Bearing capacity factors for a conical footing using lower- and upper-bound finite elements limit analysis

Bearing capacity factors, N-c, N-q, and N-gamma, for a conical footing are determined by using the lower and upper bound axisymmetric formulation of the limit analysis in combination with finite elements and optimization. These factors are obtained in a bound form for a wide range of the values of cone apex angle (beta) and phi with delta = 0, 0.5 phi, and phi. The bearing capacity factors for a perfectly rough (delta = phi) conical footing generally increase with a decrease in beta. On the contrary, for delta = 0 degrees, the factors N-c and N-q reduce gradually with a decrease in beta. For delta = 0 degrees, the factor N-gamma for phi >= 35 degrees becomes a minimum for beta approximate to 90 degrees. For delta = 0 degrees, N-gamma for phi <= 30 degrees, as in the case of delta = phi, generally reduces with an increase in beta. The failure and nodal velocity patterns are also examined. The results compare well with different numerical solutions and centrifuge tests' data available from the literature.

An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas

We show here a 2(Omega(root d.log N)) size lower bound for homogeneous depth four arithmetic formulas. That is, we give an explicit family of polynomials of degree d on N variables (with N = d(3) in our case) with 0, 1-coefficients such that for any representation of a polynomial f in this family of the form f = Sigma(i) Pi(j) Q(ij), where the Q(ij)'s are homogeneous polynomials (recall that a polynomial is said to be homogeneous if all its monomials have the same degree), it must hold that Sigma(i,j) (Number of monomials of Q(ij)) >= 2(Omega(root d.log N)). The above mentioned family, which we refer to as the Nisan-Wigderson design-based family of polynomials, is in the complexity class VNP. Our work builds on the recent lower bound results 1], 2], 3], 4], 5] and yields an improved quantitative bound as compared to the quasi-polynomial lower bound of 6] and the N-Omega(log log (N)) lower bound in the independent work of 7].

Upper bound on cubicity in terms of boxicity for graphs of low chromatic number

The boxicity (respectively cubicity) of a graph G is the least integer k such that G can be represented as an intersection graph of axis-parallel k-dimensional boxes (respectively k-dimensional unit cubes) and is denoted by box(G) (respectively cub(G)). It was shown by Adiga and Chandran (2010) that for any graph G, cub(G) <= box(G) log(2) alpha(G], where alpha(G) is the maximum size of an independent set in G. In this note we show that cub(G) <= 2 log(2) X (G)] box(G) + X (G) log(2) alpha(G)], where x (G) is the chromatic number of G. This result can provide a much better upper bound than that of Adiga and Chandran for graph classes with bounded chromatic number. For example, for bipartite graphs we obtain cub(G) <= 2(box(G) + log(2) alpha(G)] Moreover, we show that for every positive integer k, there exist graphs with chromatic number k such that for every epsilon > 0, the value given by our upper bound is at most (1 + epsilon) times their cubicity. Thus, our upper bound is almost tight. (c) 2015 Elsevier B.V. All rights reserved.

Reply to Discussion on ``Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis'' Comput. Geotech. 70 (2015) 138-149]

A discussion has been provided for the comments raised by the discusser (Clausen, 2015)1] on the article recently published by the authors (Chakraborty and Kumar, 2015). The effect of exponent alpha for values of GSI approximately smaller than 30 becomes more critical. On the other hand, for greater values of GSI, the results obtained by the authors earlier remain primarily independent of alpha and can be easily used. (C) 2015 Elsevier Ltd. All rights reserved.

A Closer Look at Multiple Forking: Leveraging (In)Dependence for a Tighter Bound

Boldyreva, Palacio and Warinschi introduced a multiple forking game as an extension of general forking. The notion of (multiple) forking is a useful abstraction from the actual simulation of cryptographic scheme to the adversary in a security reduction, and is achieved through the intermediary of a so-called wrapper algorithm. Multiple forking has turned out to be a useful tool in the security argument of several cryptographic protocols. However, a reduction employing multiple forking incurs a significant degradation of , where denotes the upper bound on the underlying random oracle calls and , the number of forkings. In this work we take a closer look at the reasons for the degradation with a tighter security bound in mind. We nail down the exact set of conditions for success in the multiple forking game. A careful analysis of the cryptographic schemes and corresponding security reduction employing multiple forking leads to the formulation of `dependence' and `independence' conditions pertaining to the output of the wrapper in different rounds. Based on the (in)dependence conditions we propose a general framework of multiple forking and a General Multiple Forking Lemma. Leveraging (in)dependence to the full allows us to improve the degradation factor in the multiple forking game by a factor of . By implication, the cost of a single forking involving two random oracles (augmented forking) matches that involving a single random oracle (elementary forking). Finally, we study the effect of these observations on the concrete security of existing schemes employing multiple forking. We conclude that by careful design of the protocol (and the wrapper in the security reduction) it is possible to harness our observations to the full extent.

Polymers with aligned carbon nanotubes: Active composite materials

We review the current state of the polymer-carbon nanotube composites field. The article first covers key points in dispersion and stabilization of nanotubes in a polymer matrix, with particular attention paid to ultrasonic cavitation and shear mixing. We then focus on the emerging trends in nanocomposite actuators, in particular, photo-stimulated mechanical response. The magnitude and even the direction of this actuation critically depend on the degree of tube alignment in the matrix; in this context, we discuss the affine model predicting the upper bound of orientational order of nanotubes, induced by an imposed strain. We review how photo-actuation in nanocomposites depend on nanotube concentration, alignment and entanglement, and examine possible mechanisms that could lead to this effect. Finally, we discuss properties of pure carbon nanotube networks, in form of mats or fibers. These systems have no polymer matrix, yet demonstrate pronounced viscoelasticity and also the same photomechanical actuation as seen in polymer-based composites. © 2008 Elsevier Ltd. All rights reserved.

Quantifying Cell Binding Kinetics Mediated By Surface-Bound Blood Type B Antigen To Immobilized Antibodies

Cell adhesion is crucial to many biological processes, such as inflammatory responses, tumor metastasis and thrombosis formation. Recently a commercial surface plasmon resonance (SPR)-based BIAcore biosensor has been extended to determine cell binding mediated by surface-bound biomolecular interactions. How such cell binding is quantitatively governed by kinetic rates and regulating factors, however, has been poorly understood. Here we developed a novel assay to determine the binding kinetics of surface-bound biomolecular interactions using a commercial BIAcore 3000 biosensor. Human red blood cells (RBCs) presenting blood group B antigen and CM5 chip bearing immobilized anti-B monoclonal antibody (mAb) were used to obtain the time courses of response unit, or sensorgrams, when flowing RBCs over the chip surface. A cellular kinetic model was proposed to correlate the sensorgrams with kinetic rates. Impacts of regulating factors, such as cell concentration, flow duration and rate, antibody-presenting level, as well as pH value and osmotic pressure of suspending medium were tested systematically, which imparted the confidence that the approach can be applied to kinetic measurements of cell adhesion mediated by surface-bound biomolecular interactions. These results provided a new insight into quantifying cell binding using a commercial SPR-based BIAcore biosensor.

Measuring Binding Kinetics Of Surface-Bound Molecules Using The Surface Plasmon Resonance Technique

Surface plasmon resonance (SPR) technology and the Biacore biosensor have been widely used to measure the kinetics of biomolecular interactions in the fluid phase. In the past decade, the assay was further extended to measure reaction kinetics when two counterpart molecules are anchored on apposed surfaces. However, the cell binding kinetics has not been well quantified. Here we report development of a cellular kinetic model, combined with experimental procedures for cell binding kinetic measurements, to predict kinetic rates per cell. Human red blood cells coated with bovine serum albumin and anti-BSA monoclonal antibodies (mAbs) immobilized on the chip were used to conduct the measurements. Sensor-grams for BSA-coated RBC binding onto and debinding from the anti-BSA mAb-immobilized chip were obtained using a commercial Biacore 3000 biosensor, and analyzed with the cellular kinetic model developed. Not only did the model fit the data well, but it also predicted cellular on and off-rates as well as binding affinities from curve fitting. The dependence of flow duration, flow rate, and site density of BSA on binding kinetics was tested systematically, which further validated the feasibility and reliability of the new approach. Crown copyright (c) 2008 Published by Elsevier Inc. All rights reserved.

Recognition of Membrane-Bound Fusion-Peptide/MPER Complexes by the HIV-1 Neutralizing 2F5 Antibody : Implications for Anti-2F5 Immunogenicity

13 p.