acase@tulane.edu / Cell deformability is being recognized as an easily measurable indicator to differentiate different types of cells and detect diseased cells. A recent promising and advantageous technique to assess cell deformability is the cross-channel microfluidic deformability cytometry (DC). It uses a stretching extensional flow, in which each time an individual cell undergoes deformation. Using our three-dimensional computational algorithm for multiphase viscoelastic flow, known as VECAM, this study focuses on modeling the deformation of living cells in such microfluidic channels. Through the computational simulations, we first identified the central extensional flow region in the cross section of the channel, where cells are stretched due to mostly fluid momentum and resulting normal stresses. Our simulation data indicate that the range of deformability indices observed for human cells in DC experiments (from 1.5 to 2.3) corresponds to the range of cell elasticities from 3,000 to 15,000 Pa. We have also showed that both cell size and cortical tension have a much less effect on cell deformability than cell elasticity. The study further shows the cell oscillation in the extensional flow region caused by pressure imbalance in DC experiments does not affect much how long cell stays in this region and has a very limited impact on the measured cell deformability index. Finally, our study shows offset in both Y and Z directions can alter the results of the deformability measurement in a significant way. Our fully three-dimensional parallel computational algorithm is proven to realistically simulate cell movement and deformation in the cross-channel deformability cytometry. With the acquired simulation results, the computational study provides helpful insights and future guidance that are otherwise impossible to be obtained from the experimental data to the cytometry experiments. / 1 / Zhongyi Sheng

acase@tulane.edu / Cell deformability is being recognized as an easily measurable indicator to differentiate different types of cells and detect diseased cells. A recent promising and advantageous technique to assess cell deformability is the cross-channel microfluidic deformability cytometry (DC). It uses a stretching extensional flow, in which each time an individual cell undergoes deformation. Using our three-dimensional computational algorithm for multiphase viscoelastic flow, known as VECAM, this study focuses on modeling the deformation of living cells in such microfluidic channels. Through the computational simulations, we first identified the central extensional flow region in the cross section of the channel, where cells are stretched due to mostly fluid momentum and resulting normal stresses. Our simulation data indicate that the range of deformability indices observed for human cells in DC experiments (from 1.5 to 2.3) corresponds to the range of cell elasticities from 3,000 to 15,000 Pa. We have also showed that both cell size and cortical tension have a much less effect on cell deformability than cell elasticity. The study further shows the cell oscillation in the extensional flow region caused by pressure imbalance in DC experiments does not affect much how long cell stays in this region and has a very limited impact on the measured cell deformability index. Finally, our study shows offset in both Y and Z directions can alter the results of the deformability measurement in a significant way. Our fully three-dimensional parallel computational algorithm is proven to realistically simulate cell movement and deformation in the cross-channel deformability cytometry. With the acquired simulation results, the computational study provides helpful insights and future guidance that are otherwise impossible to be obtained from the experimental data to the cytometry experiments. / 1 / Zhongyi Sheng

Given a set of circles C = {c₁, ..., cn}on the Euclidean plane with centers {(a₁, b₁), ..., (an, b_n)}and radii {r₁..., r<n},the smallest enclosing circle (of fixed circles) problem is to find the circle of minimum radius that encloses all circles in C. We survey four known approaches for this problem, including a second order cone reformulation, a subgradient approach, a quadratic programming scheme, and a randomized incremental algorithm. For the last algorithm we also give some implementation details. It turns out the quadratic programming scheme outperforms the other three in our computational experiment. / Singapore-MIT Alliance (SMA)

This report presents issues relating to the kinematics and control of dexterous robotic hands using the Utah-MIT hand as an illustrative example. The emphasis throughout is on the actual implementation and testing of the theoretical concepts presented. The kinematics of such hands is interesting and complicated owing to the large number of degrees of freedom involved. The implementation of position and force control algorithms on such tendon driven hands has previously suffered from inefficient formulations and a lack of sophisticated computer hardware. Both these problems are addressed in this report. A multiprocessor architecture has been built with high performance microcomputers on which real-time algorithms can be efficiently implemented. A large software library has also been built to facilitate flexible software development on this architecture. The position and force control algorithms described herein have been implemented and tested on this hardware.

An immersed interface method and an immersed finite element method for solving linear elasticity problems with two phases separated by an interface have been developed in this thesis. For the problem of interest, the underlying elasticity modulus is a constant in each phase but vary from phase to phase. The basic goal here is to design an efficient numerical method using a fixed Cartesian grid. The application of such a method to problems with moving interfaces driving by stresses has a great advantage: no re-meshing is needed. A local optimization strategy is employed to determine the finite difference equations at grid points near or on the interface. The bi-conjugate gradient method and the GMRES with preconditioning are both implemented to solve the resulting linear systems of equations and compared. The level set method is used to represent the interface. Numerical results are presented to show that the immersed interface method is second-order accurate.

Thesis (Ph. D.)--University of Chicago, Dept. of Computer Science, June 1999. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

All living creatures, despite their profound diversity, share a common architectural building block: the cell. Cells are the basic functional units of life, yet are themselves comprised of numerous components with distinct mechanical characteristics. It is well established that cells have the ability to sense and respond to externally applied forces. However, the detailed mechanism of mechanosensation is still not clearly understood, and is an active area of research involving experimental and theoretical works. Mathematical modeling of the mechanical stimulus correlating to different experimental stimulation procedures forms the first step to understanding the mechanosensation in cellular system. In this thesis, a continuum -based computational model of living cells that explicitly incorporate the material properties of various cellular components are developed. In the constitutive modeling of cell, the continuum standard linear solid viscoelastic model (SLS), its natural extension for large scale deformation standard Neo-Hookean solid viscoelastic model (SnHS) as well as polymer mechanics- based dynamic shear modulus model was introduced. Finite element simulations of three widely used experiments- atomic force microscopy (AFM), magnetic twisting cytometry (MTC) and micropipette aspiration in the quantification of cell properties were carried out to verify the developed constitutive model. From the results of AFM finite element simulation, it was observed that the force-deformation and strain-relaxation curves obtained fit the experimental results very well. The influences of cytoplasm shear modulus which varies due to the formation of stress fiber, and cortex shear modulus which alters with the actin filament concentration factors and load frequency were systematically studied. Similarly, in magnetic twisting cytometry (MTC) simulation, the role of cytoplasm material properties, constant/sinusoidal forcing rates and various frequencies on the overall mechanical response of a cell was obtained. Numerical results are validated against experiments results. Micropipette aspiration simulation was also carried out in which the typical creep deformation test was carried out to study the viscoelastic behavior of the cell. Based on the results from finite element simulation, the effect of pipette radius, effect of cortex shear modulus and effect of pressure rate have been derived for the interpretation of the mechanical parameters from the micropipette aspiration.

In the first part of the thesis we show black-box separations in public and private-key cryptography. Our main result answers in the negative the question of whether we can base Identity Based Encryption (IBE) on Trapdoor Permutations. Furthermore, we make progress towards the black-box separation of IBE from the Decisional Diffie-Hellman assumption. We also show the necessity of adaptivity when querying one-way permutations to construct pseudorandom generators a' la Goldreich-Levin; an issue related to streaming models for cryptography. In the second part we introduce streaming techniques in understanding randomness in efficient computation, proving lower bounds for efficiently computable problems, and in computing cryptographic primitives. We observe [Coo71] that logarithmic space-bounded Turing Machines, equipped with an unbounded stack, henceforth called Stack Machines, together with an external random tape of polynomial length characterize RP,BPP an so on. By parametrizing on the number of passes over the random tape we provide a technical perspective bringing together Streaming, Derandomization, and older works in Stack Machines. Our technical developments relate this new model with previous works in derandomization. For example, we show that to derandomize parts of BPP it is in some sense sufficient to derandomize BPNC (a class believed to be much lower than P \subseteq BPP). We also obtain a number of results for variants of the main model, regarding e.g. the fooling power of Nisan's pseudorandom generator (PRG) [N92] for the derandomization of BPNC^1, and the relation of parametrized access to NP-witnesses with width-parametrizations of SAT. A substantial contribution regards a streaming approach to lower bounds for problems in the NC-hierarchy (and above). We apply Communication Complexity to show a streaming lower bound for a model with an unbounded (free-to-access) pushdown storage. In particular, we obtain a $n^{\Omega(1)}$ lower bound simultaneously in the space and in the number of passes over the input, for a variant of inner product. This is the first lower bound for machines that correspond to poly-size circuits, can do Parity, Barrington's language, and decide problems in P-NC assuming EXP \neq PSPACE. Finally, we initiate the study of log-space streaming computation of cryptographic primitives. We observe that the work on Cryptography in NC^0 [AIK08] yields a non-black-box construction of a one-way function computable in an O(log n)-space bounded streaming model.Also, we show that relying on this work is in some sense necessary.

In the first part of the thesis we show black-box separations in public and private-key cryptography. Our main result answers in the negative the question of whether we can base Identity Based Encryption (IBE) on Trapdoor Permutations. Furthermore, we make progress towards the black-box separation of IBE from the Decisional Diffie-Hellman assumption. We also show the necessity of adaptivity when querying one-way permutations to construct pseudorandom generators a' la Goldreich-Levin; an issue related to streaming models for cryptography. In the second part we introduce streaming techniques in understanding randomness in efficient computation, proving lower bounds for efficiently computable problems, and in computing cryptographic primitives. We observe [Coo71] that logarithmic space-bounded Turing Machines, equipped with an unbounded stack, henceforth called Stack Machines, together with an external random tape of polynomial length characterize RP,BPP an so on. By parametrizing on the number of passes over the random tape we provide a technical perspective bringing together Streaming, Derandomization, and older works in Stack Machines. Our technical developments relate this new model with previous works in derandomization. For example, we show that to derandomize parts of BPP it is in some sense sufficient to derandomize BPNC (a class believed to be much lower than P \subseteq BPP). We also obtain a number of results for variants of the main model, regarding e.g. the fooling power of Nisan's pseudorandom generator (PRG) [N92] for the derandomization of BPNC^1, and the relation of parametrized access to NP-witnesses with width-parametrizations of SAT. A substantial contribution regards a streaming approach to lower bounds for problems in the NC-hierarchy (and above). We apply Communication Complexity to show a streaming lower bound for a model with an unbounded (free-to-access) pushdown storage. In particular, we obtain a $n^{\Omega(1)}$ lower bound simultaneously in the space and in the number of passes over the input, for a variant of inner product. This is the first lower bound for machines that correspond to poly-size circuits, can do Parity, Barrington's language, and decide problems in P-NC assuming EXP \neq PSPACE. Finally, we initiate the study of log-space streaming computation of cryptographic primitives. We observe that the work on Cryptography in NC^0 [AIK08] yields a non-black-box construction of a one-way function computable in an O(log n)-space bounded streaming model.Also, we show that relying on this work is in some sense necessary.