outside the field of telomere research. He also hopes this specific finding will aid in screening anti-telomerase drugs. "Right now we don't have a great telomerase inhibitor. We don't know at which step our first generation of these drugs is interfering so we don't know how to optimize these drug candidates for anti-cancer effect," Cech says. Does a drug prevent the assembly of telomerase? Does it keep telomerase from moving near telomeres? Does it prevent probing? Does it prevent telomerase from finding a telomere end? "Knowing where a drug blocks the ability of telomerase to lengthen telomeres could have broad applicability for diverse cancers," Cech says. Explore further: Researchers uncover new target for cancer research More information: Jens C. Schmidt et al, Live Cell Imaging Reveals the Dynamics of Telomerase Recruitment to Telomeres, Cell (2016). DOI: 10.1016/j.cell.2016.07.033


Foucard L.C.,CU Boulder | Pellegrino J.,CU Boulder | Vernerey F.J.,CU Boulder | Vernerey F.J.,University of Colorado at Boulder
CMES - Computer Modeling in Engineering and Sciences | Year: 2014

Many colloidal-sized particles encountered in biological and membranebased separation applications can be characterized as soft vesicles such as cells, yeast, viruses and surfactant micelles. The deformation of these vesicles is expected to critically affect permeation by accommodating pore shapes and sizes or enhancing the adhesion with a pore surface. Numerical and theoretical modelings will be critical to fully understand these processes and thus design novel filtration membranes that target, not only size, but deformability as a selection criterion. The present paper therefore introduces a multiscale strategy that enables the determination of the permeability of a fibrous network with respect to complex fluids loaded with vesicles. The contributions are two-fold. First, we introduce a particle-based moving interface method that can be used to characterized the severe deformation of vesicles interacting with an immersed fibrous network. Second, we present a homogenization strategy that permits the determination of a network permeability, based on the micromechanisms of vesicle deformation and permeation. As a proof of concept, we then investigate the role of vesicle-solvent surface tension on the permeation of both solvent and vesicle through a simple fiber network. We find that vesicles are always retarded relative to the continuum (or solvent) flow, and that the relative selectivity for the continuum versus the vesicle is inversely proportional to the capillary number. © 2014 Tech Science Press.

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