Riemannian Natural Gradient Methods

This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By introducing the notion of Fisher information matrix in the manifold setting, we propose a novel Riemannian natural gradient method, which can be viewed as a natural extension of the natural gradient method from the Euclidean setting to the manifold setting. We establish the almost-sure global convergence of our proposed method under standard assumptions. Moreover, we show that if the loss function satisfies certain convexity and smoothness conditions and the input-output map satisfies a Riemannian Jacobian stability condition, then our proposed method enjoys a local linear -- or, under the Lipschitz continuity of the Riemannian Jacobian of the input-output map, even quadratic -- rate of convergence. We then prove that the Riemannian Jacobian stability condition will be satisfied by a two-layer fully connected neural network with batch normalization with high probability, provided that the width of the network is sufficiently large. This demonstrates the practical relevance of our convergence rate result. Numerical experiments on applications arising from machine learning demonstrate the advantages of the proposed method over state-of-the-art ones

Assembling Nano-Objects with Polymers: From Hybrid Nanoarchitecture to Functional Materials

In polymer-nanoparticles hybrids materials, functions can be imparted either through the clever design of new nano-building blocks or by gaining control over the manner those nano-building blocks organize. The main goal here was to develop new functional polymer-nanoparticles hybrid materials using both strategies. A new generation of functional materials was developed by expanding our library of functional nanoparticles and by the optimization of processing tools used to prepare hybrid materials by the assembly of nano-objects and polymers. In those new functional materials, function is conferred by the combination of chemical composition and structure. In this thesis, two strategies have been used to fabricate assembled materials with new functions: 1) fabrication of new functional nano-building-blocks (nano-objects) and 2) processing of nano-building-blocks into hierarchical structured polymer/nanoparticle hybrid materials. To fulfill this goal, hybrid nanocapsules with damage self-reporting function (Chapter 3.1) and superparamagnetism (Chapter 3.5), disentangled single-chain polymer (Chapter 3.2), and inorganic nanoparticles with catalase-like activity and haloperoxidase-like activity (Chapter 3.3 and Chapter 3.4, respectively) have been synthesized and fabricated. Using processing methods allowing for the formation of complex hierarchical structures, such as Pickering emulsion followed by solvent evaporation (Chapter 3.1), electrospinning (Chapter 3.2, 3.3, and 3.4) or evaporation driven-assembly (Chapter 3.5) new functional materials based on the different nano-buildings blocks were prepared. The resulting nanoparticles/polymer hybrid materials, where functional nano-objects were dispersed in polymer matrices, were used to produce materials with “self-reporting”, wound healing and anti-biofouling functions. Moreover, a new assembly method, which combined evaporation assembly and magnetic assembly, has been developed to generate 3D anisotropic microstructures with superparamagnetic function. These new assemblies were able to be remotely controlled by a magnetic field and could find potential applications in micro-robotics (Chapter 3.5). With this work, it was clearly demonstrated how the combination of nanoparticle synthesis and processing methods can be used to prepare new functional materials with unique properties.In Polymernanopartikel basierten Hybridmaterialien, können Funktionen entweder durch ein cleveres Design neuer Nanobausteine oder durch die Kontrolle der Organisation solcher Nanobausteine eingeführt werden. Das Hauptziel hier war die Entwicklung neuer funktioneller Polymernanopartikel basierter Hybridmaterialien unter Verwendung dieser beiden Strategien. Eine neue Generation funktioneller Materialien wurde durch die Erweiterungen unserer Bandbreite funktioneller Nanopartikel und durch die Optimierung der Verarbeitungsmethoden zur Herstellung von Hybridmaterialien durch Anordnung von Nano-Objekten und Polymeren entwickelt. Diese neuen funktionellen Materialien erhalten ihre Funktion durch Kombination der chemischen Zusammensetzung und der Struktur. In dieser Doktorarbeit wurden zwei Strategien verwendet, um angeordnete Materialien mit neuen Funktionen herzustellen: 1) Herstellung neuer funktioneller Nano-Bausteine (Nano-Objekten) und 2) Verarbeitung von Nano-Bausteinen zu hierarchisch strukturierten Polymernanopartikel basierten Hybridmaterialien. Um dieses Ziel zu erreichen, wurden Hybridnanokapseln, die selbstständig eine Beschädigung anzeigen (Kapitel 3.1) oder mit Superparamagnetismus (Kapitel 3.5), nicht-verschlaufte Polymereinzelketten (Kapitel 3.2) und anorganische Nanopartikel mit catalaseähnlicher sowie haloperoxidaseähnlicher Aktivität (Kapitel 3.3 und 3.4) synthetisiert und verarbeitet. Durch die Verwendung von Verarbeitungsprozessen wie Pickeringemulsiierung (Kapitel 3.1), Elektrospinnen (Kapitel 3.2, 3.3 und 3.4) oder verdampfungsgetriebene Anordnung (Kapitel 3.5) wurden neue funktionelle Materialien basierend auf unterschiedlichen Nanobausteinen hergestellt. Die resultierenden Nanopartikel/Polymer-Hybridmaterialien, bei denen Nano-Objekte in einer Polymermatrix dispergiert sind, wurden zur Herstellung von Materialien mit “Selbstanzeige“, Wundheilung und Anti-Biofouling verwendet. Darüber hinaus wurde eine neue Methode zur Anordnung entwickelt, bei der verdampfungsgetrieben Anordnung und magnetische Anordnung kombiniert werden, um dreidimensionale anisotrope Mikrostrukturen mit superparamagnetischer Funktion herzustellen. Diese neuen Anordnungen konnten durch ein magnetisches Feld ferngesteuert werden und könnten Anwendung in der Mikrorobotik finden (Kapitel 3.5). Mit dieser Arbeit wurde klar gezeigt, wie die Kombination aus Nanopartikelsynthese und Verarbeitungsmethoden verwendet werden kann, um neue funktionelle Materialien mit einzigartigen Eigenschaften herzustellen

Kisspeptin in the medial amygdala and sexual behavior in male rats

AbstractThe medial amygdala (MeA) is crucial for sexual behavior; kisspeptin (Kiss1) also plays a role in sexual function. Kisspeptin receptor (Kiss1r) knockout mice display no sexual behavior. Recently Kiss1 and Kiss1r have been discovered in the posterodorsal subnucleus of the medial amygdala (MePD). We hypothesised that Kiss1 in the MePD may have an influence on male sexual behavior. To test this we bilaterally cannulated the MePD and infused kisspeptin-10 in male rats. This caused the rats to have multiple erections, an effect specific to Kiss1 receptor activation, because Kiss1r antagonism blocked the erectile response. When Kiss1 was infused into the lateral cerebroventricle, there were no observed erections. We also measured the plasma levels of LH when Kiss1 is infused into the MePD or lateral cerebroventricle; Kiss1 increased plasma LH to comparable levels when infused into both sites. We conclude that Kiss1 has a role in male sexual behavior, which is specific to the MePD

The Neural Responses of Visual Complexity in the Oddball Paradigm: An ERP Study

This research measured human neural responses to images of different visual complexity levels using the oddball paradigm to explore the neurocognitive responses of complexity perception in visual processing. In the task, 24 participants (12 females) were required to react to images with high complexity for all stimuli. We hypothesized that high-complexity stimuli would induce early visual and attentional processing effects and may elicit the visual mismatch negativity responses and the emergence of error-related negativity. Our results showed that the amplitude of P1 and N1 were unaffected by complexity in the early visual processing. Under the target stimuli, both N2 and P3b components were reported, suggesting that the N2 component was sensitive to the complexity deviation, and the attentional processing related to complexity may be derived from the occipital zone according to the feature of the P3b component. In addition, compared with the low-complexity stimulus, the high-complexity stimulus aroused a larger amplitude of the visual mismatch negativity. The detected error negativity (Ne) component reflected the error detection of the participants’ mismatch between visual complexity and psychological expectations

Modular assembly of microswimmers with liquid compartments

Artificial microswimmers, i.e. colloidal scale objects capable of self-propulsion, have garnered significant attention due to their central role as models for out of equilibrium systems. Moreover, their potential applications in diverse fields such as biomedicine, environmental remediation, and materials science have long been hypothesized, often in conjunction with their ability to deliver cargoes to overcome mass transport limitations. A very efficient way to load molecular cargoes is to disperse them in a liquid compartment, however, fabricating microswimmers with multiple liquid compartments remains a significant challenge. To address this challenge, we present a modular fabrication platform that combines microfluidic synthesis and sequential capillarity-assisted particle assembly (sCAPA) for microswimmers with various liquid compartments. We demonstrate the synthesis of monodisperse, small polymer-based microcapsules (Ø = 3–6 μm) with different liquid cargoes using a flow-focusing microfluidic device. By employing the sCAPA technique, we assemble multiple microcapsules into microswimmers with high precision, resulting in versatile microswimmers with multiple liquid compartments and programmable functionalities. Our work provides a flexible approach for the fabrication of modular microswimmers, which could potentially actively transport cargoes and release them on demand in the future.ISSN:0953-8984ISSN:1361-648

Sorting of heterogeneous colloids by AC-dielectrophoretic forces in a microfluidic chip with asymmetric orifices

Hypothesis: The synthesis of compositionally heterogeneous particles is central to the development of complex colloidal units for self-assembly and self-propulsion. Yet, as the complexity of particles grows, synthesis becomes more prone to “errors”. We hypothesize that alternating-current dielectrophoretic forces can efficiently sort Janus particles, as a function of patch size and material, and colloidal dumbbells by size. Experiments: We prepared Janus particles with different patch size and material by physical vapor deposition and colloidal dumbbells via capillarity-assisted particle assembly. We then performed sorting experiments in a microfluidic chip comprising electrodes with asymmetric orifices, specifically exploiting the dielectric contrast between different portions of the particles or their size difference to steer them towards different outlets. Findings: We calculated that the DEP force for Janus particles may switch from positive to negative as a function of composition at a critical AC frequency, thus enabling sorting different particles crossing the electrodes’ region. The predictions are confirmed by optical microscopy experiments. We also show that intact and “broken” dumbbells can be simply separated as they experience different DEP forces. The integration of multiple asymmetric orifices leads a larger zone with high field gradient to increase separation efficiency and makes it a promising tool to select precise particle populations, isolating fractions with narrowly distributed characteristics.ISSN:0021-9797ISSN:1095-710