Strong Continuity Research Articles

A reexamination of factor momentum: How strong is it?

AbstractRecent studies show that most financial market anomalies exhibit a momentum effect. Based on two datasets, (i) an original 22‐factor sample and (ii) a more comprehensive 187‐factor sample, we find that factor momentum effect is weak at the individual factor level. In both samples, only about 22%– 27% of the factors exhibit strong return continuation and dominate the factor momentum portfolio while the remaining factors do not. The factor momentum strategies do not outperform the corresponding long‐only strategies in either sample. The choice of factors affects the ability of factor momentum to explain individual stock momentum.

Unique continuation from a crack’s tip under Neumann boundary conditions

We derive local asymptotics of solutions to second order elliptic equations at the edge of a (N−1)-dimensional crack, with homogeneous Neumann boundary conditions prescribed on both sides of the crack. A combination of blow-up analysis and monotonicity arguments provides a classification of all possible asymptotic homogeneities of solutions at the crack’s tip, together with a strong unique continuation principle.

Pattern of spatio-temporal variability of extreme precipitation and flood-waterlogging process in Hanjiang River basin

Based on the uniform distributed rainfall data in the Hanjiang River basin, the characteristics of spatio-temporal variability of extreme precipitation and flood-waterlogging process are diagnosed in terms of index definition and mathematical statistics. The study found that: (1) no significant trends of extreme rainfall for the entire basin were tested, but there was a jump variation in 1990s from abundance to dryness, accompanied by 20-year main periodic oscillation. Since 2000, the frequency of extremely heavy rain has increased significantly. (2) there is a spatial distribution pattern of lower in the northeast and higher in the southwest, and decreasing from upstream to downstream in the annual means of extreme precipitation. High-value centers are concentrated in the southwestern mountainous areas and the plains in the downstream, which are prone to form the distribution pattern of Central-North Radiation Type and Southeast-Northwest Type. (3) basin usually suffers 5–6 waterlogging processes per year, most of which were light or moderate grade, lasting 2–4 days. Since 2000, the flood-waterlogging process has shown evolution characteristics in increasing of the intensity, frequency, duration, and fluctuation, having strong continuity in the future. (4) affecting by climate and topography, spatial distribution of flood-waterlogging is uneven. Downstream and southwest of upstream are regularly the high-value centers, which are easy to form three kinds of distribution patterns, namely Northeast Radiation Type, Middle-lower Radiation Type and Middle-upper Radiation Type. Since the 21st century, the Hanzhong area and the watershed below Xiangyang both often encountered flood-waterlogging processes of high-intensity, long-duration, and high-frequency, which easy to induce flood disasters. Spatio-temporal variability of extreme precipitation and flood-waterlogging is a direct result of the rational development and utilization of water resources. We expect the results here to provide a deep insight into flood-waterlogging and serve as a reference for the watershed flood disaster response, rain-flood utilization, and optimal allocation of water resources.

Strict convergence with equibounded area and minimal completely vertical liftings

Minimal lifting measures of vector-valued functions of bounded variation were introduced by Jerrard–Jung. They satisfy strong continuity properties with respect to the strict convergence in BV. Moreover, they can be described in terms of the action of the optimal Cartesian currents enclosing the graph of u. We deal with a good notion of completely vertical lifting for maps with values into the two dimensional Euclidean space. We then prove lack of uniqueness in the high codimension case. Relationship with the relaxed area functional in the strict convergence is also discussed.

Asymptotic multiplicities and Monge–Ampère masses (with an appendix by Sébastien Boucksom)

Ein, Lazarsfeld and Smith asked whether ‘equality’ holds between two Samuel type asymptotic multiplicities for a graded system of zero-dimensional ideals on a smooth complex variety. We find a connection of this question to complex analysis by showing that the ‘equality’ is equivalent to a particular case of Demailly’s strong continuity property on the convergence of residual Monge–Ampère masses under approximation of plurisubharmonic functions. On the other hand, in an appendix of this paper, Sébastien Boucksom gives an algebraic proof of the ‘equality’ in general, using the intersection theory of b-divisors. We then use these to show that Demailly’s strong continuity holds for a new important class of plurisubharmonic functions.

The nodal set of solutions to some nonlocal sublinear problems

We study the nodal set of stationary solutions to equations of the form (-Delta )^s u = lambda _+ (u_+)^{q-1} - lambda _- (u_-)^{q-1}quad text {in }B_1, where lambda _+,lambda _->0, q in [1,2), and u_+ and u_- are respectively the positive and negative part of u. This collection of nonlinearities includes the unstable two-phase membrane problem q=1 as well as sublinear equations for 1<q<2. We initially prove the validity of the strong unique continuation property and the finiteness of the vanishing order, in order to implement a blow-up analysis of the nodal set. As in the local case s=1, we prove that the admissible vanishing orders can not exceed the critical value k_q= 2s/(2- q). Moreover, we study the regularity of the nodal set and we prove a stratification result. Ultimately, for those parameters such that k_q< 1, we prove a remarkable difference with the local case: solutions can only vanish with order k_q and the problem admits one dimensional solutions. Our approach is based on the validity of either a family of Almgren-type or a 2-parameter family of Weiss-type monotonicity formulas, according to the vanishing order of the solution.

Multi-scale analysis of shallow-water carbonate depositional geometries from a reservoir perspective: Insights from outcrop (Middle Jurassic, Portugal) and subsurface (Lower Cretaceous, U.A.E.) contrasting case studies

Outcrop observations offer valuable insights into depositional architecture as a primary control on facies and reservoir properties variability, in contrast to subsurface cases, where observation points are limited to well locations. Two dominantly high-energy shallow-water carbonate case studies were analysed, including outcrops of a Bathonian-Callovian (Middle Jurassic) carbonate succession in the Maciço Calcário Estremenho (MCE) region, central Lusitanian Basin, Portugal and a Barremian (Lower Cretaceous) subsurface carbonate reservoir from Abu Dhabi (U.A.E.). The MCE succession comprises a range of inner ramp deposits, which consist of oobiointraclastic grainstones, biointraclastic grainstone-rudstones and coral/algal boundstones, mostly defining sandbody and coral biostrome units which represent potential reservoir facies, as suggested by their textural types and locally significant porosity, though now mostly occluded by calcite cements. The succession is exposed in recently-cut quarry faces showing minimal weathering, hence allowing for detailed observations on depositional geometries. The U.A.E. case study is a world-class reservoir characterized by mid-ramp to high-energy inner-ramp facies, ranging from biomicritic wackestones to biointraclastic packstones, bioclastic packstones, grainstones and rudstone-grainstones, interpreted using core and thin section data from four onshore wells.In the analysed outcrops, strong continuity of main major bedding surfaces is observed at larger scales (dozens to hundreds of metres), with strong spatial variability seen at smaller centimetre to metre scales and depositional geometries varying from tabular, wedge-like, lensoid bodies and coral buildups. The subsurface case also shows strong continuity of larger-scale depositional packages (at kilometre scale) and moderate to strong small-scale heterogeneities at centimetre to metre scales. Discontinuity-bounded intervals are observed in the younger section of this reservoir generally showing stronger vuggy porosity and coarser skeletal grains at the base, while the youngest set of these intervals are characterized by an abundance of rudist fragments. The interpreted depositional geometries in this reservoir consist of tabular, wedge-like and lenticular geobodies of limited lateral extension.The multi-scale heterogeneity in both these case studies is strongly influenced by depositional factors related to hydrodynamics and the balance between carbonate factory productivity and accommodation space, affecting lateral facies migration and creating complex depositional patterns. This study illustrates how the perception of heterogeneity, though reflecting an intrinsic property of carbonate rocks, is influenced by the scale of observation and, from a reservoir perspective, both cases show that addressing small-scale heterogeneities and associated geological factors in higher detail is vital in defining conceptual geological models for a better understanding of the reservoir.

Buying Sovereignty: German “Weltpolitik” and Private Enterprise, 1884–1914

AbstractWilhelmine Germany's Weltpolitik is widely regarded as a precursor to World War I, as a reckless break from the Bismarckian past, and as a counterproductive form of German deviation from European norms. Yet, when one reexamines certain German overseas expansion schemes between 1897 and the early 1900s, a strong intellectual continuity emerges between the methods of Weltpolitik and wider views about colonial sovereignty. Like Bismarck and other European imperial powers in the late nineteenth century, the actors producing Weltpolitik sought to enlist private businessmen in colonial governance, as well as to parcel and transfer sovereignty as a commodity in places like the Caribbean island of St. John. Counterintuitively, this way of treating sovereignty was highly imitative and compliant with norms, both at home and abroad. It also represented an alternative, at least at times, to a more aggressive course in foreign policy.

Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations

We study local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet boundary condition. Our analysis is based on a blow-up procedure which involves some Almgren type monotonicity formulæ and provides a classification of all possible homogeneity degrees of limiting entire profiles. As a consequence, we establish a strong unique continuation principle from boundary points.

On the asymptotic behaviour of semigroups for flows in infinite networks

We study transport processes on infinite networks. The solution of these processes can be modeled by an operator semigroup on a suitable Banach space. Classically, such semigroups are strongly continuous and therefore their asymptotic behaviour is quite well understood. However, recently new examples of transport processes emerged where the corresponding semigroup is not strongly continuous. Due to this lack of strong continuity, there are currently only few results on the long-term behaviour of these semigroups. In this paper, we discuss the asymptotic behaviour for a certain class of these transport processes. In particular, it is proved that the solution semigroups behave asymptotically periodic with respect to the operator norm as a consequence of a more general result on the long-term behaviour by positive semigroups containing a multiplication operator. Furthermore, we revisit known results on the asymptotic behaviour of transport processes on infinite networks and prove the asymptotic periodicity of their extensions to the space of bounded measures.

Continuity and Discontinuity in the Administrative Elite of the Szekler Seats between 1840-1876

"This study analyzes to what extent the frequent regime changes from the middle of the 19th century had an effect on the continuity, respectively the discontinuity of the officer corps of the Szekler seats, from the period before the Revolution of 1848 until the abolition of the Szekler seats following the administrative-territorial reform of 1876. While before 1848 we have strong continuity, the main feature of the two decades after the Revolution of 1848 was discontinuity. Beginning with the Revolution, the next two decades were marked by frequent changes and total rupture from the previous regime. The most radical break occurred in the age of neo-absolutism, when a lot of new and literally foreign people flowed into the Szeklerland administration. The next big elite change in the administration took place after the Austro-Hungarian Compromise. After the Compromise the situation stabilized again; and we find representatives of much of the same families who held the majority of offices during the pre-1848 period. This shows a high degree of stability of the county elite. Keywords: administrative elite, elite change, Szekler seats, 19th century, Transylvania, continuity, discontinuity. "

Convex analysis on polyhedral spaces

AbstractWe introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.

Systematicity, Purposiveness, Necessity: from the transcendental deduction of the ideas to the transcendental deduction of the principle of purposiveness of nature

In this paper I argue for a strong continuity between the transcendental deduction of the principle of purposiveness of nature and the transcendental deduction of the ideas from the first critique. On these grounds, I provide an interpretation of the transcendental deduction of the principle of purposiveness of nature in which I argue that: 1) the necessity of the principle of purposiveness of nature does not derive from its role in solving some specific philosophical problem (e.g. that of induction) but from its relation to a cognitive goal; 2) the representation of nature as conforming to the maxims of judgement is a direct, immediate consequence of a certain cognitive goal (in particular, of what is researched in the empirical investigation of nature; 3) that the necessity of the empirical laws mentioned by Kant in the transcendental deduction of the principle of purposiveness of nature is not so much their nomic necessity, but their necessity as consequences of higher laws.

Genetic continuity of Indo-Iranian speakers since the Iron Age in southern Central Asia

Since prehistoric times, southern Central Asia has been at the crossroads of the movement of people, culture, and goods. Today, the Central Asian populations are divided into two cultural and linguistic groups: the Indo-Iranian and the Turko-Mongolian groups. Previous genetic studies unveiled that migrations from East Asia contributed to the spread of Turko-Mongolian populations in Central Asia and the partial replacement of the Indo-Iranian populations. However, little is known about the origin of the latters. To shed light on this, we compare the genetic data on two current-day Indo-Iranian populations — Yaghnobis and Tajiks — with genome-wide data from published ancient individuals. The present Indo-Iranian populations from Central Asia display a strong genetic continuity with Iron Age samples from Turkmenistan and Tajikistan. We model Yaghnobis as a mixture of 93% Iron Age individual from Turkmenistan and 7% from Baikal. For the Tajiks, we observe a higher Baikal ancestry and an additional admixture event with a South Asian population. Our results, therefore, suggest that in addition to a complex history, Central Asia shows a remarkable genetic continuity since the Iron Age, with only limited gene flow.

Seismic Impedance Inversion Based on Residual Attention Network

Deep learning has achieved promising results for impedance inversion via seismic data. Generally, these networks, composed of convolution layers and residual blocks, tend to deliver good results with deep architectures. Nevertheless, deep networks accompany a large number of parameters and longer training time. The volume of seismic data, especially 3D scenarios, is very large. Therefore, it is particularly important to improve the accuracy while ensuring the model efficiency for practical implementation. With the flourishing new modules and techniques, deep learning has set the state-of-the-art in many applications across wide range of scientific and engineering disciplines. In this paper, we present Residual Attention Network (ResANet), a CNN incorporating with residual modules and two attention mechanisms: channel-wise attention and feature-map attention, for seismic impedance inversion. The proposed network can fuse multi-scale channel information and recalibrate channel-wise feature responses as well as receptive fields adaptively. At the same time, ResANet adopts grouped convolution, dilated convolution and dropout techniques to improve the computation efficiency and stability. Marmousi2 synthetic model and field data test results show that the proposed network outperforms several comparable neural networks in accuracy and generalization ability while ensuring efficiency for seismic data impedance inversion. For the field data test, transfer learning is also evoked to further improve the performance. ResANet tends to predict impedance with high resolution and strong lateral continuity compare with three closely related networks. The accuracy of ResANet is improved by 1 to 2 orders of magnitude on the 6 well logs provided in field dataset tests compare with commercial software (InverTrace Plus module in Jason) using Constrained Sparse Spike Inversion (CSSI) method.

О купмановском представлении гамильтоновых потоков в бесконечномерных пространствах с инвариантной мерой

We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on a Hilbert space that are invariant with respect to flows of completely integrable Hamiltonian systems and allow one to describe Hamiltonian flows in a phase space in terms of unitary groups in the space of functions squarely integrable with respect to an invariant measure are studied. The properties of the Koopman representation are described using the example of the Hamiltonian of a countable set of noninteracting harmonic oscillators. A spectral analysis of the generator of Koopman group for such a Hamiltonian is carried out. An invariant subspace of strong continuity of Koopman unitary group is described in terms of spectrum of the generator.

Optimal identification of cavities in the Generalized Plane Stress problem in linear elasticity

For the Generalized Plane Stress (GPS) problem in linear elasticity, we obtain an optimal stability estimate of logarithmic type for the inverse problem of determining smooth cavities inside a thin isotropic cylinder from a single boundary measurement of traction and displacement. The result is obtained by reformulating the GPS problem as a Kirchhoff–Love plate-like problem in terms of the Airy function, and by using the strong unique continuation at the boundary for a Kirchhoff–Love plate operator under homogeneous Dirichlet conditions, which has recently been obtained in [G. Alessandrini et al., Arch. Ration. Mech. Anal. 231 (2019)].

Visual Analytics of RNN for Thermal Power Control System Identification

<p indent="0mm">Due to the problems such as strong continuity and high complexity of the data generated by the thermal power control process, and the difficulty of establishing a semantic correlation between the model behavior of recurrent neural networks and the actual control process, the model debugging, optimization and semantic analysis cannot be carried out intuitively. Visual analytics in recurrent neural networks modeling for system identification is applied and a visual analysis system called iaRNN is proposed. Firstly, by visualizing the activation value distribution and coverage of hidden units, the combined view for model evaluation is designed to support the evaluation of model performance in many aspects including inside and outside. Then, visual views are designed from the perspectives of temporal evolution, sensitivity analysis, etc, to support the exploration of model response behavior to thermal power control parameters. Finally, based on the symbolic representation of time sequences and clustering analysis, a method for exploring association patterns between strong time-dependent real-valued time series and hidden units is proposed. A case study using real power plant data is conducted to verify the effectiveness of iaRNN in assisting users to understand the working mechanism of the model and diagnose model defects.

Method of asymptotic partial decomposition with discontinuous junctions

Method of asymptotic partial decomposition of a domain (MAPDD) proposed and justified earlier for thin domains (rod structures, tube structures consisting of a set of thin cylinders) generates some specific interface conditions between three-dimensional and one-dimensional parts. In the case of the heat equation these conditions ensure the continuity of the solution and continuity in average of the normal flux. However for some computational reasons the strong continuity condition for the solution may be undesirable. It may be preferable to replace it by more flexible condition of continuity in average over the interface cross section. In the present paper we introduce and justify this alternative junction condition allowing such discontinuity of the solution of both stationary and non-stationary problems. The closeness of solutions of these hybrid dimension problems to the solution of the fully three-dimensional setting is proved. At the discrete level, finite volume schemes are considered, an error estimate is established. The new version of the MAPDD is compared to the classical one via numerical tests. It shows better stability of the new scheme.

Differences in Accessibility of Public Health Facilities in Hierarchical Municipalities and the Spatial Pattern Characteristics of Their Services in Doumen District, China

This study used the two-step floating catchment area method and potential model to calculate facility accessibility and potential service scope of public health infrastructure distribution, and to evaluate its spatial equity. We applied the Gini coefficient to measure the spatial equilibrium at each level of public health infrastructure in Doumen District, Guangdong, China, from different perspectives. The following results were obtained: (1) Significant spatial differences were observed in the accessibility of public health facilities among different levels; the higher the health facility level, the greater the difference in spatial accessibility. Spatial differences in the accessibility of public health infrastructure at the primary level and higher were distributed in a block-like pattern, while spatial differences in the accessibility of rural health stations were distributed in a circular pattern. Administrative villages tended to have the highest and lowest accessibility of tertiary and secondary hospitals, but not of primary hospitals and rural health stations. The frequencies for administrative villages with the highest and lowest accessibility were 32.8% and 49.6% of the total number of villages in the district, respectively, for tertiary hospitals; 39.2% and 48.8% for secondary hospitals; 19.2% and 24.8% for primary hospitals; 16.8% and 21.6% for rural health stations. (2) The potential service scope was spatially dissociative for tertiary hospitals, and differed more significantly in terms of space for secondary hospitals; the potential service scope of the two overlapped. The potential service scope of primary hospitals was relatively balanced, with strong spatial continuity, while that of rural health service centers was spatially fragmented. The service scope of rural health service centers was mostly consistent with their respective village-level administrative divisions. (3) The higher the level of public health infrastructure, the less balanced its spatial layout. Conversely, the lower the level of public health infrastructure, the more balanced its spatial layout.