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We compute and compare the (intersection) cohomology of various natural geometric compactifications of the moduli space of cubic threefolds: the GIT compactification and its Kirwan blowup, as well as the Baily–Borel and toroidal compactifications of the ball quotient model, due to Allcock–Carlson–Toledo. Our starting point is Kirwan’s method. We then follow by investigating the behavior of the cohomology under the birational maps relating the various models, using the decomposition theorem in different ways, and via a detailed study of the boundary of the ball quotient model. As an easy illustration of our methods, the simpler case of the moduli space of cubic surfaces is discussed in an appendix.

We consider an

Robust infrared (IR) small target detection is critical for infrared search and track (IRST) systems and is a challenging task for complicated backgrounds. Current algorithms have poor performance on complex backgrounds, and there is a high false alarm rate or even missed detection. To address this problem, a weighted local coefficient of variation (WLCV) is proposed for IR small target detection. This method consists of three stages. First, the preprocessing stage can enhance the original IR image and extract potential targets. Second, the detection stage consists of a background suppression module (BSM) and a local coefficient of variation (LCV) module. BSM uses a special three-layer window that combines the anisotropy of the target and differences in the grayscale distribution. LCV exploits the discrete statistical properties of the target grayscale. The weighted advantages of the two modules complement each other and greatly improve the effect of small target enhancement and background suppression. Finally, the weighted saliency map is subjected to adaptive threshold segmentation to extract the true target for detection. The experimental results show that the proposed method is more robust to different target sizes and background types than other methods and has a higher detection accuracy.

We investigate the existence of 4-torsion in the integral cohomology of oriented Grassmannians. We establish bounds on the characteristic rank of oriented Grassmannians and prove some cases of our previous conjecture on the characteristic rank. We also discuss the relation between the characteristic rank and a result of Stong on the height of w 1 in the cohomology of Grassmannians. The existence of 4-torsion classes follows from the results on the characteristic rank via Steenrod square considerations. We thus exhibit infinitely many examples of 4-torsion classes for oriented Grassmannians. We also prove bounds on torsion exponents of oriented flag manifolds. The article also discusses consequences of our results for a more general perspective on the relation between the torsion exponent and deficiency for homogeneous spaces.

This paper addresses the local incidence angle dependence of several polarimetric indices corresponding to landslides in forested areas. Landslide is deeply related to the loss of human lives and their property. Various kinds of remote sensing techniques, including aerial photography, high-resolution optical satellite imagery, LiDAR and SAR interferometry (InSAR), have been available for landslide investigations. SAR polarimetry is potentially an effective measure to investigate landslides because fully-polarimetric SAR (PolSAR) data contain more information compared to conventional single- or dual-polarization SAR data. However, research on landslide recognition utilizing polarimetric SAR (PolSAR) is quite limited. Polarimetric properties of landslides have not been examined quantitatively so far. Accordingly, we examined the polarimetric scattering properties of landslides by an assessment of how the decomposed scattering power components and the polarimetric correlation coefficient change with the local incidence angle. In the assessment, PolSAR data acquired from different directions with both spaceborne and airborne SARs were utilized. It was found that the surface scattering power and the polarimetric correlation coefficient of landslides significantly decrease with the local incidence angle, while these indices of surrounding forest do not. This fact leads to establishing a method of effective detection of landslide area by polarimetric information.

Object detection is a classic problem in computer vision. The main bottleneck of object detection lies in the fusion of multi-scale features. In this paper, we systematically study the design choices of neural network architecture for real-time object detection, and propose an Align-Yolact to improve the instance segmentation accuracy. Firstly, we propose a weighted bounding box, which improves the accurate positioning of the bounding box. Secondly, we add a bi-directional feature pyramid network to the feature fusion, which improves the mask quality and small target accuracy. Owing to these optimizations and better backbones, we achieve the SOTA results including both detection efficiency and accuracy.

Based on the demands of compact heat exchangers and micro cooling channels applied for aviation thermal protection on aero-engines, the elbow local flow resistance characteristics for supercritical pressure aviation fuel RP-3 flowing in adiabatic horizontal serpentine tubes with the inner diameter of 1.8 mm and the mass flux of 1179 kg/(m2·s) were experimentally studied. The long-short-tube method was used to obtain the elbow pressure drop from the total serpentine tube pressure drop, and the effects of system pressures (P/Pc = 1.72–2.58) and geometry parameters including bend numbers (n = 5–11), bend diameters (D/d = 16.7–27.8), and bend distances (L/d = 20–60) on elbow pressure drops and local resistance coefficients are analyzed on the basis of the thermal physical property variation. The results show that both the increase in the elbow pressure drop and the decrease in the local resistance coefficient with temperatures speed up at the near pseudo-critical temperature region of T > 0.85Tpc. And the growth of the elbow local pressure drop could be inhibited by the increase of system pressures, while the local resistance coefficient is slightly affected by pressures. The influence of bend diameters on the local resistance coefficient is mild when D/d is larger than 22.2 in the premise of fully developed flow in straight tubes. Furthermore, a piecewise empirical correlation considering the bend diameter and physical property ratio is developed to predict the elbow pressure drop of the serpentine tube and optimize the layout of the cooling tube system on aero-engines.

Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial version of a differential cohomology theory. While more involved differential cohomology theories have been explicitly twisted, the same has not been done to Deligne cohomology, although existence is known at a general abstract level. We work out what it means to twist Deligne cohomology, by taking degree one twists of both integral cohomology and de Rham cohomology. We present the main properties of the new theory and illustrate its use with examples and applications. Given how versatile Deligne cohomology has proven to be, we believe that this explicit and utilizable treatment of its twisted version will be useful.

Spreaders detection is a vital issue in complex networks because spreaders can spread information to a massive number of nodes in the network. There are many centrality measures to rank nodes based on their ability to spread information. Some local and global centrality measures including DIL, degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, PageRank centrality and k-shell decomposition method are used to identify spreader nodes. However, they may have some problems such as finding inappropriate spreaders, unreliable spreader detection, higher time complexity or incompatibility with some networks. In this paper, a new local ranking measure is proposed to identify the influence of a node. The proposed method measures the spreading ability of nodes based on their important location parameters such as node degree, the degree of its neighbors, common links between a node and its neighbors and inverse cluster coefficient. The main advantage of the proposed method is to clear important hubs and low-degree bridges in an efficient manner. To test the efficiency of the proposed method, experiments are conducted on eight real and four synthetic networks. Comparisons based on Susceptible Infected Recovered and Susceptible Infected models reveal that the proposed method outperforms the compared well-known centralities.

Given a finite and connected two-dimensional CW complex K with fundamental group Π and second integer cohomology group H 2 ( K ; Z ) finite of odd order, we prove that: (1) for each local integer coefficient system α : Π → Aut ( Z ) over K , the corresponding twisted cohomology group H 2 ( K ; α Z ) is finite of odd order, we say order c ∗ ( α ) , and there exists a natural function—which resemble that one defined by the twisted degree—from the set [ K ; R P 2 ] α ∗ of the based homotopy classes of based maps inducing α on π 1 into H 2 ( K ; α Z ) , which is a bijection; (2) the set [ K ; R P 2 ] α of the (free) homotopy classes of based maps inducing α on π 1 is finite of order c ( α ) = ( c ∗ ( α ) + 1 ) / 2 ; (3) all but one of the homotopy classes [ f ] ∈ [ K ; R P 2 ] α are strongly surjective, and they are characterized by the non-nullity of the induced homomorphism f ∗ : H 2 ( R P 2 ; ϱ Z ) → H 2 ( K ; α Z ) , where ϱ is the nontrivial local integer coefficient system over the projective plane. Also some calculations of H 2 ( K ; α Z ) are provided for several two-complexes K and actions α , allowing to compare H 2 ( K ; Z ) and H 2 ( K ; α Z ) for nontrivial α .