Saturated Sets Research Articles

Establishment of a resazurin-based aortic valve tissue viability assay for dynamic culture in a microphysiological system.

Tissue pathogenesis of aortic valve (AV) stenosis is research focus in cardiac surgery. Model limitations of conventional 2D culture of human or porcine valvular interstitial/endothelial cells (VIC/VECs) isolated from aortic valve tissues but also limited ability of (small) animal models to reflect human (patho)physiological situation in AV position raise the need to establish an in vitro setup using AV tissues. Resulting aim is to approximate (patho)physiological conditions in a dynamic pulsatile Microphysiological System (MPS) to culture human and porcine AV tissue with preservation of tissue viability but also defined ECM composition. A tissue incubation chamber (TIC) was designed to implement human or porcine tissues (3×5 mm2) in a dynamic pulsatile culture in conventional cell culture ambience in a MPS. Cell viability assays based on lactate dehydrogenase (LDH)-release or resazurin-conversion were tested for applicability in the system and applied for a culture period of 14 days with interval evaluation of tissue viability on every other day. Resazurin-assay setup was compared in static vs. dynamic culture using varying substance saturation settings (50-300μM), incubation times and tissue masses and was consequently adapted. Sterile dynamic culture of human and porcine AV tissue segments was established at a pulsatile flow rate range of 0.9-13.4μl/s. Implementation of tissues was realized by stitching the material in a thermoplastic polyurethane (TPU)-ring and insertion in the TIC-MPS-system. Culture volume of 2 ml caused LDH dilution not detectable in standard membrane integrity assay setup. Therefore, detection of resazurin-conversion of viable tissue was investigated. Optimal incubation time for viability conversion was determined at two hours at a saturated concentration of 300μM resazurin. Measurement in static conditions was shown to offer comparable results as dynamic condition but allowing optimal handling and TIC sterilization protocols for long term culture. Preliminary results revealed favourable porcine AV tissue viability over a 14 day period confirmed via resazurin-assay comparing statically cultured tissue counterparts. Human and porcine AV tissue can be dynamically cultured in a TIC-MPS with monitoring of tissue viability using an adapted resazurin-assay setup. Preliminary results reveal advantageous viability of porcine AV tissues after dynamic TIC-MPS culture compared to static control.

David Blackstock and the physics of nonlinear sound beams

In the 1970s, David Blackstock and his students and colleagues examined nonlinear sound beams both theoretically and experimentally. Two noteworthy articles in JASA resulted from this research, one by Shooter, Muir and Blackstock (1974) and another by Lockwood, Muir and Blackstock (1973). Of particular interest was the generation of highly directive radiation at harmonics of the source frequency that at moderate source levels decreased in beamwidth with harmonic order. Additional sidelobes were also observed in the harmonics. The main lobe in both the fundamental and the harmonics eventually broadened with increasing source level as shock waves were formed. Eventually finite-amplitude absorption became significant, acoustic saturation set in, and the medium did not permit further increase in amplitude. David’s application of weak-shock theory to model this process was validated by underwater acoustic experiments at the Applied Research Laboratories Lake Travis Test Station involving transducers driven at high intensities, at several hundred kilohertz, with waveforms and beams measured at ranges of several hundred meters. The results provided guidance for many applications, ranging from audio frequency tools in ocean acoustics to ultrasonic biomedical instruments now used worldwide in diagnostic and therapeutic applications. [Work supported by ARL:UT.]

Effect of acupuncture combined with rehabilitation on cognitive and motor functions in poststroke patients.

The aim of the study was to explore the effect of acupuncture combined with rehabilitation on cognitive and motor functions in poststroke patients. All patients were divided into Group A and Group B based on different interventions (Group A: acupuncture + conventional rehabilitation, Group B: conventional rehabilitation alone). Acupuncture was conducted once a day, five times a week for 8 weeks, and rehabilitation (including physical therapy and occupational therapy) was conducted for 2 hr per session, once a day, five times a week for 8 weeks. Mini-mental State Examination (MMSE) and Fugl-Meyer Assessment (FMA) were used to assess the motor and cognitive functions at baseline and the end of 8 weeks. After the intervention, FMA and MMSE scores were improved significantly in the two groups (p <.05), compared with the scores prior to intervention. After 8 weeks of intervention, a statistically significant difference in the FMA and MMSE scores was observed between the Group A and the Group B. The results suggested that the combined intervention is more effective than the conventional rehabilitation alone in improving cognitive and motor functions in poststroke patients.

Estimation of construction waste composition based on bulk density: A big data-probability (BD-P) model

Estimating the composition of construction waste is crucial to the efficient operation of various waste management facilities, such as landfills, public fills, and sorting plants. However, this estimating task is often challenged by the desire of quickness and accuracy in real-life scenarios. By harnessing a valuable data set in Hong Kong, this research develops a big data-probability (BD-P) model to estimate construction waste composition based on bulk density. Using a saturated data set of 4.27 million truckloads of construction waste, the probability distribution of construction waste bulk density is derived, and then, based on the Law of Joint Probability, the BD-P model is developed. A validation experiment using 604 ground truth data entries indicates a model accuracy of 90.2%, Area Under Curve (AUC) of 0.8775, and speed of around 52 s per load in estimating the composition of each incoming construction waste load. The BD-P model also informed a linear model which can perform the estimation with an accuracy of 88.8% but consuming 0.4 s per case. The major novelty of this research is to harmonize big data analytics and traditional probability theories in improving the classic challenge of predictive analyses. In the practical sphere, it satisfactorily solves the construction waste estimation problem faced by many waste management facility operators. In the academic sphere, this research provides a vivid example that big data and theories are not adversaries, but allies.

Some characterizations of weak sobriety and upper spaces

Weak sobriety is a topological property that gives rise to a categorical equivalence between topological spaces and distributive lattices without a least element. In this paper, we give some characterizations of weak sobriety and obtain some characterizations of local compactness, core-compactness and coherence of the special topological space by its upper space, where the upper space of a space is the set of all nonempty saturated compact sets equipped with the upper Vietoris topology. We obtain that a weak well-filtered space is core-compact iff it is locally compact. We also show that Ψχp-fine is equal to Ψωp-fine for a topological space under the condition of local compactness, which answers an open problem.

A Volumetric Analysis of the 1H NMR Chemical Shielding in Supramolecular Systems.

The liquid state NMR chemical shift of protons is a parameter frequently used to characterize host–guest complexes. Its theoretical counterpart, that is, the 1H NMR chemical shielding affected by the solvent (1H CS), may provide important insights into spatial arrangements of supramolecular systems, and it can also be reliably obtained for challenging cases of an aggregation of aromatic and antiaromatic molecules in solution. This computational analysis is performed for the complex of coronene and an antiaromatic model compound in acetonitrile by employing the GIAO-B3LYP-PCM approach combined with a saturated basis set. Predicted 1H CS values are used to generate volumetric data, whose properties are thoroughly investigated. The 1H CS isosurface, corresponding to a value of the proton chemical shift taken from a previous experimental study, is described. The presence of the 1H CS isosurface should be taken into account in deriving structural information about supramolecular hosts and their encapsulation of small molecules.

Coincidence of the upper Vietoris topology and the Scott topology

For a T0 space X, let K(X) be the poset of all non-empty compact saturated sets of X with the reverse inclusion order. The space X is said to have property Q if for any K1,K2∈K(X), K1≪K2 in K(X) iff K2⊆intK1. In this paper, we give several connections among the well-filteredness of X, the sobriety of X, the local compactness of X, the core compactness of X, the property Q of X, the coincidence of the upper Vietoris topology and Scott topology on K(X), and the continuity of x↦↑x:X⟶ΣK(X) (where ΣK(X) is the Scott space of K(X)). It is shown that for a well-filtered space X for which its Smyth power space PS(X) is first-countable, the following three properties are equivalent: the local compactness of X, the core compactness of X and the continuity of K(X). It is also proved that for a first-countable T0 space X in which the set of minimal elements of K is countable for any compact saturated subset K of X, the Smyth power space PS(X) is first-countable. For the Alexandroff double circle Y, which is Hausdorff and first-countable, we show that its Smyth power space PS(Y) is not first-countable.

Modeling the dynamic response of rock masses with multiple compliant fluid saturated joint sets—Part I: Mesoscale simulations

Recently a mesoscale model was developed that includes thermomechanically consistent constitutive equations with dissipation due to porous compaction, inelastic distortional deformation rate, and slipping on persistent dry joint surfaces. In this Part I of a two-part paper, enhancements of the mesoscale model are described which include: normal compliance with hysteresis, non-persistent joints with finite area, joint sets with angular deviation, and the weakening effect of fluid pressure in the joints. Examples study the influences of these effects on average strength. These computationally expensive simulations are used to inspire functional forms in a continuum model, described in Part II, which is needed for large scale simulations of real applications.

Modeling the dynamic response of rock masses with multiple compliant fluid saturated joint sets - Part II: Continuum modeling

Part I of this two-part paper describes enhancements of a mesoscale model to include: many non-persistent fluid saturated joints with finite area, normal compliance with hysteresis and the weakening effects of angular deviation in the joint sets and of fluid pressure in the joints. The objective of this Part II is to use the results of the mesoscale model as simulated data to inspire functional forms in a continuum model for rock masses with multiple compliant fluid saturated joint sets which include these enhancements. Also, an algorithm is proposed for reducing the number of joint sets being modeled. Examples are presented which show that the continuum model can predict similar anisotropic response to that observed in mesoscale simulations. In contrast with the mesoscale model, the continuum model can be used for large scale simulations of real applications, smoothly transitioning from coupled inelastic thermomechanical response near an explosive source to orthotropic elastic response far from the source.

A novel egg shell-based bio formulation for remediation of RDX (hexahydro-1,3,5-trinitro-1,3,5-triazine) contaminated soil

Environmental contamination by secondary explosive has been posing threat to human health and the ecosystem. We investigated the potential of a novel bioformulation developed from poultry waste for the bioremediation of hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) contaminated soils. Eggshells and additives immobilized with an indigenous explosive degrading microbe Janibacter cremeus were utilized for the development of the wettable powder bioformulation. Treatments carried out under unsaturated and saturated soil conditions resulted in 62 and 73 % removal of RDX respectively in 35 days meeting the soil clean up goals. The saturated treatment sets exhibited better microbial growth during the study in terms of live cell count and total enzyme activity. The bacteria, J. cremeus was observed to exhibit significant release of nitrite under both unsaturated as well as saturated conditions. Mass spectrometric studies showed that, both the conditions lead to the formation of nitroso-derivatives of RDX. But under saturated condition, an intermediate, 5-hydroxy-4-nitro-2,4-diazapentanal was observed which is a precursor to 4-nitro-2,4-diazabuatnal ultimately leading to mineralization. An accessible bio resource from poultry waste when used as a carrier for explosive degrading microbe has proven effective for in situ remediation of explosive contaminated soils.

Sober Scott spaces are not always co-sober

A nonempty compact saturated subset F of a topological space is called k-irreducible if it cannot be written as a union of two compact saturated proper subsets. A topological space is said to be co-sober if each of its k-irreducible compact saturated sets is the saturation of a point. Wen and Xu (2018) proved that Isbell's non-sober complete lattice equipped with the lower topology is sober but not co-sober. So far, it is still unknown whether every sober Scott space is co-sober. In this paper, we construct a dcpo whose Scott space is sober but not co-sober, which strengthens Wen and Xu's result.

Approximate controllability for Navier–Stokes equations in \rm3D cylinders under Lions boundary conditions by an explicit saturating set

<p style='text-indent:20px;'>An explicit saturating set consisting of eigenfunctions of Stokes operator in general 3D Cylinders is proposed. The existence of saturating sets implies the approximate controllability for Navier–Stokes equations in <inline-formula><tex-math id="M2">\begin{document}$ \rm 3D $\end{document}</tex-math></inline-formula> Cylinders under Lions boundary conditions.

Undrained Shear and Pore Space Characteristics of Treated Loose Sands with Lime-Activated Zeolite in Saturated Settings

Abstract This research investigates the mechanical behavior of artificially cemented sandy soils formed by lime alkali activation of natural zeolite under saturation settings. In order to verify the bar capability of cemented sands with this new method, an analysis of the undrained shear strength of the soil with pore water pressure ratio measurements was performed from the interpretation of the results of unconfined compression tests. The effect of zeolite-lime blend on treated sands was also visualized by scanning electron microscopy. For the studied soils, it was concluded from the unconfined compression stress values that the soil is fully capable of withstanding compressions due to overburden pressure. Additionally, this study seeks to evaluate the effect of the void ratio on the pore space and undrained shear strength. The results showed that pore water B-ratio increases with the decrease of the void ratio. Moreover, with the increase of zeolite content, confining pressure, and curing age, the peak failure strength increases. The results indicated a promising consistency of treated samples with lime and zeolite under various values of undrained shearing and B-ratios, making this method an ideal treatment for loose sand deposits.

Some invariant and inverse invariant characters of information systems under homomorphisms based on data compression

ABSTRACTHomomorphisms between information systems as a kind of tools to study communication between information systems are based on data compression, i.e. a complex massive information system is compressed into a relatively small-scale information system by means of homomorphisms under the premise that some of the same data structures are maintained. This paper is devoted to obtaining some invariant and inverse invariant characters of information systems under homomorphisms based on data compression. Saturation reductions of an information system is first proposed. Then, relationships between reductions and saturation reductions of the same information system are given. Next, information structures in information systems are further investigated. Finally, it is proved that coordinate sets, necessary attributes, necessary s-attributes, saturated coordinate sets, saturation reductions, some dependence and independence between information structures in an information system are both invariant and inverse invariant under homomorphisms based on data compression, in other words, some of the same data structures of an information system are obtained. Moreover, an example is used to illustrate that information granulation, rough entropy, information entropy and information amount are neither invariant nor inverse invariant under homomorphisms based on data compression.

Delay distribution estimation at a signalized intersection

Previous studies found that delay at signalized intersection accounted for more than one-third of total travel time. Different level of services tends to have different delay probability. An early assumption was made that multimodality occurs because of two traffic states experienced by the traveler; delay and non-delay at the signalized intersection. This study proposed a method to quantify delay distribution at a signalized intersection by analyzing the patterns in the speed time and speed distance profiles when passing two consecutive intersections and redrawing vehicle trajectory generated by ‘second by second’ GPS data. The searching algorithm was developed to search for the times when the vehicle enters and leaves the delay section by checking the ‘second by second’ speed data. To differentiate between the queue, move up and stop and go traffic, the algorithm searches for the idle time (i.e. when the speed less than 3.5 km/h). Along with Sydney Coordinates, Adaptive Traffic Systems (SCATS) degree of saturation and signal settings (green and red time) generating from SCATS systems at upstream loop detectors, a realistic delay probability model also was developed. This model used the General Additive Model for Location, Shape, and Scale (GAMLSS) which allows location, scale and shape parameter of selected distribution as a function of the explanatory variable. Signal settings and SCATS degrees of saturation were used as an explanatory variable. This model enables us to estimate delay experiencing by traveler depending on traffic parameters including traffic flow, signal settings and degree of saturation that are readily available on the site.

Comparison of laboratory and field electrical resistivity measurements of a gypsum rock for mining prospection applications

Geophysical surveys are frequently applied in mining prospection to detect the presence and volume of ore bodies of different nature. Particularly, in gypsum ore bodies exploitation, electrical resistivity measurements are usually the most used methodology. However, it has been observed that different electrical resistivity values can be obtained depending on geometrical features and composition of gypsum. Indeed, electrical resistivity of gypsum rocks depends on several parameters, such as gypsum purity, nature of secondary minerals, porosity, saturation and interstitial fluid properties. Saturation and hydrogeological setting, in particular, were recognized as the most influencing parameters. Hydrogeological conditions of gypsum rock masses are also very relevant for exploitability, safety conditions and economic feasibility and should be accurately known during the prospection and planning phases of the quarries. In this work, a relationship between electrical resistivity and saturation degree of gypsum is proposed. The possibility to estimate gypsum porosity with the use of this relationship is also investigated. The reliability of laboratory measurements is finally verified in comparison with field and modelled resistivity data. The reported results underline the potentiality of the proposed approach to obtain a reliable characterization of the studied ore body.

Equiangular lines and the Lemmens–Seidel conjecture

In this paper, claims by Lemmens and Seidel in 1973 about equiangular sets of lines with angle 1∕5 are proved by carefully analyzing pillar decomposition, with the aid of the uniqueness of two-graphs on 276 vertices. The Neumann Theorem is generalized in the sense that if there are more than 2r−2 equiangular lines in Rr, then the angle is quite restricted. Together with techniques on finding saturated equiangular sets, we determine the maximum size of equiangular sets “exactly” in an r-dimensional Euclidean space for r=8, 9, and 10.

Distributional chaos in multifractal analysis, recurrence and transitivity

There is much research on the dynamical complexity on irregular sets and level sets of ergodic average from the perspective of density in base space, the Hausdorff dimension, Lebesgue positive measure, positive or full topological entropy (and topological pressure), etc. However, this is not the case from the viewpoint of chaos. There are many results on the relationship of positive topological entropy and various chaos. However, positive topological entropy does not imply a strong version of chaos, called DC1. Therefore, it is non-trivial to study DC1 on irregular sets and level sets. In this paper, we will show that, for dynamical systems with specification properties, there exist uncountable DC1-scrambled subsets in irregular sets and level sets. Meanwhile, we prove that several recurrent level sets of points with different recurrent frequency have uncountable DC1-scrambled subsets. The major argument in proving the above results is that there exists uncountable DC1-scrambled subsets in saturated sets.

Induced Topologies on the Poset of Finitely Generated Saturated Sets

In [R. Heckmann, K. Keimel, Quasicontinuous Domains and the Smyth Powerdomain, Electronic Notes in Theoretical Computer Science 298 (2013), 215–232], Heckmann and Keimel proved that a dcpo P is quasicontinuous iff the poset FinP of nonempty finitely generated upper sets ordered by reverse inclusion is continuous. We generalize this result to general topological spaces in this paper. More precisely, for any T0 space (X,τ) and U∈τ, we construct a topology τF generated by the basic open subsets UF={↑F∈FinX:F⊆U}. It is shown that a T0 space (X,τ) is a hypercontinuous lattice iff τF is a completely distributive lattice. In particular, we prove that if a poset P satisfies property DINTop, then P is quasi-hypercontinuous iff FinP is hypercontinuous.

New covering codes of radius R, codimension tR and $$tR+\frac{R}{2}$$, and saturating sets in projective spaces

The length function $$\ell _q(r,R)$$ is the smallest length of a q-ary linear code of codimension r and covering radius R. In this work we obtain new constructive upper bounds on $$\ell _q(r,R)$$ for all $$R\ge 4$$ , $$r=tR$$ , $$t\ge 2$$ , and also for all even $$R\ge 2$$ , $$r=tR+\frac{R}{2}$$ , $$t\ge 1$$ . The new bounds are provided by infinite families of new covering codes with fixed R and increasing codimension. The new bounds improve upon the known ones. We propose a general regular construction (called “Line+Ovals”) of a minimal $$\rho $$ -saturating $$((\rho +1)q+1)$$ -set in the projective space $$\mathrm {PG}(2\rho +1,q)$$ for all $$\rho \ge 0$$ . Such a set corresponds to an $$[Rq+1,Rq+1-2R,3]_qR$$ locally optimal code of covering radius $$R=\rho +1$$ . Basing on combinatorial properties of these codes regarding to spherical capsules, we give constructions for code codimension lifting and obtain infinite families of new surface-covering codes with codimension $$r=tR$$ , $$t\ge 2$$ . In addition, we obtain new 1-saturating sets in the projective plane $$\mathrm {PG}(2,q^2)$$ and, basing on them, construct infinite code families with fixed even radius $$R\ge 2$$ and codimension $$r=tR+\frac{R}{2}$$ , $$t\ge 1$$ .