Locally Compact Research Articles

On the defect tolerance of fetal membranes.

A series of mechanical experiments were performed to quantify the strength and fracture toughness of human amnion and chorion. The experiments were complemented with computational investigations using a 'hybrid' model that includes an explicit representation of the collagen fibre network of amnion. Despite its much smaller thickness, amnion is shown to be stiffer, stronger and tougher than chorion, and thus to determine the mechanical response of fetal membranes, with respect to both, deformation and fracture behaviour. Data from uniaxial tension and fracture tests were used to inform and validate the computational model, which was then applied to rationalize measurements of the tear resistance of tissue samples containing crack-like defects. Experiments and computations show that the strength of amnion is not significantly reduced by defects smaller than 1 mm, but the crack size induced by perforations for amniocentesis and fetal membrane suturing during fetal surgery might be larger than this value. In line with previous experimental observations, the computational model predicts a very narrow near field at the crack tip of amnion, due to localized fibre alignment and collagen compaction. This mechanism shields the tissue from the defect and strongly reduces the interaction of multiple adjacent cracks. These findings were confirmed through corresponding experiments, showing that no interaction is expected for multiple sutures for an inter-suture distance larger than 1 mm and 3 mm for amnion and chorion, respectively. The experimental procedures and numerical models applied in the present study might be used to optimize needle and/or staple dimensions and inter-suture distance, and thus to reduce the risk of iatrogenic preterm premature rupture of the membranes from amniocentesis, fetoscopic and open prenatal surgery.

Simulation of localized compaction in Tuffeau de Maastricht based on evidence from X-ray tomography

Deformation experiments with concurrent X-ray microtomography are used to characterize the mechanical properties of a high-porosity carbonate rock from Central Europe (the Tuffeau de Maastricht). Evidence of deformation behavior and pressure-dependent strain localization for this rock are taken into account to define the parameters of an elastoplastic constitutive law with competing hardening and softening mechanisms. Full-field data regarding the compaction localization regime have been used to identify a compromise between compaction hardening and structure deterioration. It was shown that by placing emphasis on the destructuration behavior it was possible to reproduce features such as the elongation of the deformation plateau emerging during compaction band formation, as well as the pressure-dependent inclination of the ensuing compaction bands. Most notably, the comparison between measurements and simulations showed that the strategy here used to constrain the model parameters allows a satisfactory depiction of both the macroscopic deformations and the portion of sample volume across which the compaction zones develop and propagate. These results point out the major benefits of parameter calibration strategies accounting synergistically for global measurements and spatially-distributed deformations, especially in the presence of constitutive laws meant to replicate compaction localization.

Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems

<p style="text-indent:20px;">In this paper, we first prove that the property of being a gradient-like general dynamical system and the existence of a Morse decomposition are equivalent. Next, the stability of gradient-like general dynamical systems is analyzed. In particular, we show that a gradient-like general dynamical system is stable under perturbations, and that Morse sets are upper semi-continuous with respect to perturbations. Moreover, we prove that any solution of perturbed general dynamical systems should be close to some Morse set of the unperturbed gradient-like general dynamical system. We do not assume local compactness for the metric phase space <inline-formula><tex-math id="M1">\begin{document}$ X $\end{document}</tex-math></inline-formula>, unlike previous results in the literature. Finally, we extend the Morse decomposition theory of single-valued nonautonomous dynamical systems to the multi-valued case, without imposing any compactness of the parameter spaces.

Fluorescence fluctuation spectroscopy: an invaluable microscopy tool for uncovering the biophysical rules for navigating the nuclear landscape.

Nuclear architecture is fundamental to the manner by which molecules traverse the nucleus. The nucleoplasm is a crowded environment where dynamic rearrangements in local chromatin compaction locally redefine the space accessible toward nuclear protein diffusion. Here, we review a suite of methods based on fluorescence fluctuation spectroscopy (FFS) and how they have been employed to interrogate chromatin organization, as well as the impact this structural framework has on nuclear protein target search. From first focusing on a set of studies that apply FFS to an inert fluorescent tracer diffusing inside the nucleus of a living cell, we demonstrate the capacity of this technology to measure the accessibility of the nucleoplasm. Then with a baseline understanding of the exploration volume available to nuclear proteins during target search, we review direct applications of FFS to fluorescently labeled transcription factors (TFs). FFS can detect changes in TF mobility due to DNA binding, as well as the formation of TF complexes via changes in brightness due to oligomerization. Collectively, we find that FFS-based methods can uncover how nuclear proteins in general navigate the nuclear landscape.

Micromechanics of High‐Pressure Compaction in Granular Quartz Aggregates

AbstractThe mechanical behavior of porous sandstones is generally modeled using concepts from granular mechanics, often overlooking the effect of cementation. To probe the key differences between sand and sandstone mechanics, we performed triaxial deformation experiments on Ottawa quartz sand at 5‐ to 40 MPa effective confining pressure. At 5 MPa, the samples are able to dilate. At higher confinement, the aggregates show continuous compaction, displaying strain hardening. The stress‐strain behavior is nonlinear, and the exact onset of inelastic compaction could not be determined accurately. Measured P‐wave velocities show the development of anisotropy. With increasing axial strain, the along‐axis velocities tend to increase, while velocities perpendicular to the compression axis tend to decrease (at low pressure) or remain constant (at high pressure). In samples deformed under elevated pressure conditions, acoustic emission event locations are diffuse. Microstructural investigations show an increase in grain chipping and crushing with increasing confining pressure, but no evidence of localized compaction could be observed. The nature of the pore fluid, either decane or water, does not significantly influence the mechanical behavior at strain rates of 10−6 to 10−4 s−1. Grain angularity and grain‐size distribution also did not significantly change the mechanical behavior. We infer that our observations indicate that the lack of cementation introduces additional degrees of freedom for grains to slide, rotate, and reorganize at the sample scale, precluding the existence and sustainability of stress concentrations beyond the grain scale. This results in progressive compaction and hardening, and lack of compaction localization.

The convolution equation $$\varvec{\sigma *\mu =\mu }$$ on non-compact non-abelian semigroups

In probability theory, often in connection with problems on weak convergence, and also in other contexts, convolution equations of the form $$\sigma *\mu =\mu $$ come up. Many years ago, Choqet and Deny (C. R. Acad. Sci. Paris 250 (1960) 799–801) studied these equations in locally compact abelian groups. Later, Szekely and Zeng (J. Theoret. Probab. 3(2) (1990) 361–365) studied these equations in abelian semigroups. Like in [2], the results in [7] are also complete. Thus, these equations are studied here for the first time on non-compact non-abelian semigroups. Our main results are Theorems 3.1 and 3.3 in section 3. They are new results as far as we know, and also the best possible under a minor condition. All semigroups in this paper are, unless otherwise mentioned, locally compact Hausdorff second countable topological semigroups. Theorems 3.1 and 3.3 hold for these semigroups. Local compactness may not be necessary when all measures appearing in this context are assumed to be regular.

On the decomposition principle and a Persson type theorem for general regular Dirichlet forms

We present a decomposition principle for general regular Dirichlet forms satisfying a spatial local compactness condition. We use the decomposition principle to derive a Persson type theorem for the corresponding Dirichlet forms. In particular our setting covers Laplace–Beltrami operators on Riemannian manifolds, and Dirichlet forms associated to \alpha -stable processes in Euclidean space.

Simultaneous Subspace Clustering and Cluster Number Estimating Based on Triplet Relationship.

In this paper, we propose a unified framework to discover the number of clusters and group the data points into different clusters using subspace clustering simultaneously. Real data distributed in a high-dimensional space can be disentangled into a union of low-dimensional subspaces, which can benefit various applications. To explore such intrinsic structure, state-of-the-art subspace clustering approaches often optimize a self-representation problem among all samples, to construct a pairwise affinity graph for spectral clustering. However, a graph with pairwise similarities lacks robustness for segmentation, especially for samples which lie on the intersection of two subspaces. To address this problem, we design a hyper-correlation-based data structure termed as the triplet relationship, which reveals high relevance and local compactness among three samples. The triplet relationship can be derived from the self-representation matrix, and be utilized to iteratively assign the data points to clusters. Based on the triplet relationship, we propose a unified optimizing scheme to automatically calculate clustering assignments. Specifically, we optimize a model selection reward and a fusion reward by simultaneously maximizing the similarity of triplets from different clusters while minimizing the correlation of triplets from the same cluster. The proposed algorithm also automatically reveals the number of clusters and fuses groups to avoid over-segmentation. Extensive experimental results on both synthetic and real-world datasets validate the effectiveness and robustness of the proposed method.

Local compactness and nonvanishing for weakly singular nonlocal quadratic forms

In this work we study a class of nonlocal quadratic forms given by Ej(u,v)=12∫RN∫RN(u(x)−u(y))(v(x)−v(y))j(x−y)dxdy,where j:RN→[0,∞] is a measurable even function with min{1,|⋅|2}j∈L1(RN). Assuming merely j∉L1(RN), we show local compactness of the embedding Dj(RN)↪L2(RN), where Dj(RN) denotes the space of functions u∈L2(RN) with Ej(u,u)<∞. Using this local compactness, we establish an alternative which allows to distinguish vanishing and nonvanishing of bounded sequences in Dj(RN). As an application, we show the existence of maximizers for a class of integral functionals defined on the unit sphere in Dj(RN). Our main results extend to cylindrical unbounded sets of the type Ω=U×Rk, where U⊂RN−k is open and bounded. Finally, we note that a Poincaré inequality associated with Ej holds for unbounded domains of this type, thereby extending the corresponding result in Felsinger et al. (2015) for bounded domains.

Histomorphometric Analysis of Callus Formation Stimulated by Axial Dynamisation in a Standardised Ovine Osteotomy Model.

The cyclic axial dynamisation of a stabilised fracture is intended to promote callus formation and bone healing. Most studies focused on biomechanical properties or the quantity of new bone formation. Far less is known about the quality of newly formed callus tissues, such as tissue distribution and arrangement within the callus. The aim of this current study was to investigate the effect of cyclic, axial dynamisation on the quantity and quality of callus in an established delayed fracture healing model. In 41 sheep transverse osteotomies with a gap size of 3 mm were stabilised with a unilateral external fixator. In 32 of these, fracture ends were axially stimulated with displacement amplitudes of 0.8 mm, 0.4 mm, 0.2 mm, or 0.0 mm, respectively, for six weeks. In the remaining 9 sheep of the control group, an additional external fixator was mounted to achieve almost total rigidity. Animal material originating from a past animal experiment was reanalysed in this study. Histological thin-ground sections were histomorphometrically analysed regarding the histological structure and composition of the defect region. A slight tendency towards an increase in size of total callus area, area of new bone (nB.Ar), and cartilage (Cg.Ar) was detected with increasing displacement amplitudes compared to the control group. At the anterior callus side nB.Ar and Cg.Ar were significantly larger than at the posterior side in all groups independent of treatment. Regarding the quality of callus, areas of very compact bone were predominant in the treatment groups whereas in the control group a slight shift to more porous bone was observed. No difference of callus compactness was observed between the anterior and the posterior side. The established method to assess the local compactness of callus areas is a useful tool to quantitatively determine the spatial distribution of new bone tissue within the callus. The application of this method in combination with biomechanical testing might reveal interesting relations between tissue distribution and bone strength that, with traditional histomorphometry, cannot be identified.

Fréchet–Urysohn subspaces of free topological groups III

Let F(X) be the free topological group on a Tychonoff space X. For all natural numbers n we denote by Fn(X) the subset of F(X) consisting of all words of reduced length ≤n. In [11], the author found equivalent conditions on a metrizable space X for F3(X) to be Fréchet–Urysohn, and for Fn(X) to be Fréchet–Urysohn for n≥5. However, no equivalent condition on X for n=4 was found. Two years ago, we showed that for a locally compact separable metrizable space X, if the set of all non-isolated points of X is compact, then F4(X) is Fréchet–Urysohn, and recently, we proved that ‘separability’ of X is not necessary. In this paper, we show that ‘local compactness’ can be also omitted. Consequently, we obtain an equivalent condition on a metrizable space X for F4(X) to be Fréchet–Urysohn.

Dynamical Signatures of Local DNA Damage in Live Cells

The dynamic organization of chromatin inside the eukaryotic cell nucleus is essential to the regulation of the genome such as maintaining its integrity, gene expression and replication. However, the physical picture of chromatin structure and dynamics remains unclear and requires identifying the dynamical and structural signatures of specific biological processes. In this work, we study the chromatin dynamics in interphase, time between two cell divisions, in response to DNA damage. As shown previously, chromatin dynamics across the whole nucleus change dramatically after DNA damage; chromatin's coherent motion is eliminated, while its local mobility increases and its compaction decreases [1]. Here, we explore the local chromatin dynamics and compaction in response to local DNA damage in human cells. To do so, we induce double stranded DNA breaks (DSBs), which we visualize using 53BP1-mCherry, and observe the spatiotemporal evolution of their dynamics using single particle tracking. Simultaneously, we use histone H2B-GFP as a reporter on the chromatin compaction, to compare DSB dynamics inside the heterochromatin and euchromatin. To elucidate the dynamic signature of the local DNA damage response, we vary the number of DSBs as well as explore the ATP-dependence of these processes. Our preliminary results show the local subdiffusive dynamics of the DSBs changes with an increasing DSB count inside the cell nucleus. We also explore the relationship between the protein aggregation, diffusion coefficient and chromatin compaction at a DSB. [1] Zidovska A, Weitz DA & Mitchison TJ, Proc. Natl. Acad. Sci., 110(39), 15555-60, 2013.

Selective stiffening of fibrin hydrogels with micron resolution via photocrosslinking

Fibrin hydrogels are used as a model system for studying cell-ECM biophysical interactions. Bulk mechanical stiffness of these hydrogels has been correlated to mechanotransduction and downstream signaling. However, stiffness values proximal to cells can vary by orders of magnitude at the length scale of microns. Patterning of matrix stiffness at this spatial scale can be useful in studying such interactions. Here we present and evaluate a technique to selectively stiffen defined regions within a fibrin hydrogel. Laser scanning illumination activates ruthenium-catalyzed crosslinking of fibrin tyrosine residues, resulting in tunable stiffness changes spanning distances as small as a few microns and a localized compaction of the material. As probed by active microrheology, stiffness increases by as much as 25X, similar to previously observed stiffness changes around single cells in 3D culture. In summary, our method allows for selective modification of fibrin stiffness at the micron scale with the potential to create complex patterns, which could be valuable for the investigation of mechanotransduction in a biologically meaningful way. Statement of SignificanceFibrin hydrogels are used as a naturally derived model to study interactions between cells and their surrounding extracellular matrix (ECM). ECM stiffness influences cell state. Cells in 3D culture considerably modify the stiffness of their pericellular space, which can be quite heterogeneous at the micron-scale. Here we present and evaluate a method to pattern stiffness within fibrin hydrogels using a laser scanning confocal microscope and selective photo crosslinking. We believe that this technique can aid future studies of cell-ECM interactions by enabling researchers to modify the pericellular distribution of stiffness.

PSDSD-A Superpixel Generating Method Based on Pixel Saliency Difference and Spatial Distance for SAR Images.

Superpixel methods are widely used in the processing of synthetic aperture radar (SAR) images. In recent years, a number of superpixel algorithms for SAR images have been proposed, and have achieved acceptable results despite the inherent speckle noise of SAR images. However, it is still difficult for existing algorithms to obtain satisfactory results in the inhomogeneous edge and texture areas. To overcome those problems, we propose a superpixel generating method based on pixel saliency difference and spatial distance for SAR images in this article. Firstly, a saliency map is calculated based on the Gaussian kernel function weighted local contrast measure, which can not only effectively suppress the speckle noise, but also enhance the fuzzy edges and regions with intensity inhomogeneity. Secondly, superpixels are generated by the local k-means clustering method based on the proposed distance measure, which can efficiently sort pixels to different clusters. In this step, the distance measure is calculated by combining the saliency difference and spatial distance with a proposed adaptive local compactness parameter. Thirdly, post-processing is utilized to clean up small segments. The evaluation experiments on the simulated SAR image demonstrate that our proposed method dramatically outperforms four state-of-the-art methods in terms of boundary recall, under-segmentation error, and achievable segmentation accuracy under almost all of the experimental parameters at a moderate segment speed. The experiments on real-world SAR images of different sceneries validate the superiority of our method. The superpixel results of the proposed method adhere well to the contour of targets, and correctly reflect the boundaries of texture details for the inhomogeneous regions.

Assessment of Reinforced Concrete Building for Disaster Reduction Strategy in Padang City, West Sumatra, Indonesia

Padang City, West Sumatra province is one of the most vulnerable cities in the west coast of Indonesia. Together with the increase in population in Padang City, the number of the building is also increasing. Meanwhile, researchers predicted that Padang City is facing the impendence of mega-earthquake with magnitude more than 8 in scale Richter (SR). The last Earthquake with magnitude 7.6 SR caused fatality with more than 1200 people died and almost 3000 others were injured. Most of the victims injured due to the collapse and damage of buildings, especially the Reinforced Concrete (RC) structure. To reduce the damage due to seismic load as the preparation for the future earthquake, the assessment of the element at risk subjected to the seismic load in Padang City is essential. The predominant building typology in Padang City is RC building. Using the Applied Element Method that can show structural response till collapse state, has been simulated typical low-rise RC infilled wall building in Padang City with the consideration of its different on concrete quality based on local concreting workmanship. Incremental Dynamic Analysis (IDA) by using some ground motion has been used to observe the structural response. The damage states and damage pattern has been judged based on HAZUS criteria. The results show that local compaction method affected the concrete compression quality, that also influences the building performance which is subjected to earthquake loads.

Characterizing early drug resistance-related events using geometric ensembles from HIV protease dynamics

The use of antiretrovirals (ARVs) has drastically improved the life quality and expectancy of HIV patients since their introduction in health care. Several millions are still afflicted worldwide by HIV and ARV resistance is a constant concern for both healthcare practitioners and patients, as while treatment options are finite, the virus constantly adapts via complex mutation patterns to select for resistant strains under the pressure of drug treatment. The HIV protease is a crucial enzyme for viral maturation and has been a game changing drug target since the first application. Due to similarities in protease inhibitor designs, drug cross-resistance is not uncommon across ARVs of the same class. It is known that resistance against protease inhibitors is associated with a wider active site, but results from our large scale molecular dynamics simulations combined with statistical tests and network analysis further show, for the first time, that there are regions of local expansions and compactions associated with high levels of resistance conserved across eight different protease inhibitors visible in their complexed form within closed receptor conformations. The observed conserved expansion sites may provide an alternative drug-targeting site. Further, the method developed here is novel, supplementary to methods of variation analysis at sequence level, and should be applicable in analysing the structural consequences of mutations in other contexts using molecular ensembles.

Local dilation and compaction of granular materials induced by plate drag

The response of granular materials to plate drag is numerically studied using a large-scale discrete element method (DEM) simulation. The effect of the initial volume fraction of the materials on the drag force acting on the plate is examined. The results show that a volume-fraction-dependent bifurcation occurs in the force; in an initially loose granular bed, the force reaches an approximately constant value as the plate advances, while in an initially dense bed, the force oscillates with a large amplitude. The force oscillation is attributed to the periodic evolution of a shear band formed only in the dense bed. The behaviors of the drag force and shear band, which depend on the initial volume fraction in the DEM simulation, are in close agreement with those obtained experimentally in previous studies [N. Gravish et al., Phys. Rev. Lett. 105, 128301 (2010); Phys. Rev. E 89, 042202 (2014)]. Further analysis using the DEM simulation shows that the formation of the shear band is explained by the local dilation and compaction of the granular materials induced by the plate drag. Independent of the volume fraction, materials dilate in a wedge-shaped flow region that formed in front of the plate. In the loose bed, a compacted front builds up ahead of the flow region. Because the compacted front advances into a weaker undisturbed region, the flow region behind the front can constantly advance. On the other hand, in the dense bed, the materials largely dilate in a disturbed flow region formed in front of the plate. Because a denser undisturbed region is more stable compared to the flow region, the flow region is strongly confined. As a result, the shear strain is localized along a flow boundary between these regions, and the shear band develops.

Time and Temperature Dependent Creep in Tournemire Shale

AbstractWe conducted a series of triaxial creep experiments on shale specimens coming from Tournemire, France, using the stress‐stepping method up to failure, at a confining pressure of 80 MPa, on two orientations (parallel and perpendicular to bedding), and at temperatures of 26 and 75 °C. In these week‐long experiments, stress, strains, and P wave ultrasonic velocities were recorded (quasi‐) continuously. The strength at creep failure of Tournemire shale was ~70% higher than the peak strength measured during constant strain rate (~10−7/s) experiments, and failure was reached at larger strains. An overall transition from P wave velocity increase at moderate differential stress to P wave velocity decrease closer to brittle failure was also observed. At a smaller timescale, P wave velocities initially decreased and then increased gradually during each step of creep deformation. The magnitude of these variations showed important (i) stress, (ii) orientation, and (iii) temperature dependences: larger increase was observed for P wave propagating along the main compressive stress orientation, larger decrease for P wave propagating perpendicular to it, and a changing behavior enhanced at a higher temperature. Scanning electron microscopy performed postmortem revealed evidence of time‐dependent pressure solution, localized compaction, crack growth, and sealing/healing. Our data reveal that shale deformation is highly stress sensitive only in a narrow stress domain where stress corrosion cracking‐induced brittle dilatant creep deformation is dominant. At stresses below, pressure solution compaction creep dominates the deformation and shales compact, consolidate, and heal. This has important implications for the mechanics of shallow fault zones and accretionary prisms.

Oat-Sowing Methods on Drained Lands

The article presents the results of research on oat-sowing methods on drained lands. The research was carried out on the experimental fields of the Federal State Budgetary Scientific Institution All-Russia Research Institute of Reclaimed Lands (VNIIMZ). In experiments, ordinary row (SZ-3.6), surface-scattered, and comb-like band-scattered sowing methods were compared. It has been established that oats on desiccated lands should be grown on crests 40–80 mm high with local compaction of soil under the crest and pressing seeds into the soil. The yield increments with the comb method of sowing are 0.13–0.39 t/ha or 3.6–13.9% in relation to the existing sowing technology (SZ-3.6), and direct costs for the production of 1 t of grain are reduced by 2.9–10.5%. The yield of oats was increased, mainly due to an increase in the number of grains in a panicle by 4.2–9.8 pieces, and its total productivity was increased by 11.3–34.7%. Pressing seeds into the soil with the comb method of sowing increased the yield of oats against the background of cultivation by 0.21–0.28 t/ha, increased the safety of oat plants, increased the number of stems with a panicle at 9.2–11.5%, and the mass of the grain in a panicle by 1.9–6.5% due to the increase in the number of grains. A certain interest for the conditions of the northwest of the Nonchernozem zone, especially of small peasant holdings, is also represented by the scattered method of sowing oats without coulter. Labor productivity in sowing increases 1.5–3 times, labor costs per 1 hectare during sowing operations are reduced by 37.6–58.4%, and fuel consumption is reduced by 7.4–39.2%. When using trailed spreaders of mineral fertilizers for sowing seeds, there is no need for separate auxiliary operations, special loaders and transport for seed transportation. At the same time, the terms of field work are reduced, the adaptation of seeding technology to soil-meliorative conditions is increased, and the sealing effect of running systems of tractors and machines on soil is reduced (by 2–4 times).

Locally compact groups with totally disconnected space of subgroups

Abstract The closed subsets ℱ ⁢ ( X ) {\mathcal{F}(X)} of any topological space can be given a topology, called the Chabauty–Fell topology, in which ℱ ⁢ ( X ) {\mathcal{F}(X)} is quasi-compact. If X is a locally compact space, then ℱ ⁢ ( X ) {\mathcal{F}(X)} is Hausdorff. If X = G {X=G} is a locally compact group, then the subset 𝒮 ⁢ 𝒰 ⁢ ℬ ⁢ ( G ) {\mathcal{S\kern-0.853583ptU\kern-0.569055ptB}(G)} of closed subgroups is closed in ℱ ⁢ ( G ) {\mathcal{F}(G)} , and the set of closed subgroups inherits its own compact topology, called the Chabauty topology. We develop some of the important properties of this topology. More precisely, the results contained in this paper deal with the following question: Given a locally compact topological group, when is ℱ ⁢ ( G ) {\mathcal{F}(G)} (resp. 𝒮 ⁢ 𝒰 ⁢ ℬ ⁢ ( G ) {\mathcal{S\kern-0.853583ptU\kern-0.569055ptB}(G)} ) a totally disconnected space?