The cost-sensitive approximation of neighborhood rough sets and granular layer selection

Neighborhood rough sets (NRS) are the extended model of the classical rough sets. The NRS describe the target concept by upper and lower neighborhood approximation boundaries. However, the method of approximately describing the uncertain target concept with existed neighborhood information granules is not given. To solve this problem, the cost-sensitive approximation model of the NRS is proposed in this paper, and its related properties are analyzed. To obtain the optimal approximation granular layer, the cost-sensitive progressive mechanism is proposed by considering user requirements. The case study shows that the reasonable granular layer and its approximation can be obtained under certain constraints, which is suitable for cost-sensitive application scenarios. The experimental results show that the advantage of the proposed approximation model, moreover, the decision cost of the NRS approximation model will monotonically decrease with granularity being finer.

Relativistic motion on Gaussian quantum steering for two-mode localized Gaussian states

Realistic quantum systems always exhibit gravitational and relativistic features. In this paper, we investigate the properties of Gaussian steering and its asymmetry by the localized two-mode Gaussian quantum states, instead of the traditional single-mode approximation method in the relativistic setting. We find that the one-side Gaussian quantum steering will monotonically decrease with increasing observers of acceleration. Meanwhile, our results also reveal the interesting behavior of the Gaussian steering asymmetry, which increases for a specific range of accelerated parameter and then gradually approaches to a finite value. Such findings is well consistent and explained by the well-known Unruh effect, which could significantly destroy the one-side Gaussian quantum steering. Finally, our results could also be applied to the dynamical studies of Gaussian steering between the Earth and satellites, since the effects of acceleration is equal to the effects of gravity according to the equivalence principle.

Surface defect, anomalies and b-extremization

Quantum field theories (QFT) in the presence of defects exhibit new types of anomalies which play an important role in constraining the defect dynamics and defect renormalization group (RG) flows. Here we study surface defects and their anomalies in conformal field theories (CFT) of general spacetime dimensions. When the defect is conformal, it is characterized by a conformal b-anomaly analogous to the c-anomaly of 2d CFTs. The b-theorem states that b must monotonically decrease under defect RG flows and was proven by coupling to a spurious defect dilaton. We revisit the proof by deriving explicitly the dilaton effective action for defect RG flow in the free scalar theory. For conformal surface defects preserving $$ \mathcal{N} $$ N = (0, 2) supersymmetry, we prove a universal relation between the b-anomaly and the ’t Hooft anomaly for the U(1)r symmetry. We also establish the b-extremization principle that identifies the superconformal U(1)r symmetry from $$ \mathcal{N} $$ N = (0, 2) preserving RG flows. Together they provide a powerful tool to extract the b-anomaly of strongly coupled surface defects. To illustrate our method, we determine the b-anomalies for a number of surface defects in 3d, 4d and 6d SCFTs. We also comment on manifestations of these defect conformal and ’t Hooft anomalies in defect correlation functions.

The influence of lithospheric rheology on escarpment evolution at divergent margins: a numerical approach

<p>The evolution of escarpments bordering the coast during the post-rift phase is numerically simulated mostly by landscape surface processes models. However, there are few thermomechanical models that were applied to study the post-rift evolution of these escarpments. In the present work, we used a finite element thermomechanical model to simulate lithospheric extension and evaluate the sensitivity of escarpment amplitude over time under different geological and rheological conditions from the onset of lithospheric extension to the post-rift phase. The results showed that the evolution of escarpment amplitude and its preservation for tens of millions of years are sensitive to crustal and lithospheric thicknesses. We observed that escarpment preservation is higher for scenarios with a thinner crust with a strong lower crust and a thicker lithospheric mantle. This behavior is related to the degree of coupling between the crust and lithospheric mantle that affect the vertical displacement of the lithosphere due to flexural and isostatic response. Additionally, even without surface processes of erosion and sedimentation, the amplitude of the escarpment can monotonically decrease with time due to the lateral flow of the lower crust. This effect is expressive in the scenarios where the effective viscosity of the lower crust is relatively low and the upper crust is rheologically decoupled from the lithospheric mantle. In these cases, the amplitude of the escarpment can decrease from 2-3 km during the rifting phase to less 1 km after 40 Myr after the onset of lithospheric extension. On the other hand, in scenarios where the crust is rheologically coupled, the amplitude of the escarpment after 100 Myr since the lithospheric stretching is only ~25% smaller than maximum amplitude observed during the rifting phase. We conclude that the rheological structure of the lithosphere can play an important role in the formation and preservation of escarpments at divergent margins simultaneously with surface process.</p>

Improved Geotechnical Behavior of an Expansive Soil Amended with Tire-Derived Aggregates Having Different Gradations

This experimental laboratory study examines the potential use of tire-derived aggregate (TDA) products as an additive to alleviate the inferior geotechnical properties of a subgrade deposit of clay soil with high expansivity. A total of ten mix designs—the unamended soil and nine soil–TDA blends prepared at 5%, 10% and 20% TDA contents (by dry mass) using three different TDA gradations/sizes—were examined. The experiments included standard Proctor compaction, oedometer swell and unconfined compression tests. The TDA materials’ lower specific gravity, hydrophobic character and higher energy absorption capacity compared with the soil solids led to notable reductions in the soil compaction characteristics. The amendment of the soil with TDA resulted in notable decreases in the rate and magnitude of swelling—the observed reductions were in favor of higher TDA contents, with larger TDA particle size being a secondary factor. Further, for any given TDA size, the variations of strength and toughness with respect to TDA content exhibited rise–fall relationships, peaking at 5% TDA and then decreasing for higher TDA contents. The stiffness and ductility parameters, however, were found to monotonically decrease and increase with the TDA content, respectively. Finally, TDA contents of up to 10%, with gradations equivalent to those of medium and coarse sands, were found to reduce the soil’s swelling potential from high to moderate expansivity, while simultaneously improving its strength-related features, and thus can be deemed as optimum mix design choices from a geotechnical perspective.

Analysis of decreasing squared-sum of Gram–Schmidt lengths for short lattice vectors

In 2015, Fukase and Kashiwabara proposed an efficient method to find a very short lattice vector. Their method has been applied to solve Darmstadt shortest vector problems of dimensions 134 to 150. Their method is based on Schnorr’s random sampling, but their preprocessing is different from others. It aims to decrease the sum of the squared lengths of the Gram–Schmidt vectors of a lattice basis, before executing random sampling of short lattice vectors. The effect is substantiated from their statistical analysis, and it implies that the smaller the sum becomes, the shorter sampled vectors can be. However, no guarantee is known to strictly decrease the sum. In this paper, we study Fukase–Kashiwabara’s method in both theory and practice, and give a heuristic but practical condition that the sum is strictly decreased. We believe that our condition would enable one to monotonically decrease the sum and to find a very short lattice vector in fewer steps.

Investigation into the structural features and microwave absorption of doped barium hexaferrites

BaFe12−xGaxO19 hexaferrites were synthesized via the usual ceramic technology; with an increase in x, the unit cell and magnetic parameters monotonically decrease.

Dehn’s algorithm for simple diagrams

Dehn gave an algorithm for deciding if two cyclic words in the standard presentation of the fundamental group of a closed oriented surface of positive genus represent the same conjugacy class. A simple diagram on a surface is a disjoint union of simple closed curves none of which bound a disk. If [Formula: see text] is a once punctured closed surface of negative Euler characteristic, simple diagrams are classified up to isotopy by their geometric intersection numbers with the edges of an ideal triangulation of [Formula: see text]. Simple diagrams on the unpunctured surface [Formula: see text] can be represented by simple diagrams on [Formula: see text]. The weight of a simple diagram is the sum of its geometric intersection numbers with the edges of the triangulation. We show that you can pass from any representative to a least weight representative via a sequence of elementary moves, that monotonically decrease weights. This leads to a geometric analog of Dehn’s algorithm for simple diagrams.

Optimal Screening by Risk-Averse Principals

This paper studies the effects of principal's risk aversion on principal-agent relationship under hidden information. It finds that the agent's equilibrium effort increases and approaches the efficient level as the principal's risk aversion increases and tends to infinity. Allowing for random participation by the agent, his effort can be efficient even when the principal's risk aversion is finite. For the case of common agency with random participation, it is optimal for the principals to make the agent the residual claimant on profits and the principals' net profits monotonically decrease to zero when their risk aversion tends to infinity.

The Hβ Index As a Chronometer of Extragalactic Globular Cluster Systems

For the first time, we have taken into account the detailed systematic variation of horizontal-branch (HB) morphology with age and metallicity in our population synthesis models and they result that the integrated Hβ index is significantly affected by the presence of blue HB stars. As a matter of fact, due to the systematic HB morphology variation, it is found that Hβ does not monotonically decrease as metallicity increases at given ages, but shows a kind of wavy feature. According to our models, a systematic difference between the globular cluster system in the Milky Way Galaxy and that in NGC 1399 in the Hβ vs. Mg2 plane is explained if globular cluster systems in giant elliptical galaxies are a couple of billion years older, in the mean, than the Galactic counterpart.