Engineering an Ecosystem : Taking Cues from Nature’s Paradigm to Build Tissue in the Lab and the Body

This manuscript took a 'top down' approach to understanding survival of inhabitant cells in the ecosystem bone, working from higher to lower length and time scales through the hierarchical ecosystem of bone. Our working hypothesis is that nature “engineered” the skeleton using a 'bottom up' approach,where mechanical properties of cells emerge from their adaptation to their local me-chanical milieu. Cell aggregation and formation of higher order anisotropic struc- ture results in emergent architectures through cell differentiation and extracellular matrix secretion. These emergent properties, including mechanical properties and architecture, result in mechanical adaptation at length scales and longer time scales which are most relevant for the survival of the vertebrate organism [Knothe Tate and von Recum 2009]. We are currently using insights from this approach to har-ness nature’s regeneration potential and to engineer novel mechanoactive materials [Knothe Tate et al. 2007, Knothe Tate et al. 2009]. In addition to potential applications of these exciting insights, these studies may provide important clues to evolution and development of vertebrate animals. For instance, one might ask why mesenchymal stem cells condense at all? There is a putative advantage to self-assembly and cooperation, but this advantage is somewhat outweighed by the need for infrastructural complexity (e.g., circulatory systems comprised of specific differentiated cell types which in turn form conduits and pumps to overcome limitations of mass transport via diffusion, for example; dif-fusion is untenable for multicellular organisms larger than 250 microns in diameter. A better question might be: Why do cells build skeletal tissue? Once cooperatingcells in tissues begin to deplete local sources of food in their aquatic environment, those that have evolved a means to locomote likely have an evolutionary advantage. Once the environment becomes less aquarian and more terrestrial, self-assembled organisms with the ability to move on land might have conferred evolutionary ad-vantages as well. So did the cytoskeleton evolve several length scales, enabling the emergence of skeletal architecture for vertebrate animals? Did the evolutionary advantage of motility over noncompliant terrestrial substrates (walking on land) favor adaptations including emergence of intracellular architecture (changes in the cytoskeleton and upregulation of structural protein manufacture), inter-cellular con- densation, mineralization of tissues, and emergence of higher order architectures?How far does evolutionary Darwinism extend and how can we exploit this knowl- edge to engineer smart materials and architectures on Earth and new, exploratory environments?[Knothe Tate et al. 2008]. We are limited only by our ability to imagine. Ultimately, we aim to understand nature, mimic nature, guide nature and/or exploit nature’s engineering paradigms without engineer-ing ourselves out of existence.

The effect of friction on indenter force and pile-up in numerical simulations of bone nanoindentation

Nanoindentation is a useful technique for probing the mechanical properties of bone, and finite element (FE) modeling of the indentation allows inverse determination of elasto-plastic constitutive properties. However, all but one FE study to date have assumed frictionless contact between indenter and bone. The aim of this study was to explore the effect of friction in simulations of bone nanoindentation. Two dimensional axisymmetric FE simulations were performed using a spheroconical indenter of tip radius 0.6 m and angle 90°. The coefficient of friction between indenter and bone was varied between 0.0 (frictionless) and 0.3. Isotropic linear elasticity was used in all simulations, with bone elastic modulus E=13.56GPa and Poisson‟s ratio f 0.3. Plasticity was incorporated using both Drucker-Prager and von Mises yield surfaces. Friction had a modest effect on the predicted force-indentation curve for both von Mises and Drucker-Prager plasticity, reducing maximum indenter displacement by 10% and 20% respectively as friction coefficient was increased from zero to 0.3 (at a maximum indenter force of 5mN). However, friction has a much greater effect on predicted pile-up after indentation, reducing predicted pile-up from 0.27 to 0.11 m with a von Mises model, and from 0.09 to 0.02 m with Drucker-Prager plasticity. We conclude that it is potentially important to include friction in nanoindentation simulations of bone if pile-up is used to compare simulation results with experiment.

A Stochastic View of Optimal Regret through Minimax Duality

We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. We use this expression to obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary. Peter L. Bartlett, Alexander Rakhlin

Board monitoring and judgement as processes of sensemaking

When organizational scandals occur, the common refrain among commentators is: 'Where was the board in all this?' 'How could the directors not have known what was going on?''Why didn't the board intervene?' The scandals demonstrate that board monitoring or oganizational performance is a matter of great importance. By monitoring, we mean the act of keeping the organization under review. In many English-speaking countries, directors have a legal duty of care, which includes duties to monitor the performance of their organizations (Hopt and von Hippel 2010). However, statutory law typically merely states the duty, while providing little guidance on how that duty can be met.

DFL: A Data Flow Language

Many novel computer architectures like array and multiprocessors which achieve high performance through the use of concurrency exploit variations of the von Neumann model of computation. The effective utilization of the machines makes special demands on programmers and their programming languages, such as the structuring of data into vectors or the partitioning of programs into concurrent processes. In comparison, the data flow model of computation demands only that the principle of structured programming be followed. A data flow program, often represented as a data flow graph, is a program that expresses a computation by indicating the data dependencies among operators. A data flow computer is a machine designed to take advantage of concurrency in data flow graphs by executing data independent operations in parallel. In this paper, we discuss the design of a high level language (DFL: Data Flow Language) suitable for data flow computers. Some sample procedures in DFL are presented. The implementation aspects have not been discussed in detail since there are no new problems encountered. The language DFL embodies the concepts of functional programming, but in appearance closely resembles Pascal. The language is a better vehicle than the data flow graph for expressing a parallel algorithm. The compiler has been implemented on a DEC 1090 system in Pascal.

Nonlinear vibration analysis of composite laminated and sandwich plates with random material properties

Nonlinear vibration analysis is performed using a C-0 assumed strain interpolated finite element plate model based on Reddy's third order theory. An earlier model is modified to include the effect of transverse shear variation along the plate thickness and Von-Karman nonlinear strain terms. Monte Carlo Simulation with Latin Hypercube Sampling technique is used to obtain the variance of linear and nonlinear natural frequencies of the plate due to randomness in its material properties. Numerical results are obtained for composite plates with different aspect ratio, stacking sequence and oscillation amplitude ratio. The numerical results are validated with the available literature. It is found that the nonlinear frequencies show increasing non-Gaussian probability density function with increasing amplitude of vibration and show dual peaks at high amplitude ratios. This chaotic nature of the dispersion of nonlinear eigenvalues is also r

Performance analysis of a slotted-ALOHA protocol on a capture channel with fading

We consider the slotted ALOHA protocol on a channel with a capture effect. There are M ergodic. Under the same rate conditions, for general regenerative arrival streams, we obtain the rates of convergence to stationarity, finiteness of stationary moments and various functional limit theorems. Our arrival streams contain all the traffic models suggested in the recent literature, including the ones which display long range dependence. We also obtain bounds on the stationary moments of waiting times which can be tight under realistic conditions. Finally, we obtain several results on the transient performance of the system, e.g., first time to overflow and the limits of the overflow process. We also extend the above results to the case of a capture channel exhibiting Markov modulated fading. Most of our results and proofs will be shown to hold also for the slotted ALOHA protocol without capture.

Spherical piston problem in water

In this paper, we study the propagation of a shock wave in water, produced by the expansion of a spherical piston with a finite initial radius. The piston path in the x, t plane is a hyperbola. We have considered the following two cases: (i) the piston accelerates from a zero initial velocity and attains a finite velocity asymptotically as t tends to infinity, and (ii) the piston decelerates, starting from a finite initial velocity. Since an analytic approach to this problem is extremely difficult, we have employed the artificial viscosity method of von Neumann & Richtmyer after examining its applicability in water. For the accelerating piston case, we have studied the effect of different initial radii of the piston, different initial curvatures of the piston path in the x, t plane and the different asymptotic speeds of the piston. The decelerating case exhibits the interesting phenomenon of the formation of a cavity in water when the deceleration of the piston is sufficiently high. We have also studied the motion of the cavity boundary up to 550 cycles.

Entropy of quantum states: Ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.

Forest observational studies in India: Past developments and considerations for the future

Long term forest research sites in India, going by different names including Linear Tree Increment Plots, Linear Increment Plots, Linear Sample Plots and Permanent Preservation Plots, cover diverse plant communities and environmental conditions. Presently, some of these long-term observational studies are functional, some are disturbed and others have almost been lost. The accumulated data will become increasingly important in the context of environmental modelling and climate change, especially if the plots and data can be maintained and/or revived. This contribution presents the history and current state of forest research plots in India, including details of locations and re-measurements. We provide a brief introduction of the National Forest Inventory (NFI), Preservation Plots in natural forests, the 50-ha Mudumalai Forest Dynamics Plot as part of the Centre for Tropical Forest Science and Smithsonian Institution Global Earth Observatories network (CTFS-SIGEO), and research plots established in plantations for tree growth studies and modelling. We also present some methodological details including assessment and analysis for two types of observational studies, the Tree Count Plots (TCP) and Tree Re-measurement Plots (TRP). Arguments are presented in favour of enumeration and analysis methods which are consistent with current approaches in forest ecological research. (c) 2013 Elsevier B.V. All rights reserved.

Optimality Conditions and Duality for Semi-Infinite Mathematical Programming Problem with Equilibrium Constraints

This article considers a semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC) defined as a semi-infinite mathematical programming problem with complementarity constraints. We establish necessary and sufficient optimality conditions for the (SIMPEC). We also formulate Wolfe- and Mond-Weir-type dual models for (SIMPEC) and establish weak, strong and strict converse duality theorems for (SIMPEC) and the corresponding dual problems under invexity assumptions.

Admissible Hierachic Sets

In this paper we present a solution concept for abstract systems called the admissible hierarchic set. The solution we propose is a refinement of the hierarchic solution, a generalization of the von Neumann and Morgenstern solution. For finite abstract systems we show that the admissible hierarchic sets and the von Neumann and Morgenstern stable sets are the only outcomes of a coalition formation procedure (Wilson, 1972 and Roth, 1984). For coalitional games we prove that the core is either a vN&M stable set or an admissible hierarchic set.

The Supercore for Normal Form Games

We study the supercore of a system derived from a normal form game. For the case of a finite game with pure strategies, we define a sequence of games and show that the supercore of that system coincides with the set of Nash equilibrium strategy profiles of the last game in the sequence. This result is illustrated with the characterization of the supercore for the n-person prisoners’ dilemma. With regard to the mixed extension of a normal form game, we show that the set of Nash equilibrium profiles coincides with the supercore for games with a finite number of Nash equilibria. For games with an infinite number of Nash equilibria this need not be no longer the case. Yet, it is not difficult to find a binary relation which guarantees the coincidence of these two sets.

Numerical solution of parabolic equations by the box scheme

The box scheme proposed by H. B. Keller is a numerical method for solving parabolic partial differential equations. We give a convergence proof of this scheme for the heat equation, for a linear parabolic system, and for a class of nonlinear parabolic equations. Von Neumann stability is shown to hold for the box scheme combined with the method of fractional steps to solve the two-dimensional heat equation. Computations were performed on Burgers' equation with three different initial conditions, and Richardson extrapolation is shown to be effective.

On contractive cyclic fuzzy maps in metric spaces and some related results on fuzzy best proximity points and fuzzy fixed points

This paper investigates some properties of cyclic fuzzy maps in metric spaces. The convergence of distances as well as that of sequences being generated as iterates defined by a class of contractive cyclic fuzzy mapping to fuzzy best proximity points of (non-necessarily intersecting adjacent subsets) of the cyclic disposal is studied. An extension is given for the case when the images of the points of a class of contractive cyclic fuzzy mappings restricted to a particular subset of the cyclic disposal are allowed to lie either in the same subset or in its next adjacent one.