Hodge Theoretic Aspects of Extended Mirror Symmetry

We formulate extended mirror symmetry of Calabi-Yau threefolds with D- branes as an equivalence between variations of mixed Hodge structure under the mirror map. After an introduction to Hodge theoretic closed string mir- ror symmetry, we review the relation between D-branes, normal functions and extensions by algebraic cycles on the side of the B-model. We define an exten- sion of the A-model variation of mixed Hodge structure whose flat connection is derived from an enhancement of the quantum product by holomorphic disks ending on Lagrangian submanifolds. Our construction is based on the Solomon- Tukachinsky axioms for open Gromov-Witten invariants together with the open WDVV equations and matches the predictions from extended mirror symmetry. For the particular case of homology spheres, we define an extension of Iritani’s Gamma-integral local system and propose an extended version of the Gamma conjecture. We demonstrate the validity of the conjecture for the standard pair of branes in case of the quintic and prove a corresponding extended Mir- ror Theorem. Using the extended holomorphic anomaly equations, we explore novel invariants from one-loop amplitudes for cycles of van Geemen-type, whose A-model geometry is at present unknown

Engaging Students in a Large Lecture: An Experiment using Sudoku Puzzles

In this paper, we describe an in-class experiment that is easy to implement with large groups of students. The experiment takes approximately 15-20 minutes to run and involves each student completing one of four types of Sudoku puzzles and recording the time it takes to completion. The resulting data set can be used as a teaching tool at an introductory level right through to an advanced level of statistics. Basic methods for describing and displaying data as well as the intricacies that arise with real data may be discussed in an introductory course. The range of more sophisticated analyses that can be taught with the data set include chi-squared tests for independence, ANOVA, t- and F-tests, logistic regression and survival analysis. We describe and provide the tools to implement the experiment and illustrate several potential teaching topics using a collected data set

Engaging Students in a Large Lecture: An Experiment using Sudoku Puzzles

In this paper, we describe an in-class experiment that is easy to implement with large groups of students. The experiment takes approximately 15-20 minutes to run and involves each student completing one of four types of Sudoku puzzles and recording the time it takes to completion. The resulting data set can be used as a teaching tool at an introductory level right through to an advanced level of statistics. Basic methods for describing and displaying data as well as the intricacies that arise with real data may be discussed in an introductory course. The range of more sophisticated analyses that can be taught with the data set include chi-squared tests for independence, ANOVA, t- and F-tests, logistic regression and survival analysis. We describe and provide the tools to implement the experiment and illustrate several potential teaching topics using a collected data set

Year-round tracking of small trans-Saharan migrants using light-level geolocators

Since 1899 ringing (or banding) remained the most important source of information about migration routes, stopover sites and wintering grounds for birds that are too small to carry satellite-based tracking systems. Despite the large quantity of migrating birds ringed in their breeding areas in Europe, the number of ring recoveries from sub-Saharan Africa is very low and therefore the whereabouts of most small bird species outside the breeding season remain a mystery. With new miniaturized light-level geolocators it is now possible to look beyond the limits of ring recovery data. Here we show for the first time year round tracks of a near passerine trans-Saharan migrant, the European Hoopoe (Upupa epops epops). Three birds wintered in the Sahel zone of Western Africa where they remained stationary for most of the time. One bird chose a south-easterly route following the Italian peninsula. Birds from the same breeding population used different migration routes and wintering sites, suggesting a low level of migratory connectivity between breeding and wintering areas. Our tracking of a near passerine bird, the European Hoopoe, with light-level geolocators opens a new chapter in the research of Palaearctic-African bird migration as this new tool revolutionizes our ability to discover migration routes, stopover sites and wintering grounds of small birds

Development of a 3D printable and highly stretchable ternary organic-inorganic nanocomposite hydrogel

Hydrogels that can be processed with additive manufacturing techniques and concomitantly possess favorable mechanical properties are interesting for many advanced applications. However, the development of novel ink materials with high intrinsic 3D printing performance has been proven to be a major challenge. Herein, a novel 3D printable organic-inorganic hybrid hydrogel is developed from three components, and characterized in detail in terms of rheological property, swelling behavior and composition. The nanocomposite hydrogel combines a thermoresponsive hydrogel with clay LAPONITE (R) XLG and in situ polymerized poly(N,N-dimethylacrylamide). Before in situ polymerization, the thermogelling and shear thinning properties of the thermoresponsive hydrogel provides a system well-suited for extrusion-based 3D printing. After chemical curing of the 3D-printed constructs by free radical polymerization, the resulting interpenetrating polymer network hydrogel shows excellent mechanical strength with a high stretchability to a tensile strain at break exceeding 550%. Integrating with the advanced 3D-printing technique, the introduced material could be interesting for a wide range of applications including tissue engineering, drug delivery, soft robotics and additive manufacturing in general.Peer reviewe

View-Independent Adjoint Light Tracing for Lighting Design Optimization

Differentiable rendering methods promise the ability to optimize various parameters of 3d scenes to achieve a desired result. However, lighting design has so far received little attention in this field. In this paper, we introduce a method that enables continuous optimization of the arrangement of luminaires in a 3d scene via differentiable light tracing. Our experiments show two major issues when attempting to apply existing methods from differentiable path tracing to this problem: first, many rendering methods produce images, which restricts the ability of a designer to define lighting objectives to image space. Second, most previous methods are designed for scene geometry or material optimization and have not been extensively tested for the case of optimizing light sources. Currently available differentiable ray-tracing methods do not provide satisfactory performance, even on fairly basic test cases in our experience. In this paper, we propose a novel adjoint light tracing method that overcomes these challenges and enables gradient-based lighting design optimization in a view-independent (camera-free) way. Thus, we allow the user to paint illumination targets directly onto the 3d scene or use existing baked illumination data (e.g., light maps). Using modern ray-tracing hardware, we achieve interactive performance. We find light tracing advantageous over path tracing in this setting, as it naturally handles irregular geometry, resulting in less noise and improved optimization convergence. We compare our adjoint gradients to state-of-the-art image-based differentiable rendering methods. We also demonstrate that our gradient data works with various common optimization algorithms, providing good convergence behaviour. Qualitative comparisons with real-world scenes underline the practical applicability of our method