The arithmetic of genus two curves with (4,4)-split Jacobians

In this paper we study genus 2 curves whose Jacobians admit a polarized (4,4)-isogeny to a product of elliptic curves. We consider base fields of characteristic different from 2 and 3, which we do not assume to be algebraically closed. We obtain a full classification of all principally polarized abelian surfaces that can arise from gluing two elliptic curves along their 4-torsion and we derive the relation their absolute invariants satisfy. As an intermediate step, we give a general description of Richelot isogenies between Jacobians of genus 2 curves, where previously only Richelot isogenies with kernels that are pointwise defined over the base field were considered. Our main tool is a Galois theoretic characterization of genus 2 curves admitting multiple Richelot isogenies.Comment: 30 page

Creating Incentives and Identifying Champions through an Open Education Award for Faculty

In an effort to boost the visibility of open educational resources (OERs) on campus, librarians from IUPUI University Library established an annual Open Education Award and corresponding event, dedicated to celebrating faculty who have committed to integrating OERs into their coursework. In a four-month period, we developed the award, sought nominations, selected a winner, and hosted an Open Education Award Ceremony. This poster will describe the development of the award, factors that contributed to its success, and how we are using the award to build our new OER program. While other universities, including Texas A&M (2019) and the University of Tennessee (2018), have implemented OER awards as part of established programs, IUPUI’s award is unique in its development and use as a tool to facilitate outreach for our newly implemented program. Initially, we were not aware how many faculty members on campus were already using OERs in their classrooms. By advertising the award broadly and soliciting self-nominations, we gained a better understanding of the number of faculty currently using OERs and those faculty members who could serve as ‘champions’ in efforts to save students money. Furthermore, the award reception served as a venue to not only reward and further incentivize OER use, but also to connect like-minded individuals and spark conversations. We identified several potential collaborators as a result of interactions at the reception. The development of an efficient project management process was a key factor in our success. We first developed a project charter and communication plan, and then used Trello, a collaborative project management tool, to create ‘boards’ of objectives and actions. Trello tracks which objectives are being worked on, who is working on what, and where they are in the process. This tool and regular meetings enabled us to easily and efficiently track our progress and overcome obstacles. We plan on using this process to create awards for other aspects of open scholarship that align with our library’s goals, including hosting a similar event for Open Access Week in October. Overall, this project was a success. We created and delivered the award in four months, received twice the anticipated nominations, and had a turnout of over 20 attendees at the reception. Our process for developing an open education award could serve as a model to others in higher education and similar institutions new to open education initiatives

Reduced order modeling of subsurface multiphase flow models using deep residual recurrent neural networks

We present a reduced order modeling (ROM) technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrent neural network for modeling the evolution of dynamical systems. The DR-RNN architecture is inspired by iterative update techniques of line search methods where a fixed number of layers are stacked together to minimize the residual (or reduced residual) of the physical model under consideration. In this manuscript, we combine DR-RNN with proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM) to reduce the computational complexity associated with high-fidelity numerical simulations. In the presented formulation, POD is used to construct an optimal set of reduced basis functions and DEIM is employed to evaluate the nonlinear terms independent of the full-order model size. We demonstrate the proposed reduced model on two uncertainty quantification test cases using Monte-Carlo simulation of subsurface flow with random permeability field. The obtained results demonstrate that DR-RNN combined with POD-DEIM provides an accurate and stable reduced model with a fixed computational budget that is much less than the computational cost of standard POD-Galerkin reduced model combined with DEIM for nonlinear dynamical systems

Multi-fidelity deep residual recurrent neural networks for uncertainty quantification

Effective propagation of uncertainty through a nonlinear dynamical system is an essential task for a number of engineering applications. One viable probabilistic approach to propagate the uncertainty from the high dimensional random inputs to the high-fidelity model outputs is Monte Carlo method. However, Monte Carlo method requires a substantial number of computationally expensive high-fidelity simulations to converge their computed estimations towards the desired statistics. Hence, performing Monte Carlo high-fidelity simulations becomes computationally prohibitive for large-scale realistic problems. Multi-fidelity approaches provide a general framework for combining a hierarchy of computationally cheap low-fidelity models to accelerate the Monte Carlo estimation of the high-fidelity model output. The objective of this thesis is to derive computationally efficient low-fidelity models and an effective multi-fidelity framework to accelerate the Monte Carlo method that uses a single high-fidelity model only. In this thesis, a physics aware recurrent neural network (RNN) called deep residual recurrent neural network (DR-RNN) is developed as an efficient low-fidelity model for nonlinear dynamical systems. The information hidden in the mathematical model representing the nonlinear dynamical system is exploited to construct the DR-RNN architecture. The developed DR-RNN is inspired by the iterative steps of line search methods in finding the residual minimiser of numerically discretized differential equations. More specifically, the stacked layers of the DR-RNN architecture is formulated to act collectively as an iterative scheme. The dynamics of DR-RNN is explicit in time with remarkable convergence and stability properties for a large time step that violates numerical stability condition. Numerical examples demonstrate that DR-RNN can effectively emulate the high-fidelity model of nonlinear physical systems with a significantly lower number of parameters in comparison to standard RNN architectures. Further, DR-RNN is combined with Proper Orthogonal Decomposition (POD) for model reduction of time dependent partial differential equations. The numerical results show the proposed DR-RNN as an explicit and stable reduced order technique. The numerical results also show significant gains in accuracy by increasing the depth of proposed DR-RNN similar to other applications of deep learning. Next, a reduced order modeling technique for subsurface multi-phase flow problems is developed building on the DR-RNN architecture. More specifically, DR-RNN is combined with POD and discrete empirical interpolation method (DEIM) to reduce the computational complexity associated with high-fidelity subsurface multi-phase flow simulations. In the presented formulation, POD is used to construct an optimal set of reduced basis functions and DEIM is employed to evaluate the nonlinear terms independent of the high-fidelity model size. The proposed ROM is demonstrated on two uncertainty quantification test cases involving Monte Carlo simulation of subsurface flow with random permeability field. The obtained results demonstrate that DR-RNN combined with POD-DEIM provides an accurate and stable ROM with a fixed computational budget that is much less than the computational cost of standard POD-Galerkin ROM combined with DEIM for nonlinear dynamical systems. Finally, this thesis focus on developing multi-fidelity framework to estimate the statistics of high-fidelity model outputs of interest. Recently, Multi-Fidelity Monte Carlo (MFMC) method and Multi-Level Monte Carlo (MLMC) method have shown to significantly accelerate the Monte Carlo estimation by making use of low cost low-fidelity models. In this thesis, the features of both the MFMC method and the MLMC method are combined into a single framework called Multi-Fidelity-Multi-Level Monte Carlo (MFML-MC) method. In MFML-MC method, MLMC framework is developed first in which a multi-level hierarchy of POD approximations of high-fidelity outputs are utilized as low-fidelity models. Next, MFMC method is incorporated into the developed MLMC framework in which the MLMC estimator is modified at each level to benefit from a level specific low-fidelity model. Finally, a variant of deep residual recurrent neural network called Model-Free DR-RNN (MF-DR-RNN) is used as a level specific low-fidelity model in the MFML-MC framework. The performance of MFML-MC method is compared to Monte Carlo estimation that uses either a high-fidelity model or a single low-fidelity model on two subsurface flow problems with random permeability field. Numerical results show that MFML-MC method provides an unbiased estimator and show speedups by orders of magnitude compared to Monte Carlo estimation that uses a single high-fidelity model

Involving users in OPAC interface design: Perspective from a UK study

This is the post-print versoin of the Article. The official published version can be accessed from the link below - Copyright @ 2007 SpringerThe purpose of this study was to determine user suggestions for a typical OPAC (Online Public Library Catalogue) application’s functionality and features. An experiment was undertaken to find out the type of interactions features that users prefer to have in an OPAC. The study revealed that regardless of users’ Information Technology (IT) backgrounds, their functionality expectations of OPACs are the same. However, based on users’ previous experiences with OPACs, their requirements with respect to specific features may change. Users should be involved early in the OPAC development cycle process in order to ensure usable and functional interface

Magnonic Einstein–de Haas Effect: Ultrafast Rotation of Magnonic Microspheres

Magnons, collective spin excitations in magnetic crystals, have attracted much interest due to their ability to couple strongly to microwaves and other quantum systems. In compact magnetic crystals, we show that there are magnonic modes that can support orbital angular momentum and that these modes can be driven by linearly polarized microwave fields. Because of conservation of angular momentum, exciting such magnon modes induces a mechanical torque on the crystal. We study a levitated magnetic crystal, a yttrium iron garnet (YIG) microsphere, where such orbital angular momentum magnon modes are driven by microwaves held in a microwave high-Q microwave cavity. We find that the YIG sphere experiences a mechanical torque and can be spun up to ultralarge angular speeds exceeding 10 GHz

REAM intensity modulator-enabled 10Gb/s colorless upstream transmission of real-time optical OFDM signals in a single-fiber-based bidirectional PON architecture

Reflective electro-absorption modulation-intensity modulators (REAM-IMs) are utilized, for the first time, to experimentally demonstrate colorless ONUs in single-fiber-based, bidirectional, intensity-modulation and direct-detection (IMDD), optical OFDM PONs (OOFDM-PONs) incorporating 25km SSMFs and OLT-side-seeded CW optical signals. The colorlessness of the REAM-IMs is characterized, based on which optimum REAM-IM operating conditions are identified. In the aforementioned PON architecture, 10Gb/s colorless upstream transmissions of end-to-end realtime OOFDM signals are successfully achieved for various wavelengths within the entire C-band. Over such a wavelength window, corresponding minimum received optical powers at the FEC limit vary in a range as small as <0.5dB. In addition, experimental measurements also indicate that Rayleigh backscattering imposes a 2.8dB optical power penalty on the 10Gb/s over 25km upstream OOFDM signal transmission. Furthermore, making use of on-line adaptive bit and power loading, a linear trade-off between aggregated signal line rate and optical power budget is observed, which shows that, for the present PON system, a 10% reduction in signal line rate can improve the optical power budget by 2.6dB. © 2012 Optical Society of America