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We explore the concept of separating systems of vertex sets of graphs. A separating system of a set$X$is a collection of subsets of$X$such that for any pair of distinct elements in$X$ , there exists a set in the separating system that contains exactly one of the two elements. A separating system of the vertex set of a graph$G$is called a vertex-separating path (tree) system of$G$if the elements of the separating system are paths (trees) in the graph$G$ . In this paper, we focus on the size of the smallest vertex-separating path (tree) system for different types of graphs, including trees, grids, and maximal outerplanar graphs. Comment: 23 page, 3 figures dmtcs final version

This survey paper is concerned with vortex shedding from bodies in unsteady flow due either to time dependent motion of the body in a still fluid or unsteady motion of the fluid about a fixed body. The fluid is treated as incompressible, and the main emphasis is on starting flows and oscillatory flows. Much of the discussion describes 2D flow around sections of long or slender bodies. The first part of the paper covers the inviscid flow scaling of the forces induced by vortex shedding in time dependent flows which drive the shedding. This is followed by application of Wu’s impulse integral of the moment of vorticity to predict the forces induced by vortex shedding from a body in both inviscid and viscous flows. Vortex shedding phenomena involving small amplitude, high-frequency oscillatory flow such as vortex-induced vibration (VIV) and fluid-structure interaction (FSI) are not included in this discussion as in these cases the unsteady flow controls rather than drives the vortex shedding and they are well covered elsewhere. The second part of the paper describes a vortex force mapping (VFM) method derived by considering the Lamb–Gromyko formulation for the pressure contribution which allows the integral of the vorticity field to be restricted to regions which are not far from the body. It is applied to both inviscid and viscous flows. The section finishes with discussion of application of the VFM to the calculation of forces induced on bodies from flow field measurements, such as particle image velocimetry (PIV).

We provide a dynamic, game-theoretic model to examine a firm’s quality and pricing decisions for its new experience goods. Early consumers do not observe product quality prior to purchase but can learn it after purchase and share that product-quality information with later consumers—for example, through online reviews. Both the firm’s quality decision and its cost efficiency are the firm’s private information and not directly observed by the consumer. The early consumers can make a rational inference from the firm’s price about its cost and quality taking into account the firm’s profit incentive from the later informed consumers. We find that in equilibrium a more cost-efficient firm chooses higher quality than does an inefficient firm. One might intuit that a firm will offer higher quality if its high efficiency is known to consumers than if its efficiency is not known, because it will no longer need to convince consumers that it is not the inefficient firm. Our analysis shows that, surprisingly, the opposite may be true—when a firm’s high efficiency is publicly known, the firm may reduce its product quality rather than increase it. Furthermore, consumers’ knowledge about the firm’s cost efficiency can reduce the consumer surplus. We also show that an improvement in the average cost efficiency in the market can lower the consumer surplus. The online appendix is available at https://doi.org/10.1287/mnsc.2017.2930 . This paper was accepted by J. Miguel Villas-Boas, marketing.

At present, the potato’s mechanized harvesting rate in hilly and mountainous areas is very low. The reasons for this are that in heavy soil, the separation of potato rhizomes from soil or vines is not sufficient, harvesting machinery is seriously damaged by the potato epidermis, and the harvested potato is easily buried in soil, resulting in a missed harvest. In this paper, a two-stage cleaning potato harvester with wave-type and roller-group-type separating mechanisms was designed, and its overall structure and working principle are introduced in detail. The new cleaning mechanism can increase the effective separating length and effective contact area of the potato–soil mixture so as to achieve the purpose of removing clay and heavy soil. The main separator uses a structure that combines offset waves with opposite waves and a staggered arrangement of large–small diameter straight bars. The secondary separator adopts a device combining left-hand and right-hand separating rollers. The discrete element model of the whole machine was established, and the results of the theoretical analysis were verified by simulation. The key factors affecting the harvest quality were analyzed by variance analysis and response surface analysis, and the field experiment was carried out with the rate of clean potatoes, damaged potatoes, and peeled potatoes harvested as the indexes. The field experiments showed that the machine achieved a rate of photos on or out of the earth of 98.87%, a damaged potato rate of 0.91%, and a peeled potato rate of 1.13%. The research results provide theoretical support and a technical reference for the design and optimization of potato harvesters, as well as the improvement of the potato–soil separating efficiency and harvest quality.

Many of the membraneless organelles inside cells are multiphasic condensates with complex structural organizations driven by the demixing of phase‐separating proteins. Tailoring the structures of multiphasic condensates by controlling their demixing states is a challenge. Here, we employ two proteins with distinctly different features, including thermal responsiveness, hydrophobicity, and charges: a positively charged RGGRGG protein, which forms phase‐separated condensates below an upper critical solution temperature, and a protein based on an elastin‐like polypeptide, which forms condensates above a lower critical solution temperature. These two proteins demix to form multiphasic condensates with nested and core‐shell structures under variable conditions, which can be tailored by altering the physical and chemical environments. The demixed multiphasic condensates can also be constructed inside Escherichia coli cells, recapitulating the properties of membraneless organelles. We also show that nucleic acids preferentially enrich in the positively charged segment of the multiphasic condensates. Lastly, multiphasic condensates can deliver nucleic acids across the plasma membrane into mammalian cells, enabling cell transfection. Multiphasic protein condensates transform structural organizations and deliver nucleic acids.

Extracellular vesicles (EV) which play critical roles in intercellular communication, have garnered interest as biomarkers with researchers studying brain‐related disease processes due to their ability to be isolated from various biofluids. Astrocytes, a type of glial cell, play a critical role in neuronal regulation and function. As such, EV enriched from astrocytes can be used to interrogate cargo and identify mechanisms by which astrocytes communicate with other cells of the central nervous system or shed light on pathophysiological conditions. This manuscript compared five EV isolation methods (differential ultracentrifugation [dUC], precipitation, precipitation + purification, silicon carbon resin and size exclusion chromatography [SEC]) using small volumes of human plasma and serum with a focus on immunocapture of astrocyte‐enriched EV (AEEV), with the excitatory amino acid transporter 1, or GLAST. Methods were evaluated on yield, purity, recovery and downstream application to include immunoassays for tetraspanin, immune and astrocyte markers. Results revealed that whilst precipitation‐based methods such as ExoQuick yielded higher EV concentrations, size exclusion (SmartSEC, qEV) provided greater purity, emphasizing a trade‐off between yield and purity. This study provides a comprehensive resource for researchers in selecting EV isolation methods tailored to small biobanked clinical samples, with the goal of advancing biomarker discovery in Neuroscience. Experimental workflow for total EV isolation and AEEV enrichment. A. Human serum or plasma samples were collected from blood and stored at −80°C until isolation of total EV. B. Depiction of several methods that were used to isolate TEV, which can be stored in researcher's desired buffer. C. Steps for immunoaffinity capture of GLAST‐positive AEEV with the use of covalently‐linked streptavidin magnetic beads conjugated to biotin‐GLAST antibody. AEEV were separated with a magnetic stand and used for downstream analyses.

We will consider soft topologies defined on the same universe X with E as the set of parameters. It is shown that soft topologies are not equivalent to the general topologies defined on X . Moreover, some implications between soft separating axioms are different than those for ordinary topological spaces. The relation of similarity of soft topological spaces is also introduced and examined. The soft topologies T 1 and T 2 on X are called similar, if the families T 1 and T 2 are mutually coinitial. We study some basic properties of similar soft topological spaces: we check whether the family of all such spaces forms a lattice, we examine the relationship between similarity and being homeomorphic and consider the similarity of e -parameterized topologies.

Liquid–liquid phase separation regulates biological processes through dynamic condensates. Despite its significance, experimentally validated phase-separating proteins in plants remain limited, complicating predictions. We overcome this gap by applying positive-unlabeled learning, a semi-supervised approach optimized for imbalanced datasets. Leveraging 6,559 reported plant phase-separating proteins from eight species, we train a model integrating sequence-structural features, enabling prediction of 174,656 high-confidence candidates across 14 species. Experimental validation confirms liquid–liquid phase separation in 67.9% of the candidate proteins from Arabidopsis , rice, and maize. This positive-unlabeled framework demonstrates robust predictive power while providing open resources to advance plant phase separation research.

Past research shows that consumers evaluate bundles with complementary items more favorably than they evaluate bundles with noncomplementary items. In a series of four experiments that involve evaluation, willingness to pay, and real choice, we show that this well-established effect is moderated by the level of mindset abstraction. Complementarity (vs. noncomplementarity) among bundle items prompts relatively concrete (vs. abstract) thinking (study 1). Consequently, consumers evaluate complementary (vs. noncomplementary) bundles more favorably when they think in more concrete (vs. abstract) terms (study 2) or when the consumption context involves lower (vs. higher) spatial (study 3) or temporal (study 4) distance. These effects are mediated by consumers’ heightened sense of “feeling right” during decision making under construal fit (study 4). Finally, the level of complementarity among bundle items differentially influences mental abstraction because of consumers’ tendency to perceive bundles as a single inseparable unit. Therefore, the effect attenuates when consumers adopt a separating—rather than a connecting—mindset (study 3). Overall, this work significantly extends past research on product bundles and offers several managerial implications.

Let 𝒜 be a unital Banach algebra, 𝓜 be a unital 𝒜-bimodule, and 𝓦 be a separating point of 𝓜. We show that if linear mappings δ and τ from 𝒜 into 𝓜 satisfy δ(AB) = δ(A)B + Aτ(B) for each A, B in 𝒜 with AB = W, then τ is a Jordan derivation and δ is a generalized Jordan derivation. Based on this result, if linear mappings δ and τ from a unital semisimple Banach algebra 𝒜 into itself satisfy δ(W) = δ(A)B + Aτ(B) for each A, B ϵ 𝒜 with AB = W, then τ is a Jordan derivation and δ(A) = τ(A) + δ(I)A for every A in 𝒜. As an application, we present a characterization of linear mappings δ and τ on a unital semisimple Banach *-algebra 𝒜 satisfying δ(W) = δ(A)B* + Aτ(B)* for each A, B ϵ 𝒜 with AB∗ = W.