18 research outputs found
The hydrodynamics of swimming microorganisms
Cell motility in viscous fluids is ubiquitous and affects many biological
processes, including reproduction, infection, and the marine life ecosystem.
Here we review the biophysical and mechanical principles of locomotion at the
small scales relevant to cell swimming (tens of microns and below). The focus
is on the fundamental flow physics phenomena occurring in this inertia-less
realm, and the emphasis is on the simple physical picture. We review the basic
properties of flows at low Reynolds number, paying special attention to aspects
most relevant for swimming, such as resistance matrices for solid bodies, flow
singularities, and kinematic requirements for net translation. Then we review
classical theoretical work on cell motility: early calculations of the speed of
a swimmer with prescribed stroke, and the application of resistive-force theory
and slender-body theory to flagellar locomotion. After reviewing the physical
means by which flagella are actuated, we outline areas of active research,
including hydrodynamic interactions, biological locomotion in complex fluids,
the design of small-scale artificial swimmers, and the optimization of
locomotion strategies.Comment: Review articl
Minimal chordal sense of direction and circulant graphs
A sense of direction is an edge labeling on graphs that follows a globally
consistent scheme and is known to considerably reduce the complexity of several
distributed problems. In this paper, we study a particular instance of sense of
direction, called a chordal sense of direction (CSD). In special, we identify
the class of k-regular graphs that admit a CSD with exactly k labels (a minimal
CSD). We prove that connected graphs in this class are Hamiltonian and that the
class is equivalent to that of circulant graphs, presenting an efficient
(polynomial-time) way of recognizing it when the graphs' degree k is fixed
Computational Indistinguishability between Quantum States and Its Cryptographic Application
We introduce a computational problem of distinguishing between two specific
quantum states as a new cryptographic problem to design a quantum cryptographic
scheme that is "secure" against any polynomial-time quantum adversary. Our
problem, QSCDff, is to distinguish between two types of random coset states
with a hidden permutation over the symmetric group of finite degree. This
naturally generalizes the commonly-used distinction problem between two
probability distributions in computational cryptography. As our major
contribution, we show that QSCDff has three properties of cryptographic
interest: (i) QSCDff has a trapdoor; (ii) the average-case hardness of QSCDff
coincides with its worst-case hardness; and (iii) QSCDff is computationally at
least as hard as the graph automorphism problem in the worst case. These
cryptographic properties enable us to construct a quantum public-key
cryptosystem, which is likely to withstand any chosen plaintext attack of a
polynomial-time quantum adversary. We further discuss a generalization of
QSCDff, called QSCDcyc, and introduce a multi-bit encryption scheme that relies
on similar cryptographic properties of QSCDcyc.Comment: 24 pages, 2 figures. We improved presentation, and added more detail
proofs and follow-up of recent wor
Dominance Driven Search
Abstract. Recently, a generic method for identifying and exploiting dominance relations using dominance breaking constraints was proposed. In this method, sufficient conditions for a solution to be dominated are identified and these conditions are used to generate dominance breaking constraints which prune off the dominated solutions. We propose to use these dominance relations in a different way in order to boost the search for good/optimal solutions. In the new method, which we call dominance jumping, when search reaches a point where all solutions in the current domain are dominated, rather than simply backtrack as in the original dominance breaking method, we jump to the subtree which dominates the current subtree. This new strategy allows the solver to move from a bad subtree to a good one, significantly increasing the speed with which good solutions can be found. Experiments across a range of problems show that the method can be very effective when the original search strategy was not very good at finding good solutions.