Wasserstein Auto-Encoders of Merge Trees (and Persistence Diagrams)

This paper presents a computational framework for the Wasserstein auto-encoding of merge trees (MT-WAE), a novel extension of the classical auto-encoder neural network architecture to the Wasserstein metric space of merge trees. In contrast to traditional auto-encoders which operate on vectorized data, our formulation explicitly manipulates merge trees on their associated metric space at each layer of the network, resulting in superior accuracy and interpretability. Our novel neural network approach can be interpreted as a non-linear generalization of previous linear attempts [79] at merge tree encoding. It also trivially extends to persistence diagrams. Extensive experiments on public ensembles demonstrate the efficiency of our algorithms, with MT-WAE computations in the orders of minutes on average. We show the utility of our contributions in two applications adapted from previous work on merge tree encoding [79]. First, we apply MT-WAE to merge tree compression, by concisely representing them with their coordinates in the final layer of our auto-encoder. Second, we document an application to dimensionality reduction, by exploiting the latent space of our auto-encoder, for the visual analysis of ensemble data. We illustrate the versatility of our framework by introducing two penalty terms, to help preserve in the latent space both the Wasserstein distances between merge trees, as well as their clusters. In both applications, quantitative experiments assess the relevance of our framework. Finally, we provide a C++ implementation that can be used for reproducibility.Comment: arXiv admin note: text overlap with arXiv:2207.1096

Demonstration and Benchmarking of Next-Gen Graphics APIs

Cílem diplomové práce bylo demonstrovat vlastnosti a změřit výkonost při různých úrovních optimalizace v grafických API Mantle a Vulkan. Navrhuje vykreslovací nástroj s optimalizacemi založenými na paralelním generování command bufferů, kopírování dat na GPU pomocí perzistentně mapovaných staging bufferů, efektivních změn konfigurace vykreslovacího řetězce a descriptor setů, alokaci paměti GPU z předalokovaných stránek se sdílením regionů mezi více zdroji. Výsledkem práce je referenční implementace, která dokáže vykreslit tisíce samostatných objektů v reálném čase.The goal of master’s thesis was to demonstrate and benchmark peformance of Mantle and Vulkan APIs with different optimization methods. This thesis proposes a rendering toolkit with optimization methods based on parallel command buffer generating, persistent staging buffers mapping, minimal pipeline configuration and descriptor sets changing, device memory pre-allocating with managing and sharing between multiple resources. The result is reference implementation that could render dynamic scene with thousands of objects in real time.

Multiresolution Techniques for Real–Time Visualization of Urban Environments and Terrains

In recent times we are witnessing a steep increase in the availability of data coming from real–life environments. Nowadays, virtually everyone connected to the Internet may have instant access to a tremendous amount of data coming from satellite elevation maps, airborne time-of-flight scanners and digital cameras, street–level photographs and even cadastral maps. As for other, more traditional types of media such as pictures and videos, users of digital exploration softwares expect commodity hardware to exhibit good performance for interactive purposes, regardless of the dataset size. In this thesis we propose novel solutions to the problem of rendering large terrain and urban models on commodity platforms, both for local and remote exploration. Our solutions build on the concept of multiresolution representation, where alternative representations of the same data with different accuracy are used to selectively distribute the computational power, and consequently the visual accuracy, where it is more needed on the base of the user’s point of view. In particular, we will introduce an efficient multiresolution data compression technique for planar and spherical surfaces applied to terrain datasets which is able to handle huge amount of information at a planetary scale. We will also describe a novel data structure for compact storage and rendering of urban entities such as buildings to allow real–time exploration of cityscapes from a remote online repository. Moreover, we will show how recent technologies can be exploited to transparently integrate virtual exploration and general computer graphics techniques with web applications

Simulation of networks of spiking neurons: A review of tools and strategies

We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks.Comment: 49 pages, 24 figures, 1 table; review article, Journal of Computational Neuroscience, in press (2007

The Peano software---parallel, automaton-based, dynamically adaptive grid traversals

We discuss the design decisions, design alternatives, and rationale behind the third generation of Peano, a framework for dynamically adaptive Cartesian meshes derived from spacetrees. Peano ties the mesh traversal to the mesh storage and supports only one element-wise traversal order resulting from space-filling curves. The user is not free to choose a traversal order herself. The traversal can exploit regular grid subregions and shared memory as well as distributed memory systems with almost no modifications to a serial application code. We formalize the software design by means of two interacting automata—one automaton for the multiscale grid traversal and one for the application-specific algorithmic steps. This yields a callback-based programming paradigm. We further sketch the supported application types and the two data storage schemes realized before we detail high-performance computing aspects and lessons learned. Special emphasis is put on observations regarding the used programming idioms and algorithmic concepts. This transforms our report from a “one way to implement things” code description into a generic discussion and summary of some alternatives, rationale, and design decisions to be made for any tree-based adaptive mesh refinement software