Branes, fermions, and superspace dualities

We use the superspace formulation of supergravity in eleven and ten dimensions to compute fermion couplings on the M2-brane and on Dp-branes. In this formulation fermionic couplings arise naturally from the θ-expansion of the superfields from which the brane actions are constructed. The techniques we use and develop can in principle be applied to determine the fermionic couplings to general background fields up to arbitrary order. Starting with the superspace formulation of 11-dimensional supergravity, we use a geometric technique known as the ‘normal coordinate’ method to obtain the θ-expansion of the M2-brane action. We then present a method which allows us to translate the knowledge of fermionic couplings on the M2-brane to knowledge of such couplings on the D2-brane, and then to any Dp-brane. This method is based on superspace generalizations of both the compactification taking 11-dimensional supergravity to type IIA supergravity and the T-duality rules connecting the type IIA and type IIB supergravities.

Geometric estimation of volcanic eruption column height from GOES-R near-limb imagery – Part 1: Methodology

A geometric technique is introduced to estimate the height of volcanic eruption columns using the generally discarded near-limb portion of geostationary imagery. Such oblique observations facilitate a height-by-angle estimation method by offering close-to-orthogonal side views of eruption columns protruding from the Earth ellipsoid. Coverage is restricted to daytime point estimates in the immediate vicinity of the vent, which nevertheless can provide complementary constraints on source conditions for the modeling of near-field plume evolution. The technique is best suited to strong eruption columns with minimal tilting in the radial direction. For weak eruptions with severely bent plumes or eruptions with expanded umbrella clouds the radial tilt/expansion has to be corrected for either visually or using ancillary wind profiles. Validation on a large set of mountain peaks indicates a typical height uncertainty of ±500 m for near-vertical eruption columns, which compares favorably with the accuracy of the common temperature method.

Direct measurement of malrotation of traumatic femoral neck fractures after osteosynthesis: Introduction of a novel method and interrater reliability

Background In elderly patients, displaced femoral neck fractures are mostly treated by arthroplasty; however for younger patients (<50 years), open reduction and internal fixation is considered the gold standard approach. Despite there being no consensus on the specific procedure, everyday clinical practice in a level I trauma center has shown that postoperative maltorsion after internal fixation of femoral neck fractures can have a significantly worse impact on mobilization and outcome. Different methods for measurement of malrotations are reported in literature. However, any reported method for the assessment of a shaft malrotation in the femur does not work here. In femoral neck fractures, the pointer function of the femoral neck, which is absolutely essential for these techniques, is lost and cannot be set in relation to the condylar plane. These circumstances are not addressed in literature thus far. Therefore, we propose here a novel method to fill this diagnostic gap. Methods and findings Three investigators (1 orthopaedic surgeons and 2 radiologists) measured the torsion of 20 legs on 10 patients using the Jarret method and a new geometric technique. To determine the intraobserver reliability the torsional angles were calculated again after 3 months. We applied a new geometric technique, without the need to include the femoral condyles in the measurement, to directly measure the angulation. For torsional difference, the interrater reliability -ICC (interclass correlation) between all investigators was 0.887 (good) (significance level: 95%CI, 0.668–0.969; p<0.001), by using the method of Jarret et al. and 0.933 (good) for the novel technique (significance level: 95%CI, 0.802–0.982; p<0.001). If the examinations are classified according to the patient side, our data show that for established methods, an ICC between the examiners on the right lower extremity is 0.978 (good) (95%CI, 0.936–0.994; p<0.001) and that on the left extremity is 0.955 (good) (95%CI, 0.867–0.988; p<0.001). Comparing with the new method, the right side assumes an ICC of 0.971 (good) (95%CI, 0.914–0.992; p<0.001), while the left side assumes an ICC of 0.910 (good) (95%CI, 0,736–0.976; p<0.001). When it comes to the intraobserver reliability, the measured cohort shows a significant better ICC for the novel method compared to Jarrett et al, with 0.907 respectively 0.786 for comparison in torsional differences. Conclusion The established methods may fail in assessing this special aspect of malrotation after femoral neck fractures. Here, the method presented results in a significant difference between the injured and uninjured side and shows significant differences in results compared to conventional measurement methods. The inter- and intraobserver reliability determined in this study is excellent and even higher in the assessment of torsional differences than the established method. We believe that the measurement method presented in this study is a useful tool to objectify the postoperative deformities in this area and making therapy recommendations in the future.

Geometric estimation of volcanic eruption column height from GOES-R near-limb imagery – Part 1: Methodology

A geometric technique is introduced to estimate the height of volcanic eruption columns using the generally discarded near-limb portion of geostationary imagery. Such oblique observations facilitate a height-by-angle estimation method by offering close to orthogonal side views of eruption columns protruding from the Earth ellipsoid. Coverage is restricted to daytime point estimates in the immediate vicinity of the vent, which nevertheless can provide complementary constraints on source conditions for the modelling of near-field plume evolution. The technique is best suited to strong eruption columns with minimal tilting in the radial direction. For weak eruptions with severely bent plumes or eruptions with expanded umbrella clouds the radial tilt/expansion has to be corrected for either visually or using ancillary wind profiles. Validation on a large set of mountain peaks indicates a typical height uncertainty of ±500 m for near-vertical eruption columns, which compares favourably with the accuracy of the common temperature method.

Effective Algorithms for the Economic Lot-Sizing Problem with Bounded Inventory and Linear Fixed-Charge Cost Structure

Efficient algorithms for the economic lot-sizing problem with storage capacity are proposed. On the one hand, for the cost structure consisting of general linear holding and ordering costs and fixed setup costs, an dynamic programming algorithm is introduced, where is the number of time periods. The new approach induces an accurate partition of the planning horizon, discarding most of the infeasible solutions. Moreover, although there are several algorithms based on dynamic programming in the literature also running in quadratic time, even considering more general cost structures and assumptions, the new solution uses a geometric technique to speed up the algorithm for a class of subproblems generated by dynamic programming, which can now be solved in linearithmic time. To be precise, the computational results show that the average occurrence percentage of this class of subproblems ranges between 13% and 45%, depending on both the total number of periods and the percentage of storage capacity availability. Furthermore, this percentage significantly increases from 13% to 35% as the capacity availability decreases. This reveals that the usage of the geometric technique is predominant under restrictive storage capacities. Specifically, when the percentage of capacity availability is below 50%, the average running times are on average 100 times faster than those when this percentage is above 50%. On the other hand, an on-line array searching method in Monge arrays can be used when the costs are non-speculative costs.

A survey on the blow-up method for fast-slow systems

In this document we review a geometric technique, called the blow-up method, as it has been used to analyze and understand the dynamics of fast-slow systems around non-hyperbolic points. The blow-up method, having its origins in algebraic geometry, was introduced to the study of fast-slow systems in the seminal work by Dumortier and Roussarie in 1996, whose aim was to give a geometric approach and interpretation of canards in the van der Pol oscillator. Following Dumortier and Roussarie, many efforts have been performed to expand the capabilities of the method and to use it in a wide range of scenarios. Our goal is to present in a concise and compact form those results that, based on the blow-up method, are now the foundation of the geometric theory of fast-slow systems with non-hyperbolic singularities. Due to their great importance in the theory of fast-slow systems, we cover fold points as one of the main topics. Furthermore, we also present several other singularities such as Hopf, pitchfork, transcritical, cusp, and Bogdanov-Takens, in which the blow-up method has been proved to be extremely useful. Finally, we survey further directions as well as examples of specific applied models, where the blow-up method has been used successfully.

A cross-linguistic comparison of Spanish and English semantic norms: Looking at core features

It has been suggested that human communities that share their basic cultural foundations evince no remarkable differences concerning the characterization of core concepts. However, the small but existing differences among them reflect their sociocultural diversity. This study compares 219 concrete concepts common to both Spanish and English semantic feature norms in order to assess whether core features of concepts follow a universal or cultural language-specific pattern. Concepts were compared through a geometric technique of vector comparison in the Euclidean n-dimensional space alongside the calculation of the network’s degree of centrality. The role of cognate status was also explored by repeating the former analysis separating cognate from noncognate words. Taken together, our data show that languages are structurally similar independent of the cognate status of words, further suggesting that there are some sort of core features common to both languages.

Controlling the deformation space of soft membranes using fiber reinforcement

Recent efforts in soft-body control have been hindered by the infinite dimensionality of soft bodies. Without restricting the deformation space of soft bodies to desired degrees of freedom, it is difficult, if not impossible, to guarantee that the soft body will remain constrained within a desired operating range. In this article, we present novel modeling and fabrication techniques for leveraging the reorientation of fiber arrays in soft bodies to restrict their deformation space to a critical case. Implementing this fiber reinforcement introduces unique challenges, especially in complex configurations. To address these challenges, we present a geometric technique for modeling fiber reinforcement on smooth elastomeric surfaces and a two-stage molding process to embed the fiber patterns dictated by that technique into elastomer membranes. The variable material properties afforded by fiber reinforcement are demonstrated with the canonical case of a soft, circular membrane reinforced with an embedded, intersecting fiber pattern such that it deforms into a prescribed hemispherical geometry when inflated. It remains constrained to that configuration, even with an additional increase in internal pressure. Furthermore, we show that the fiber-reinforced membrane is capable of maintaining its hemispherical shape under a load, and we present a practical application for the membrane by using it to control the buoyancy of a bioinspired autonomous underwater robot developed in our lab. An additional experiment on a circular membrane that inflates to a conical frustum is presented to provide additional validation of the versatility of the proposed model and fabrication techniques.