A single facility problem in the plane is considered, where an optimal location has to be
identified for each of finitely many time-steps with respect to time-dependent weights and
demand points. It is shown that the median objective can be reduced to a special case of the
static multifacility median problem such that results from the latter can be used to tackle the
dynamic location problem. When using block norms as distance measure between facilities,
a Finite Dominating Set (FDS) is derived. For the special case with only two time-steps, the
resulting algorithm is analyzed with respect to its worst-case complexity. Due to the relation
between dynamic location problems for T time periods and T-facility problems, this algorithm
can also be applied to the static 2-facility location problem.
We present a numerical scheme to simulate a moving rigid body with arbitrary shape suspended in a rarefied gas micro flows, in view of applications to complex computations of moving structures in micro or vacuum systems. The rarefied gas is simulated by solving the Boltzmann equation using a DSMC particle method. The motion of the rigid body is governed by the Newton-Euler equations, where the force and the torque on the rigid body is computed from the momentum transfer of the gas molecules colliding with the body. The resulting motion of the rigid body affects in turn again the gas flow in the surroundings. This means that a two-way coupling has been modeled. We validate the scheme by performing various numerical experiments in 1-, 2- and 3-dimensional computational domains. We have presented 1-dimensional actuator problem, 2-dimensional cavity driven flow problem, Brownian diffusion of a spherical particle both with translational and rotational motions, and finally thermophoresis on a spherical particles. We compare the numerical results obtained from the numerical simulations with the existing theories in each test examples.
The present research combines different paradigm in the area of visual perception of letter and words. These experiments aimed to understand the deficit underlying the problem associated with the faulty visual processing of letters and words. The present work summarizes the findings from two different types of population: (1) Dyslexics (reading-disabled children) and (2) Illiterates (adults who cannot read). In order to compare the results, comparisons were made between literate and illiterate group; dyslexics and control group (normal reading children). Differences for Even related potentials (ERP’s) between dyslexics and control children were made using mental rotation task for letters. According to the ERP’s, the effect of the mental rotation task of letter perception resulted as a delayed positive component and the component becomes less positive when the task becomes more difficult (Rotation related Negativity – RRN). The component was absent for dyslexics and present for controls. Dyslexics also showed some late effects in comparison to control children and this could be interpreted as problems at the decision stage where they are confused as to the letter is normal or mirrored. Dyslexics also have problems in responding to the letters having visual or phonological similarities (e.g. b vs d, p vs q). Visually similar letters were used to compare dyslexics and controls on a symmetry generalization task in two different contrast conditions (low and high). Dyslexics showed a similar pattern of response, and were overall slower in responding to the task compared to controls. The results were interpreted within the framework of the Functional Coordination Deficit (Lachmann, 2002). Dyslexics also showed delayed response in responding to the word recognition task during motion. Using red background decreases the Magnocellular pathway (M-pathway) activity, making more difficult to identify letters and this effect was worse for dyslexics because their M-pathway is weaker. In dyslexics, the M-pathway is worse; using a red background decreases the M activity and increases the difficulty in identifying lexical task in motion. This effect generated worse response to red compared to the green background. The reaction times with red were longer than those with green background. Further, Illiterates showed an analytic approach to responding to letters as well as on shapes. The analytic approach does not result from an individual capability to read, but is a primary base of visual organization or perception.
Real-time systems are systems that have to react correctly to stimuli from the environment within given timing constraints.
Today, real-time systems are employed everywhere in industry, not only in safety-critical systems but also in, e.g., communication, entertainment, and multimedia systems.
With the advent of multicore platforms, new challenges on the efficient exploitation of real-time systems have arisen:
First, there is the need for effective scheduling algorithms that feature low overheads to improve the use of the computational resources of real-time systems.
The goal of these algorithms is to ensure timely execution of tasks, i.e., to provide runtime guarantees.
Additionally, many systems require their scheduling algorithm to flexibly react to unforeseen events.
Second, the inherent parallelism of multicore systems leads to contention for shared hardware resources and complicates system analysis.
At any time, multiple applications run with varying resource requirements and compete for the scarce resources of the system.
As a result, there is a need for an adaptive resource management.
Achieving and implementing an effective and efficient resource management is a challenging task.
The main goal of resource management is to guarantee a minimum resource availability to real-time applications.
A further goal is to fulfill global optimization objectives, e.g., maximization of the global system performance, or the user perceived quality of service.
In this thesis, we derive methods based on the slot shifting algorithm.
Slot shifting provides flexible scheduling of time-constrained applications and can react to unforeseen events in time-triggered systems.
For this reason, we aim at designing slot shifting based algorithms targeted for multicore systems to tackle the aforementioned challenges.
The main contribution of this thesis is to present two global slot shifting algorithms targeted for multicore systems.
Additionally, we extend slot shifting algorithms to improve their runtime behavior, or to handle non-preemptive firm aperiodic tasks.
In a variety of experiments, the effectiveness and efficiency of the algorithms are evaluated and confirmed.
Finally, the thesis presents an implementation of a slot-shifting-based logic into a resource management framework for multicore systems.
Thus, the thesis closes the circle and successfully bridges the gap between real-time scheduling theory and real-world implementations.
We prove applicability of the slot shifting algorithm to effectively and efficiently perform adaptive resource management on multicore systems.
Self-adaptation allows software systems to autonomously adjust their behavior during run-time by handling all possible
operating states that violate the requirements of the managed system. This requires an adaptation engine that receives adaptation
requests during the monitoring process of the managed system and responds with an automated and appropriate adaptation
response. During the last decade, several engineering methods have been introduced to enable self-adaptation in software systems.
However, these methods lack addressing (1) run-time uncertainty that hinders the adaptation process and (2) the performance
impacts resulted from the complexity and the large number of the adaptation space. This paper presents CRATER, a framework
that builds an external adaptation engine for self-adaptive software systems. The adaptation engine, which is built on Case-based
Reasoning, handles the aforementioned challenges together. This paper is braced with an experiment illustrating the benefits of
this framework. The experimental results shows the potential of CRATER in terms handling run-time uncertainty and adaptation
remembrance that enhances the performance for large number of adaptation space.
Specification of asynchronous circuit behaviour becomes more complex as the
complexity of today’s System-On-a-Chip (SOC) design increases. This also causes
the Signal Transition Graphs (STGs) – interpreted Petri nets for the specification
of asynchronous circuit behaviour – to become bigger and more complex, which
makes it more difficult, sometimes even impossible, to synthesize an asynchronous
circuit from an STG with a tool like petrify [CKK+96] or CASCADE [BEW00].
It has, therefore, been suggested to decompose the STG as a first step; this
leads to a modular implementation [KWVB03] [KVWB05], which can reduce syn-
thesis effort by possibly avoiding state explosion or by allowing the use of library
elements. A decomposition approach for STGs was presented in [VW02] [KKT93]
[Chu87a]. The decomposition algorithm by Vogler and Wollowski [VW02] is based
on that of Chu [Chu87a] but is much more generally applicable than the one in
[KKT93] [Chu87a], and its correctness has been proved formally in [VW02].
This dissertation begins with Petri net background described in chapter 2.
It starts with a class of Petri nets called a place/transition (P/T) nets. Then
STGs, the subclass of P/T nets, is viewed. Background in net decomposition
is presented in chapter 3. It begins with the structural decomposition of P/T
nets for analysis purposes – liveness and boundedness of the net. Then STG
decomposition for synthesis from [VW02] is described.
The decomposition method from [VW02] still could be improved to deal with
STGs from real applications and to give better decomposition results. Some
improvements for [VW02] to improve decomposition result and increase algorithm
efficiency are discussed in chapter 4. These improvement ideas are suggested in
[KVWB04] and some of them are have been proved formally in [VK04].
The decomposition method from [VW02] is based on net reduction to find
an output block component. A large amount of work has to be done to reduce
an initial specification until the final component is found. This reduction is not
always possible, which causes input initially classified as irrelevant to become
relevant input for the component. But under certain conditions (e.g. if structural
auto-conflicts turn out to be non-dynamic) some of them could be reclassified as
irrelevant. If this is not done, the specifications become unnecessarily large, which
intern leads to unnecessarily large implemented circuits. Instead of reduction, a
new approach, presented in chapter 5, decomposes the original net into structural
components first. An initial output block component is found by composing the
structural components. Then, a final output block component is obtained by net
reduction.
As we cope with the structure of a net most of the time, it would be useful
to have a structural abstraction of the net. A structural abstraction algorithm
[Kan03] is presented in chapter 6. It can improve the performance in finding an
output block component in most of the cases [War05] [Taw04]. Also, the structure
net is in most cases smaller than the net itself. This increases the efficiency of the
decomposition algorithm because it allows the transitions contained in a node of
the structure graph to be contracted at the same time if the structure graph is
used as internal representation of the net.
Chapter 7 discusses the application of STG decomposition in asynchronous
circuit design. Application to speed independent circuits is discussed first. Af-
ter that 3D circuits synthesized from extended burst mode (XBM) specifications
are discussed. An algorithm for translating STG specifications to XBM specifi-
cations was first suggested by [BEW99]. This algorithm first derives the state
machine from the STG specification, then translates the state machine to XBM
specification. An XBM specification, though it is a state machine, allows some
concurrency. These concurrencies can be translated directly, without deriving
all of the possible states. An algorithm which directly translates STG to XBM
specifications, is presented in chapter 7.3.1. Finally DESI, a tool to decompose
STGs and its decomposition results are presented.
In automotive testrigs we apply load time series to components such that the outcome is as close as possible to some reference data. The testing procedure should in general be less expensive and at the same time take less time for testing. In my thesis, I propose a testrig damage optimization problem (WSDP). This approach improves upon the testrig stress optimization problem (TSOP) used as a state of the art by industry experts.
In both (TSOP) and (WSDP), we optimize the load time series for a given testrig configuration. As the name suggests, in (TSOP) the reference data is the stress time series. The detailed behaviour of the stresses as functions of time are sometimes not the most important topic. Instead the damage potential of the stress signals are considered. Since damage is not part of the objectives in the (TSOP) the total damage computed from the optimized load time series is not optimal with respect to the reference damage. Additionally, the load time series obtained is as long as the reference stress time series and the total damage computation needs cycle counting algorithms and Goodmann corrections. The use of cycle counting algorithms makes the computation of damage from load time series non-differentiable.
To overcome the issues discussed in the previous paragraph this thesis uses block loads for the load time series. Using of block loads makes the damage differentiable with respect to the load time series. Additionally, in some special cases it is shown that damage is convex when block loads are used and no cycle counting algorithms are required. Using load time series with block loads enables us to use damage in the objective function of the (WSDP).
During every iteration of the (WSDP), we have to find the maximum total damage over all plane angles. The first attempt at solving the (WSDP) uses discretization of the interval for plane angle to find the maximum total damage at each iteration. This is shown to give unreliable results and makes maximum total damage function non-differentiable with respect to the plane angle. To overcome this, damage function for a given surface stress tensor due to a block load is remodelled by Gaussian functions. The parameters for the new model are derived.
When we model the damage by Gaussian function, the total damage is computed as a sum of Gaussian functions. The plane with the maximum damage is similar to the modes of the Gaussian Mixture Models (GMM), the difference being that the Gaussian functions used in GMM are probability density functions which is not the case in the damage approximation presented in this work. We derive conditions for a single maximum for Gaussian functions, similar to the ones given for the unimodality of GMM by Aprausheva et al. in [1].
By using the conditions for a single maximum we give a clustering algorithm that merges the Gaussian functions in the sum as clusters. Each cluster obtained through clustering is such that it has a single maximum in the absence of other Gaussian functions of the sum. The approximate point of the maximum of each cluster is used as the starting point for a fixed point equation on the original damage function to get the actual maximum total damage at each iteration.
We implement the method for the (TSOP) and the two methods (with discretization and with clustering) for (WSDP) on two example problems. The results obtained from the (WSDP) using discretization is shown to be better than the results obtained from the (TSOP). Furthermore we show that, (WSDP) using clustering approach to finding the maximum total damage, takes less number of iterations and is more reliable than using discretization.
This bachelor thesis is concerned with arrangements of hyperplanes, that
is, finite collections of hyperplanes in a finite-dimensional vector
space. Such arrangements can be studied using methods from
combinatorics, topology or algebraic geometry. Our focus lies on an
algebraic object associated to an arrangement \(\mathcal{A}\), the module \(\mathcal{D(A)}\) of
logarithmic derivations along \(\mathcal{A}\). It was introduced by K. Saito in the
context of singularity theory, and intensively studied by Terao and
others. If \(\mathcal{D(A)}\) admits a basis, the arrangement \(\mathcal{A}\) is called free.
Ziegler generalized the concept of freeness to so-called
multiarrangements, where each hyperplane carries a multiplicity. Terao
conjectured that freeness of arrangements can be decided based on the
combinatorics. We pursue the analogous question for multiarrangements in
special cases. Firstly, we give a new proof of a result of Ziegler
stating that generic multiarrangements are totally non-free, that is,
non-free for any multiplicity. Our proof relies on the new concept of
unbalanced multiplicities. Secondly, we consider freeness asymptotically
for increasing multiplicity of a fixed hyperplane. We give an explicit
bound for the multiplicity where the freeness property has stabilized.
An efficient multiscale approach is established in order to compute the macroscopic response of nonlinear composites. The micro problem is rewritten in an integral form of the Lippmann-Schwinger type and solved efficiently by Fast Fourier Transforms. Using realistic microstructure models complex nonlinear effects are reproduced and validated with measured data of fiber reinforced plastics. The micro problem is integrated in a Finite Element framework which is used to solve the macroscale. The scale coupling technique and a consistent numerical algorithm is established. The method provides an efficient way to determine the macroscopic response considering arbitrary microstructures, constitutive behaviors and loading conditions.
We consider the problem of finding efficient locations of surveillance cameras, where we distinguish
between two different problems. In the first, the whole area must be monitored and the number of cameras
should be as small as possible. In the second, the goal is to maximize the monitored area for a fixed number of
cameras. In both of these problems, restrictions on the ability of the cameras, like limited depth of view or range
of vision are taken into account. We present solution approaches for these problems and report on results of
their implementations applied to an authentic problem. We also consider a bicriteria problem with two objectives:
maximizing the monitored area and minimizing the number of cameras, and solve it for our study case.
A Finite Dominating Set Algorithm for a Dynamic Location Problem in the Plane
(2014)
