Comparing methods for modelling spreading cell fronts

Spreading cell fronts play an essential role in many physiological processes. Classically, models of this process are based on the Fisher-Kolmogorov equation; however, such continuum representations are not always suitable as they do not explicitly represent behaviour at the level of individual cells. Additionally, many models examine only the large time asymptotic behaviour, where a travelling wave front with a constant speed has been established. Many experiments, such as a scratch assay, never display this asymptotic behaviour, and in these cases the transient behaviour must be taken into account. We examine the transient and asymptotic behaviour of moving cell fronts using techniques that go beyond the continuum approximation via a volume-excluding birth-migration process on a regular one-dimensional lattice. We approximate the averaged discrete results using three methods: (i) mean-field, (ii) pair-wise, and (iii) one-hole approximations. We discuss the performace of these methods, in comparison to the averaged discrete results, for a range of parameter space, examining both the transient and asymptotic behaviours. The one-hole approximation, based on techniques from statistical physics, is not capable of predicting transient behaviour but provides excellent agreement with the asymptotic behaviour of the averaged discrete results, provided that cells are proliferating fast enough relative to their rate of migration. The mean-field and pair-wise approximations give indistinguishable asymptotic results, which agree with the averaged discrete results when cells are migrating much more rapidly than they are proliferating. The pair-wise approximation performs better in the transient region than does the mean-field, despite having the same asymptotic behaviour. Our results show that each approximation only works in specific situations, thus we must be careful to use a suitable approximation for a given system, otherwise inaccurate predictions could be made.

On the hardness of the sum of K mins problem

The sum of k mins protocol was proposed by Hopper and Blum as a protocol for secure human identification. The goal of the protocol is to let an unaided human securely authenticate to a remote server. The main ingredient of the protocol is the sum of k mins problem. The difficulty of solving this problem determines the security of the protocol. In this paper, we show that the sum of k mins problem is NP-Complete and W[1]-Hard. This latter notion relates to fixed parameter intractability. We also discuss the use of the sum of k mins protocol in resource-constrained devices.

NTRUCCA : how to strengthen NTRUEncrypt to chosen-ciphertext security in the standard model

NTRUEncrypt is a fast and practical lattice-based public-key encryption scheme, which has been standardized by IEEE, but until recently, its security analysis relied only on heuristic arguments. Recently, Stehlé and Steinfeld showed that a slight variant (that we call pNE) could be proven to be secure under chosen-plaintext attack (IND-CPA), assuming the hardness of worst-case problems in ideal lattices. We present a variant of pNE called NTRUCCA, that is IND-CCA2 secure in the standard model assuming the hardness of worst-case problems in ideal lattices, and only incurs a constant factor overhead in ciphertext and key length over the pNE scheme. To our knowledge, our result gives the first IND-CCA2 secure variant of NTRUEncrypt in the standard model, based on standard cryptographic assumptions. As an intermediate step, we present a construction for an All-But-One (ABO) lossy trapdoor function from pNE, which may be of independent interest. Our scheme uses the lossy trapdoor function framework of Peikert and Waters, which we generalize to the case of (k − 1)-of-k-correlated input distributions.

The molecular structure of the borate mineral rhodizite (K, Cs)Al4Be4(B, Be)12O28 – A vibrational spectroscopic study

We have studied the borate mineral rhodizite (K, Cs)Al4Be4(B, Be)12O28 using a combination of DEM with EDX and vibrational spectroscopic techniques. The mineral occurs as colorless, gray, yellow to white crystals in the triclinic crystal system. The studied sample is from the Antandrokomby Mine, Sahatany valley, Madagascar. The mineral is prized as a semi-precious jewel. Semi-quantitative chemical composition shows a Al, Ca, borate with minor amounts of K, Mg and Cs. The mineral has a characteristic borate Raman spectrum and bands are assigned to the stretching and bending modes of B, Be and Al. No Raman bands in the OH stretching region were observed.

Improved healing of large segmental defects in the rat femur by reverse dynamization in the presence of bone morphogenetic protein-2

Background Large segmental defects in bone do not heal well and present clinical challenges. This study investigated modulation of the mechanical environment as a means of improving bone healing in the presence of bone morphogenetic protein (BMP)-2. Although the influence of mechanical forces on the healing of fractures is well established, no previous studies, to our knowledge, have described their influence on the healing of large segmental defects. We hypothesized that bone-healing would be improved by initial, low-stiffness fixation of the defect, followed by high-stiffness fixation during the healing process. We call this reverse dynamization. Methods A rat model of a critical-sized femoral defect was used. External fixators were constructed to provide different degrees of stiffness and, importantly, the ability to change stiffness during the healing process in vivo. Healing of the critical-sized defects was initiated by the implantation of 11 mg of recombinant human BMP (rhBMP)-2 on a collagen sponge. Groups of rats receiving BMP-2 were allowed to heal with low, medium, and high-stiffness fixators, as well as under conditions of reverse dynamization, in which the stiffness was changed from low to high at two weeks. Healing was assessed at eight weeks with use of radiographs, histological analysis, microcomputed tomography, dual x-ray absorptiometry, and mechanical testing. Results Under constant stiffness, the low-stiffness fixator produced the best healing after eight weeks. However, reverse dynamization provided considerable improvement, resulting in a marked acceleration of the healing process by all of the criteria of this study. The histological data suggest that this was the result of intramembranous, rather than endochondral, ossification. Conclusions Reverse dynamization accelerated healing in the presence of BMP-2 in the rat femur and is worthy of further investigation as a means of improving the healing of large segmental bone defects. Clinical Relevance These data provide the basis of a novel, simple, and inexpensive way to improve the healing of critical-sized defects in long bones. Reverse dynamization may also be applicable to other circumstances in which bonehealing is problematic.

Calibration functions for estimating soil moisture from GPR dielectric constant measurements

Ground-penetrating radar (GPR) is widely used for assessment of soil moisture variability in field soils. Because GPR does not measure soil water content directly, it is common practice to use calibration functions that describe its relationship with the soil dielectric properties and textural parameters. However, the large variety of models complicates the selection of the appropriate function. In this article an overview is presented of the different functions available, including volumetric models, empirical functions, effective medium theories, and frequency-specific functions. Using detailed information presented in summary tables, the choice for which calibration function to use can be guided by the soil variables available to the user, the frequency of the GPR equipment, and the desired level of detail of the output. This article can thus serve as a guide for GPR practitioners to obtain soil moisture values and to estimate soil dielectric properties.

ORIGO Stepping Stones Grade K Student Journal

A mathematics curriculum for the Common Core Curriculum at the Kindergarten level for the USA

Top-k retrieval using facility location analysis

The top-k retrieval problem aims to find the optimal set of k documents from a number of relevant documents given the user’s query. The key issue is to balance the relevance and diversity of the top-k search results. In this paper, we address this problem using Facility Location Analysis taken from Operations Research, where the locations of facilities are optimally chosen according to some criteria. We show how this analysis technique is a generalization of state-of-the-art retrieval models for diversification (such as the Modern Portfolio Theory for Information Retrieval), which treat the top-k search results like “obnoxious facilities” that should be dispersed as far as possible from each other. However, Facility Location Analysis suggests that the top-k search results could be treated like “desirable facilities” to be placed as close as possible to their customers. This leads to a new top-k retrieval model where the best representatives of the relevant documents are selected. In a series of experiments conducted on two TREC diversity collections, we show that significant improvements can be made over the current state-of-the-art through this alternative treatment of the top-k retrieval problem.

Power buffer with model predictive control for stability of vehicular power systems with constant power loads

Electrification of vehicular systems has gained increased momentum in recent years with particular attention to constant power loads (CPLs). Since a CPL potentially threatens system stability, stability analysis of hybrid electric vehicle with CPLs becomes necessary. A new power buffer configuration with battery is introduced to mitigate the effect of instability caused by CPLs. Model predictive control (MPC) is applied to regulate the power buffer to decouple source and load dynamics. Moreover, MPC provides an optimal tradeoff between modification of load impedance, variation of dc-link voltage and battery current ripples. This is particularly important during transients or starting of system faults, since battery response is not very fast. Optimal tradeoff becomes even more significant when considering low-cost power buffer without battery. This paper analyzes system models for both voltage swell and voltage dip faults. Furthermore, a dual mode MPC algorithm is implemented in real time offering improved stability. A comprehensive set of experimental results is included to verify the efficacy of the proposed power buffer.

Modeling and analysis of a novel variable-speed cage induction generator

This paper introduces a novel cage induction generator and presents a mathematical model, through which its behavior can be accurately predicted. The proposed generator system employs a three-phase cage induction machine and generates single-phase and constant-frequency electricity at varying rotor speeds without an intermediate inverter stage. The technique uses any one of the three stator phases of the machine as the excitation winding and the remaining two phases, which are connected in series, as the power winding. The two-series-connected-and-one-isolated (TSCAOI) phase winding configuration magnetically decouples the two sets of windings, enabling independent control. Electricity is generated through the power winding at both sub- and super-synchronous speeds with appropriate excitation to the isolated single winding at any frequency of generation. A dynamic mathematical model, which accurately predicts the behavior of the proposed generator, is also presented and implemented in MATLAB/Simulink. Experimental results of a 2-kW prototype generator under various operating conditions are presented, together with theoretical results, to demonstrate the viability of the TSCAOI power generation. The proposed generator is simple and capable of both storage and retrieval of energy through its excitation winding and is expected to be suitable for applications, such as small wind turbines and microhydro systems.

Hydrolysis of triasulfuron, metsulfuron-methyl and chlorsulfuron in alkaline soil and aqueous solutions

The hydrolysis of triasulfuron, metsulfuron-methyl and chlorsulfuron in aqueous buffer solutions and in soil suspensions at pH values ranging from 5.2 to 11.2 was investigated. Hydrolysis of all three compounds in both aqueous buffer and soil suspensions was highly pH-sensitive. The rate of hydrolysis was much faster in the acidic pH range (5.2-6.2) than under neutral and moderately alkaline conditions (8.2-9.4), but it increased rapidly as the pH exceeded 10.2. All three compounds degraded faster at pH 5.2 than at pH 11.2. Hydrolysis rates of all three compounds could be described well with pseudo-first-order kinetics. There were no significant differences (P =0.05) in the rate constants (k, day-1) of the three compounds in soil suspensions from those in buffer solutions within the pH ranges studied. A functional relationship based on the propensity of nonionic and anionic species of the herbicides to hydrolyse was used to describe the dependence of the 'rate constant' on pH. The hydrolysis involving attack by neutral water was at least 100-fold faster when the sulfonylurea herbicides were undissociated (acidic conditions) than when they were present as the anion at near neutral pH. In aqueous buffer solution at pH > 11, a prominent degradation pathway involved O-demethylation of metsulfuron-methyl to yield a highly polar degradate, and hydrolytic opening of the triazine ring. It is concluded that these herbicides are not likely to degrade substantially through hydrolysis in most agricultural (C) 2000 Society of Chemical Industry.