Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds

Suppose $(X,\Omega,g)$ is a compact Spin(7)-manifold, e.g. a Riemannian 8-manifold with holonomy Spin(7), or a Calabi-Yau 4-fold. Let $G$ be U$(m)$ or SU$(m)$, and $P\to X$ be a principal $G$-bundle. We show that the infinite-dimensional moduli space ${\mathcal B}_P$ of all connections on $P$ modulo gauge is orientable, in a certain sense. We deduce that the moduli space ${\mathcal M}_P^{Spin(7)}\subset{\mathcal B}_P$ of irreducible Spin(7)-instanton connections on $P$ modulo gauge, as a manifold or derived manifold, is orientable. This improves theorems of Cao and Leung arXiv:1502.01141 and Mu\~noz and Shahbazi arXiv:1707.02998. If $X$ is a Calabi-Yau 4-fold, the derived moduli stack $\boldsymbol{\mathscr M}$ of (complexes of) coherent sheaves on $X$ is a $-2$-shifted symplectic derived stack $(\boldsymbol{\mathcal M},\omega)$ by Pantev-To\"en-Vaqui\'e-Vezzosi arXiv:1111.3209, and so has a notion of orientation by Borisov-Joyce arXiv:1504.00690. We prove that $(\boldsymbol{\mathscr M},\omega)$ is orientable, by relating algebro-geometric orientations on $(\boldsymbol{\mathscr M},\omega)$ to differential-geometric orientations on ${\mathcal B}_P$ for U$(m)$-bundles $P\to X$, and using orientability of ${\mathcal B}_P$. This has applications to the programme of defining Donaldson-Thomas type invariants counting moduli spaces of (semi)stable coherent sheaves on a Calabi-Yau 4-fold, as in Donaldson and Thomas 1998, Cao and Leung arXiv:1407.7659, and Borisov and Joyce arXiv:1504.00690. This is the third in a series arXiv:1811.01096, arXiv:1811.02405 on orientations of gauge-theoretic moduli spaces.Comment: 57 pages. (v2) Major rewrite: new title, added author, new material on Calabi-Yau manifold

A 3D microfluidic device fabrication method using thermopress bonding with multiple layers of polystyrene film

In this article, we present a fabrication method that is capable of making (3D) microfluidic devices with multiple layers of homogeneous polystyrene (PS) film. PS film was chosen as the primary device material because of its advantageous features for microfluidics applications. Thermopress is used as a bonding method because it provides sufficient bonding strength while requiring no heterogeneous bonding materials. By aligning and sequentially stacking multiple layers (3 to 20) of patterned PS film that were achieved by a craft cutter, complicated 3D structured microfluidic devices can be fabricated by multiple steps of thermopress bonding. The smallest feature that can be achieved with this method is approximately 100 μm, which is limited by the resolution of the cutter (25 μm) as well as the thickness of the PS films. Bonding characteristics of PS films are provided in this article, including a PS film bonding strength test, bonding precision assessment, and PS surface wettability manipulation. To demonstrate the capability of this method, the design, fabrication, and testing results of a 3D interacting L-shaped passive mixer are presented

Non-bisphosphonate inhibitors of isoprenoid biosynthesis identified via computer-aided drug design.

The relaxed complex scheme, a virtual-screening methodology that accounts for protein receptor flexibility, was used to identify a low-micromolar, non-bisphosphonate inhibitor of farnesyl diphosphate synthase. Serendipitously, we also found that several predicted farnesyl diphosphate synthase inhibitors were low-micromolar inhibitors of undecaprenyl diphosphate synthase. These results are of interest because farnesyl diphosphate synthase inhibitors are being pursued as both anti-infective and anticancer agents, and undecaprenyl diphosphate synthase inhibitors are antibacterial drug leads

Mobile Sensor Networks for Inspection Tasks in Harsh Industrial Environments

Recent advances in sensor technology have enabled the fast development of mobile sensor networks operating in various unknown and sometimes hazardous environments. In this paper, we introduce one integrative approach to design, analyze and test distributed control algorithms to coordinate a network of autonomous mobile sensors by utilizing both simulation tools and a robotic testbed. The research has been carried out in the context of the mobile sensing project, PicoSmart, in the northern provinces of the Netherlands for the inspection of natural gas pipelines

Input space dependent controller for civil structures exposed to multi-hazard excitations

A challenge in the control of civil structures exposed to multiple types of hazards is in the tuning of control parameters to ensure a prescribed level of performance under substantially different excitation dynamics, which could be considered as largely uncertain. A solution is to leverage data driven control algorithms, which, in their adaptive formulation, can self-tune to uncertain environments. The authors have recently proposed a new type of data-driven controller, termed input space dependent controller (ISDC), that has the particularity to adapt its input space in real-time to identify key measurements that represent the essential dynamics of the system. Previous studies have focused on time delay formulations, where the adaptive control rule would use time delayed measurements as inputs. In this configuration, termed variable multi-delay controller (VMDC), the time delay itself was adaptive, which provided the input space dependence capabilities. However, the size, or embedding dimension, of the input space was kept constant. In this paper, the authors formulate and study a strategy to also have the embedding dimension vary, therefore providing full adaptive input space capabilities. This generalization of the ISDC algorithm will allow the controller to adapt to excitations with higher levels of chaos, such as a seismic event. The performance of ISDC under multi-hazard excitations is first investigated on a single-degree-of-freedom system and compared with the previously developed and demonstrated VMDC. Results show that the adaptive embedding dimension provides significantly enhanced mitigation performance. After, the ISDC performance is assessed on two benchmark buildings equipped with a semi-active friction device and subjected to non-simultaneous multi-hazard excitations (wind, blast and earthquake). Results are compared with a sliding mode controller, where the ISDC is shown to provide better mitigation capabilities

Robust Variable Input Observer for Structural Health Monitoring of Systems Experiencing Harsh Extreme Environments

Systems experiencing events in the order of 10μs-10ms timescales, for instance highrate dynamics or harsh extreme environments, may encounter rapid damaging effects. If the structural health of such systems could be accurately estimated in a timely manner, preventative measures could be employed to minimize adverse effects. Previously, a Variable Input Observer (VIO) coupled with a neuro-observer was proposed by the authors as a potential solution in monitoring their structural health. The objective of the VIO is to provide state estimation based on an optimal input space allowed to vary as a function of time. The VIO incorporates the use of mutual information and false nearest neighbors techniques to automatically compute the time delay and embedding dimension at set time intervals. The time delay and embedding dimensions are then used to vary the input space to achieve optimal performance for the estimator based on the observed measurements from sensors. Here, we augment the VIO with a smooth transitioning technique to provide enhanced robustness. The performance of the algorithm is investigated using experimental data obtained from a complex engineering system experiencing a harsh extreme environment. Results show that the enhanced VIO incorporating a smooth transitioning input space outperforms the previous VIO strategies which allowed rapid input space adaptation

Variable input observer for nonstationary high-rate dynamic systems

Engineering systems experiencing events of amplitudes higher than 100 gn for a duration under 100 ms, here termed high-rate dynamics, can undergo rapid damaging effects. If the structural health of such systems could be accurately estimated in a timely manner, preventative measures could be employed to minimize adverse effects. For complex high-rate problems, adaptive observers have shown promise due to their capability to deal with nonstationary, noisy, and uncertain systems. However, adaptive observers have slow convergence rates, which impede their applicability to the high-rate problems. To improve on the convergence rate, we propose a variable input space concept for optimizing the use of data history of high-rate dynamics, with the objective to produce an optimal representation of the system of interest. Using the embedding theory, the algorithm sequentially selects and adapts a vector of inputs that preserves the essential dynamics of the high-rate system. In this paper, the variable input space is integrated in a wavelet neural network, which constitutes a variable input observer. The observer is simulated using experimental data from a high-rate system. Different input space adaptation methods are studied, and the performance is also compared against an optimized fixed input strategy. It is found that a smooth transition of the input space eliminates error spikes and yields faster convergence. The variable input observer is further studied in a hybrid model-/data-driven formulation, and results demonstrate significant improvement in performance gained from the added physical knowledge

Variable input observer for state estimation of high-rate dynamics

High-rate systems operating in the 10 μs to 10 ms timescale are likely to experience damaging effects due to rapid environmental changes (e.g., turbulence, ballistic impact). Some of these systems could benefit from real-time state estimation to enable their full potential. Examples of such systems include blast mitigation strategies, automotive airbag technologies, and hypersonic vehicles. Particular challenges in high-rate state estimation include: 1) complex time varying nonlinearities of system (e.g. noise, uncertainty, and disturbance); 2) rapid environmental changes; 3) requirement of high convergence rate. Here, we propose using a Variable Input Observer (VIO) concept to vary the input space as the event unfolds. When systems experience high-rate dynamics, rapid changes in the system occur. To investigate the VIO’s potential, a VIO-based neuro-observer is constructed and studied using experimental data collected from a laboratory impact test. Results demonstrate that the input space is unique to different impact conditions, and that adjusting the input space throughout the dynamic event produces better estimations than using a traditional fixed input space strategy