Dynamic Relative Compression, Dynamic Partial Sums, and Substring Concatenation

Given a static reference string $R$ and a source string $S$, a relative compression of $S$ with respect to $R$ is an encoding of $S$ as a sequence of references to substrings of $R$. Relative compression schemes are a classic model of compression and have recently proved very successful for compressing highly-repetitive massive data sets such as genomes and web-data. We initiate the study of relative compression in a dynamic setting where the compressed source string $S$ is subject to edit operations. The goal is to maintain the compressed representation compactly, while supporting edits and allowing efficient random access to the (uncompressed) source string. We present new data structures that achieve optimal time for updates and queries while using space linear in the size of the optimal relative compression, for nearly all combinations of parameters. We also present solutions for restricted and extended sets of updates. To achieve these results, we revisit the dynamic partial sums problem and the substring concatenation problem. We present new optimal or near optimal bounds for these problems. Plugging in our new results we also immediately obtain new bounds for the string indexing for patterns with wildcards problem and the dynamic text and static pattern matching problem

Dynamic Relative Compression, Dynamic Partial Sums, and Substring Concatenation

Given a static reference string R and a source string S, a relative compression of S with respect to R is an encoding of S as a sequence of references to substrings of R. Relative compression schemes are a classic model of compression and have recently proved very successful for compressing highly-repetitive massive data sets such as genomes and web-data. We initiate the study of relative compression in a dynamic setting where the compressed source string S is subject to edit operations. The goal is to maintain the compressed representation compactly, while supporting edits and allowing efficient random access to the (uncompressed) source string. We present new data structures that achieve optimal time for updates and queries while using space linear in the size of the optimal relative compression, for nearly all combinations of parameters. We also present solutions for restricted and extended sets of updates. To achieve these results, we revisit the dynamic partial sums problem and the substring concatenation problem. We present new optimal or near optimal bounds for these problems. Plugging in our new results we also immediately obtain new bounds for the string indexing for patterns with wildcards problem and the dynamic text and static pattern matching problem

Dynamic compressive response of additively manufactured AlSi10Mg alloy hierarchical honeycomb structures

Periodic honeycombs have been used for their high strength, low weight and multifunctionality. The quasi-static and dynamic compressive responses of three types of additively manufactured AlSi10Mg honeycomb structures, specifically a single-scale honeycomb and two hierarchical honeycombs with two and three levels of hierarchy, respectively, have been investigated using experimental measurement and finite element (FE) simulations. The validated FE simulation has been employed to investigate the effects of relative density of the honeycombs and the key experimental parameters. The following failure modes of the three types of honeycombs have been observed both under quasi-static and dynamic compression: (1) the single-scale honeycomb experienced a transition of failure mechanism from local plastic buckling of walls to local damage of the parent material without buckling with the increase of the relative density of the honeycomb; (2) the hierarchical honeycombs all failed with parent material damage without buckling at different relative densities. For both quasi-static and dynamic compression, the hierarchical honeycombs offer higher peak nominal wall stresses compared to the single-scale honeycomb at low relative density of ; the difference is diminished as relative density increases, i.e. the three types of honeycombs can achieve similar peak wall stresses when Numerical results have suggested the hierarchical honeycombs can offer better energy absorption capacity than the single-scale honeycomb. The two-scale and three-scale hierarchical honeycombs achieved similar peak nominal wall stresses for both quasi-static and dynamic compression, which may suggest that the structural performance under out-of-plane compression is not sensitive to the hierarchical architecture. This work indicates that the structural advantage of hierarchical honeycombs can be utilised to develop high performance lightweight structural components

Rheological properties of aging thermosensitive suspensions

Aging observed in soft glassy materials inherently affects the rheological properties of these systems and has been described by the soft glassy rheology (SGR) model [S. M. Fielding et al., J. Rheol. 44, 323 (2000)]. In this paper, we report the measured linear rheological behavior of thermosensitive microgel suspensions and compare it quantitatively with the predictions of the SGR model. The dynamic moduli [G[prime](omega,t) and G[double-prime](omega,t)] obtained from oscillatory measurements are in good agreement with the model. The model also predicts quantitatively the creep compliance J(t−tw,tw), obtained from step stress experiments, for the short time regime [(t−tw)<tw]. The relative effective temperature [script X]/[script X]g obtained from both the oscillatory and the step stress experiments is indeed less than 1 ([script X]/[script X]g<1) in agreement with the definition of aging. Moreover, the elasticity of the compressed particles (Gp) increases with increased compression, i.e., the degree of hindrance and consequently also the bulk elasticity (G[prime] and 1/J) increases with the degree of compression

Influence of texture on the recrystallization mechanisms in an AZ31 Mg sheet alloy at dynamic rates

An AZ31 rolled sheet alloy has been tested at dynamic strain rates View the MathML source at 250 °C up to various intermediate strains before failure in order to investigate the predominant deformation and restoration mechanisms. In particular, tests have been carried out in compression along the rolling direction (RD), in tension along the RD and in compression along the normal direction (ND). It has been found that dynamic recrystallization (DRX) takes place despite the limited diffusion taking place under the high strain rates investigated. The DRX mechanisms and kinetics depend on the operative deformation mechanisms and thus vary for different loading modes (tension, compression) as well as for different relative orientations between the loading axis and the c-axes of the grains. In particular, DRX is enhanced by the operation of 〈c + a〉 slip, since cross-slip and climb take place more readily than for other slip systems, and thus the formation of high angle boundaries is easier. DRX is also clearly promoted by twinning

Unexpected dynamic transformation from α phase to β phase in zirconium alloy revealed by in-situ neutron diffraction during high temperature deformation

Dynamic transformation from alpha (HCP) to beta (BCC) phase in a zirconium alloy was revealed by the use of in-situ neutron diffraction during hot compression. The dynamic transformation was unexpectedly detected during isothermal compression at temperatures of 900°C and 950°C (alpha + beta two-phase region) and strain rates of 0.01 s⁻¹ and 0.001 s⁻¹, even though equilibrium two-phase states were achieved prior to the hot compression. Dynamic transformation was accompanied by diffusion of Sn from beta to alpha phase, which resulted in changes of lattice parameters and a characteristic microstructure of alpha grains. The lattice constant of alpha phase measured by the in-situ neutron diffraction increased during the hot compression, while the lattice constant of beta phase exhibited an initial increase and subsequent decrease during the hot compression. As a result, the magnitude of lattice (elastic) strain as well as stress (elastic stress, or phase stress) in alpha phase was found to become much greater than those in beta phase. According to an atomistic simulation, the Gibbs free energy of alpha phase increased with hydrostatic compressive pressure more evidently than that of beta phase. It could be concluded from such results that the occurrence of the dynamic transformation from alpha to beta is attributed to an increase in the Gibbs free energy of alpha phase relative to beta phase owing to the difference in the phase stress; i.e., the larger lattice distortion made alpha phase thermodynamically more unstable than beta phase. The present result suggests that deformation of two-phase materials can dynamically make Gibbs free energy of plastically harder phase higher than that of the softer phase through increasing elastic energy in the harder phase, which might lead to dynamic transformation from harder phase to softer phase

Can Dynamic Compression in the Absence of Growth Factors Induce Chondrogenic Differentiation of Bone Marrow Derived MSCs Encapsulated in Agarose Hydrogels?

The objectives of this study were twofold; to determine if cartilage specific matrix synthesis by mesenchymal stem cells (MSCs) is regulated by the magnitude and/or duration of dynamic compression in the absence of growth factors, and to investigate if expanding MSCs in the presence of both fibroblast growth factor-2 (FGF-2) and transforming growth factor β-3 (TGF-β3) would influence their subsequent response to dynamic compression following encapsulation in agarose hydrogels. Porcine bone marrow derived MSCs were suspended in agarose and cast to produce cylinders (Ø5×3mm). Constructs were maintained in a chemically defined medium. Dynamic compression was applied at 1 Hz at strain amplitudes of 5%, 10% and 5% superimposed upon a 5% pre-strain for durations of 1, 3 and 12 hours. MSCs were also expanded in the presence of FGF-2 and TGF-β3. The biochemical constituents of constructs were analyzed. Under strain magnitudes of 5% and 10% and durations of 1 and 3 hours small increases in sGAG accumulation relative to unloaded controls were observed. However this was orders of magnitude lower than that induced by TGF-β3 stimulation. Expansion in FGF-2 and TGF-β3 did not positively modulate chondrogenesis of MSCs in either unloaded or loaded culture