TY - THES
AB - Computer graphics is an extremely exciting field for two reasons. On the one hand,
there is a healthy injection of pragmatism coming from the visual effects industry
that want robust algorithms that work so they can produce results at an increasingly
frantic pace. On the other hand, they must always try to push the envelope and
achieve the impossible to wow their audiences in the next blockbuster, which means
that the industry has not succumb to conservatism, and there is plenty of room to
try out new and crazy ideas if there is a chance that it will pan into something
useful.
Water simulation has been in visual effects for decades, however it still remains
extremely challenging because of its high computational cost and difficult artdirectability.
The work in this thesis tries to address some of these difficulties.
Specifically, we make the following three novel contributions to the state-of-the-art
in water simulation for visual effects.
First, we develop the first algorithm that can convert any sequence of closed
surfaces in time into a moving triangle mesh. State-of-the-art methods at the time
could only handle surfaces with fixed connectivity, but we are the first to be able to
handle surfaces that merge and split apart. This is important for water simulation
practitioners, because it allows them to convert splashy water surfaces extracted
from particles or simulated using grid-based level sets into triangle meshes that can
be either textured and enhanced with extra surface dynamics as a post-process.
We also apply our algorithm to other phenomena that merge and split apart, such
as morphs and noisy reconstructions of human performances.
Second, we formulate a surface-based energy that measures the deviation of a
water surface froma physically valid state. Such discrepancies arise when there is a
mismatch in the degrees of freedom between the water surface and the underlying
physics solver. This commonly happens when practitioners use a moving triangle
mesh with a grid-based physics solver, or when high-resolution grid-based surfaces
are combined with low-resolution physics. Following the direction of steepest
descent on our surface-based energy, we can either smooth these artifacts or turn
them into high-resolution waves by interpreting the energy as a physical potential.
Third, we extend state-of-the-art techniques in non-reflecting boundaries to handle spatially and time-varying background flows. This allows a novel new
workflow where practitioners can re-simulate part of an existing simulation, such
as removing a solid obstacle, adding a new splash or locally changing the resolution.
Such changes can easily lead to new waves in the re-simulated region that would
reflect off of the new simulation boundary, effectively ruining the illusion of a
seamless simulation boundary between the existing and new simulations. Our
non-reflecting boundaries makes sure that such waves are absorbed.
AU - Bojsen-Hansen, Morten
ID - 1122
TI - Tracking, correcting and absorbing water surface waves
ER -
TY - THES
AB - Motivated by topological Tverberg-type problems in topological combinatorics and by classical
results about embeddings (maps without double points), we study the question whether a finite
simplicial complex K can be mapped into Rd without triple, quadruple, or, more generally, r-fold points (image points with at least r distinct preimages), for a given multiplicity r ≤ 2. In particular, we are interested in maps f : K → Rd that have no global r -fold intersection points, i.e., no r -fold points with preimages in r pairwise disjoint simplices of K , and we seek necessary and sufficient conditions for the existence of such maps.
We present higher-multiplicity analogues of several classical results for embeddings, in particular of the completeness of the Van Kampen obstruction for embeddability of k -dimensional
complexes into R2k , k ≥ 3. Speciffically, we show that under suitable restrictions on the dimensions(viz., if dimK = (r ≥ 1)k and d = rk \ for some k ≥ 3), a well-known deleted product criterion (DPC ) is not only necessary but also sufficient for the existence of maps without global r -fold points. Our main technical tool is a higher-multiplicity version of the classical Whitney trick , by which pairs of isolated r -fold points of opposite sign can be eliminated by local modiffications of the map, assuming codimension d – dimK ≥ 3.
An important guiding idea for our work was that suffciency of the DPC, together with an old
result of Özaydin's on the existence of equivariant maps, might yield an approach to disproving the remaining open cases of the the long-standing topological Tverberg conjecture , i.e., to construct maps from the N -simplex σN to Rd without r-Tverberg points when r not a prime power and
N = (d + 1)(r – 1). Unfortunately, our proof of the sufficiency of the DPC requires codimension d – dimK ≥ 3, which is not satisfied for K = σN .
In 2015, Frick [16] found a very elegant way to overcome this \codimension 3 obstacle" and
to construct the first counterexamples to the topological Tverberg conjecture for all parameters(d; r ) with d ≥ 3r + 1 and r not a prime power, by a reduction1 to a suitable lower-dimensional skeleton, for which the codimension 3 restriction is satisfied and maps without r -Tverberg points exist by Özaydin's result and sufficiency of the DPC.
In this thesis, we present a different construction (which does not use the constraint method) that yields counterexamples for d ≥ 3r , r not a prime power.
AU - Mabillard, Isaac
ID - 1123
TI - Eliminating higher-multiplicity intersections: an r-fold Whitney trick for the topological Tverberg conjecture
ER -
TY - THES
AU - Morri, Maurizio
ID - 1124
TI - Optical functionalization of human class A orphan G-protein coupled receptors
ER -
TY - THES
AB - Natural environments are never constant but subject to spatial and temporal change on
all scales, increasingly so due to human activity. Hence, it is crucial to understand the
impact of environmental variation on evolutionary processes. In this thesis, I present
three topics that share the common theme of environmental variation, yet illustrate its
effect from different perspectives.
First, I show how a temporally fluctuating environment gives rise to second-order
selection on a modifier for stress-induced mutagenesis. Without fluctuations, when
populations are adapted to their environment, mutation rates are minimized. I argue
that a stress-induced mutator mechanism may only be maintained if the population is
repeatedly subjected to diverse environmental challenges, and I outline implications of
the presented results to antibiotic treatment strategies.
Second, I discuss my work on the evolution of dispersal. Besides reproducing
known results about the effect of heterogeneous habitats on dispersal, it identifies
spatial changes in dispersal type frequencies as a source for selection for increased
propensities to disperse. This concept contains effects of relatedness that are known
to promote dispersal, and I explain how it identifies other forces selecting for dispersal
and puts them on a common scale.
Third, I analyse genetic variances of phenotypic traits under multivariate stabilizing
selection. For the case of constant environments, I generalize known formulae of
equilibrium variances to multiple traits and discuss how the genetic variance of a focal
trait is influenced by selection on background traits. I conclude by presenting ideas and
preliminary work aiming at including environmental fluctuations in the form of moving
trait optima into the model.
AU - Novak, Sebastian
ID - 1125
TI - Evolutionary proccesses in variable emvironments
ER -
TY - THES
AB - Traditionally machine learning has been focusing on the problem of solving a single
task in isolation. While being quite well understood, this approach disregards an
important aspect of human learning: when facing a new problem, humans are able to
exploit knowledge acquired from previously learned tasks. Intuitively, access to several
problems simultaneously or sequentially could also be advantageous for a machine
learning system, especially if these tasks are closely related. Indeed, results of many
empirical studies have provided justification for this intuition. However, theoretical
justifications of this idea are rather limited.
The focus of this thesis is to expand the understanding of potential benefits of information
transfer between several related learning problems. We provide theoretical
analysis for three scenarios of multi-task learning - multiple kernel learning, sequential
learning and active task selection. We also provide a PAC-Bayesian perspective on
lifelong learning and investigate how the task generation process influences the generalization
guarantees in this scenario. In addition, we show how some of the obtained
theoretical results can be used to derive principled multi-task and lifelong learning
algorithms and illustrate their performance on various synthetic and real-world datasets.
AU - Pentina, Anastasia
ID - 1126
TI - Theoretical foundations of multi-task lifelong learning
ER -