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This thesis comprises several independent research studies on transition metal complexes as trapped ions in isolation. Electrospray Ionization (ESI) serves to transfer ions from solution into the gas phase for mass spectrometric investigations. Subsequently, a variety of experimental and theoretical methods provide fundamental insights into molecular properties of the isolated complexes: InfraRed (Multiple) Photon Dissociation (IR-(M)PD) spectroscopy provides information on binding motifs and molecular structures at cryo temperatures as well as at room temperature. Collision Induced Dissociation (CID) serves to elucidate molecular fragmentation pathways as well as relative stabilities of the complexes at room temperature. Quantum chemical calculations via Density Functional Theory (DFT) substantiate the experimental results and deepen the fundamental insights into the molecular properties of the complexes. Magnetic couplings between metal centers in oligonuclear complexes are investigated by Broken Symmetry DFT modelling and X Ray Magnetic Circular Dichroism (XMCD) spectroscopy.

”In contemporary electronics 80% of a chip may perform digital functions but the 20%
of analog functions may take 80% of the development time.” [1]. Aggravating this, the
demands on analog design is increasing with rapid technology scaling. Most designs
have moved away from analog to digital domains, where possible, however, interacting
with the environment will always require analog to digital data conversion. Adding to
this problem, the number of sensors used in consumer and industry related products are
rapidly increasing. Designers of ADCs are dealing with this problem in several ways, the
most important is the migration towards digital designs and time domain techniques.
Time to Digital Converters (TDC) are becoming increasingly popular for robust signal
processing. Biological neurons make use of spikes, which carry spike timing information
and will not be affected by the problems related to technology scaling. Neuromorphic
ADCs still remain exotic with few implementations in sub-micron technologies Table 2.7.
Even among these few designs, the strengths of biological neurons are rarely exploited.
From a previous work [2], LUCOS, a high dynamic range image sensor, the efficiency
of spike processing has been validated. The ideas from this work can be generalized to
make a highly effective sensor signal conditioning system, which carries the promise to
be robust to technology scaling.
The goal of this work is to create a novel spiking neural ADC as a novel form of a
Multi-Sensor Signal Conditioning and Conversion system, which
• Will be able to interface with or be a part of a System on Chip with traditional
analog or advanced digital components.
• Will have a graceful degradation.
• Will be robust to noise and jitter related problems.
• Will be able to learn and adapt to static errors and dynamic errors.
• Will be capable of self-repair, self-monitoring and self-calibration
Sensory systems in humans and other animals analyze the environment using several
techniques. These techniques have been evolved and perfected to help the animal sur-
vive. Different animals specialize in different sense organs, however, the peripheral
neural network architectures remain similar among various animal species with few ex-
ceptions. While there are many biological sensing techniques present, most popularly
used engineering techniques are based on intensity detection, frequency detection, and
edge detection. These techniques are used with traditional analog processing (e.g., colorvi
sensors using filters), and with biological techniques (e.g. LUCOS chip [2]). The local-
ization capability of animals has never been fully utilized.
One of the most important capabilities for animals, vertebrates or invertebrates, is the
capability for localization. The object of localization can be predator, prey, sources of
water, or food. Since these are basic necessities for survival, they evolve much faster
due to the survival of the fittest. In fact, localization capabilities, even if the sensors
are different, have convergently evolved to have same processing methods (coincidence
detection) in their peripheral neurons (for e.g., forked tongue of a snake, antennae of
a cockroach, acoustic localization in fishes and mammals). This convergent evolution
increases the validity of the technique. In this work, localization concepts based on
acoustic localization and tropotaxis are investigated and employed for creation of novel
ADCs.
Unlike intensity and frequency detection, which are not linear (for e.g. eyes saturate in
bright light, loose color perception in low light), localization is inherently linear. This
is mainly because the accurate localization of predator or prey can be the difference
between life and death for an animal.
Figure 1 visually explains the ADC concept proposed in this work. This has two parts.
(1) Sensor to Spike(time) Conversion (SSC), (2) Spike(time) to Digital Conversion(SDC).
Both of the structures have been designed with models of biological neurons. The
combination of these two structures is called SSDC.
To efficiently implement the proposed concept, a comparison of several biological neural
models is made and two models are shortlisted. Various synapse structures are also
studied. From this study, Leaky Integrate and Fire neuron (LIF) is chosen since it
fulfills all the requirements of the proposed structure. The analog neuron and synapse
designs from Indiveri et. al. [3], [4] were taken, and simulations were conducted using
cadence and the behavioral equivalence with biological counterpart was checked. The
LIF neuron had features, that were not required for the proposed approach. A simple
LIF neuron stripped of these features and was designed to be as fast as allowed by the
technology.
The SDC was designed with the neural building blocks and the delays were designed
using buffer chains. This SDC converts incoming Time Interval Code (TIC) to sparse
place coding using coincidence detection. Coincidence detection is a property of spiking
neurons, which is a time domain equivalent of a Gaussian Kernel. The SDC is designed to
have an online reconfigurable Gaussian kernel width, weight, threshold, and refractory
period. The advantage of sparse place codes, which contain rank order coding wasvii
Figure 1: ADC as a localization problem (right), Jeffress model of sound localization
visualized (left). The values t 1 and t 2 indicate the time taken from the source to s1 and
s2 respectively.
described in our work [5]. A time based winner take all circuit with memory was created
based on a previous work [6] for reading out of sparse place codes asynchronously.
The SSC was also initially designed with the same building blocks. Additionally, a
differential synapse was designed for better SSC. The sensor element considered wasviii
a Wheatstone full bridge AMR sensor AFF755 from Sensitec GmbH. A reconfigurable
version of the synapse was also designed for a more generic sensor interface.
The first prototype chip SSDCα was designed with 257 modules of coincidence detectors
realizing the SDC and the SSC. Since the spike times are the most important information,
the spikes can be treated as digital pulses. This provides the capability for digital
communication between analog modules. This creates a lot of freedom for use of digital
processing between the discussed analog modules. This advantage is fully exploited
in the design of SSDCα. Three SSC modules are multiplexed to the SDC. These SSC
modules also provide outputs from the chip simultaneously. A rising edge detecting fixed
pulse width generation circuit is used to create pulses that are best suited for efficient
performance of the SDC. The delay lines are made reconfigurable to increase robustness
and modify the span of the SDC. The readout technique used in the first prototype is
a relatively slow but safe shift register. It is used to analyze the characteristics of the
core work. This will be replaced by faster alternatives discussed in the work. The area
of the chip is 8.5 mm 2 . It has a sampling rate from DC to 150 kHz. It has a resolution
from 8-bit to 13-bit. It has 28,200 transistors on the chip. It has been designed in 350
nm CMOS technology from ams. The chip has been manufactured and tested with a
sampling rate of 10 kHz and a theoretical resolution of 8 bits. However, due to the
limitations of our Time-Interval-Generator, we are able to confirm for only 4 bits of
resolution.
The key novel contributions of this work are
• Neuromorphic implementation of AD conversion as a localization problem based
on sound localization and tropotaxis concepts found in nature.
• Coincidence detection with sparse place coding to enhance resolution.
• Graceful degradation without redundant elements, inherent robustness to noise,
which helps in scaling of technologies
• Amenable to local adaptation and self-x features.
Conceptual goals have all been fulfilled, with the exception of adaptation. The feasibility
for local adaptation has been shown with promising results and further investigation is
required for future work. This thesis work acts as a baseline, paving the way for R&D
in a new direction. The chip design has used 350 nm ams hitkit as a vehicle to prove
the functionality of the core concept. The concept can be easily ported to present
aggressively-scaled-technologies and future technologies.

In this thesis we explicitly solve several portfolio optimization problems in a very realistic setting. The fundamental assumptions on the market setting are motivated by practical experience and the resulting optimal strategies are challenged in numerical simulations.
We consider an investor who wants to maximize expected utility of terminal wealth by trading in a high-dimensional financial market with one riskless asset and several stocks.
The stock returns are driven by a Brownian motion and their drift is modelled by a Gaussian random variable. We consider a partial information setting, where the drift is unknown to the investor and has to be estimated from the observable stock prices in addition to some analyst’s opinion as proposed in [CLMZ06]. The best estimate given these observations is the well known Kalman-Bucy-Filter. We then consider an innovations process to transform the partial information setting into a market with complete information and an observable Gaussian drift process.
The investor is restricted to portfolio strategies satisfying several convex constraints.
These constraints can be due to legal restrictions, due to fund design or due to client's specifications. We cover in particular no-short-selling and no-borrowing constraints.
One popular approach to constrained portfolio optimization is the convex duality approach of Cvitanic and Karatzas. In [CK92] they introduce auxiliary stock markets with shifted market parameters and obtain a dual problem to the original portfolio optimization problem that can be better solvable than the primal problem.
Hence we consider this duality approach and using stochastic control methods we first solve the dual problems in the cases of logarithmic and power utility.
Here we apply a reverse separation approach in order to obtain areas where the corresponding Hamilton-Jacobi-Bellman differential equation can be solved. It turns out that these areas have a straightforward interpretation in terms of the resulting portfolio strategy. The areas differ between active and passive stocks, where active stocks are invested in, while passive stocks are not.
Afterwards we solve the auxiliary market given the optimal dual processes in a more general setting, allowing for various market settings and various dual processes.
We obtain explicit analytical formulas for the optimal portfolio policies and provide an algorithm that determines the correct formula for the optimal strategy in any case.
We also show optimality of our resulting portfolio strategies in different verification theorems.
Subsequently we challenge our theoretical results in a historical and an artificial simulation that are even closer to the real world market than the setting we used to derive our theoretical results. However, we still obtain compelling results indicating that our optimal strategies can outperform any benchmark in a real market in general.

This thesis brings together convex analysis and hyperspectral image processing.
Convex analysis is the study of convex functions and their properties.
Convex functions are important because they admit minimization by efficient algorithms
and the solution of many optimization problems can be formulated as
minimization of a convex objective function, extending much beyond
the classical image restoration problems of denoising, deblurring and inpainting.
\(\hspace{1mm}\)
At the heart of convex analysis is the duality mapping induced within the
class of convex functions by the Fenchel transform.
In the last decades efficient optimization algorithms have been developed based
on the Fenchel transform and the concept of infimal convolution.
\(\hspace{1mm}\)
The infimal convolution is of similar importance in convex analysis as the
convolution in classical analysis. In particular, the infimal convolution with
scaled parabolas gives rise to the one parameter family of Moreau-Yosida envelopes,
which approximate a given function from below while preserving its minimum
value and minimizers.
The closely related proximal mapping replaces the gradient step
in a recently developed class of efficient first-order iterative minimization algorithms
for non-differentiable functions. For a finite convex function,
the proximal mapping coincides with a gradient step of its Moreau-Yosida envelope.
Efficient algorithms are needed in hyperspectral image processing,
where several hundred intensity values measured in each spatial point
give rise to large data volumes.
\(\hspace{1mm}\)
In the \(\textbf{first part}\) of this thesis, we are concerned with
models and algorithms for hyperspectral unmixing.
As part of this thesis a hyperspectral imaging system was taken into operation
at the Fraunhofer ITWM Kaiserslautern to evaluate the developed algorithms on real data.
Motivated by missing-pixel defects common in current hyperspectral imaging systems,
we propose a
total variation regularized unmixing model for incomplete and noisy data
for the case when pure spectra are given.
We minimize the proposed model by a primal-dual algorithm based on the
proximum mapping and the Fenchel transform.
To solve the unmixing problem when only a library of pure spectra is provided,
we study a modification which includes a sparsity regularizer into model.
\(\hspace{1mm}\)
We end the first part with the convergence analysis for a multiplicative
algorithm derived by optimization transfer.
The proposed algorithm extends well-known multiplicative update rules
for minimizing the Kullback-Leibler divergence,
to solve a hyperspectral unmixing model in the case
when no prior knowledge of pure spectra is given.
\(\hspace{1mm}\)
In the \(\textbf{second part}\) of this thesis, we study the properties of Moreau-Yosida envelopes,
first for functions defined on Hadamard manifolds, which are (possibly) infinite-dimensional
Riemannian manifolds with negative curvature,
and then for functions defined on Hadamard spaces.
\(\hspace{1mm}\)
In particular we extend to infinite-dimensional Riemannian manifolds an expression
for the gradient of the Moreau-Yosida envelope in terms of the proximal mapping.
With the help of this expression we show that a sequence of functions
converges to a given limit function in the sense of Mosco
if the corresponding Moreau-Yosida envelopes converge pointwise at all scales.
\(\hspace{1mm}\)
Finally we extend this result to the more general setting of Hadamard spaces.
As the reverse implication is already known, this unites two definitions of Mosco convergence
on Hadamard spaces, which have both been used in the literature,
and whose equivalence has not yet been known.

Divide-and-Conquer is a common strategy to manage the complexity of system design and verification. In the context of System-on-Chip (SoC) design verification, an SoC system is decomposed into several modules and every module is separately verified. Usually an SoC module is reactive: it interacts with its environmental modules. This interaction is normally modeled by environment constraints, which are applied to verify the SoC module. Environment constraints are assumed to be always true when verifying the individual modules of a system. Therefore the correctness of environment constraints is very important for module verification.
Environment constraints are also very important for coverage analysis. Coverage analysis in formal verification measures whether or not the property set fully describes the functional behavior of the design under verification (DuV). if a set of properties describes every functional behavior of a DuV, the set of properties is called complete. To verify the correctness of environment constraints, Assume-Guarantee Reasoning rules can be employed.
However, the state of the art assume-guarantee reasoning rules cannot be applied to the environment constraints specified by using an industrial standard property language such as SystemVerilog Assertions (SVA).
This thesis proposes a new assume-guarantee reasoning rule that can be applied to environment constraints specified by using a property language such as SVA. In addition, this thesis proposes two efficient plausibility checks for constraints that can be conducted without a concrete implementation of the considered environment.
Furthermore, this thesis provides a compositional reasoning framework determining that a system is completely verified if all modules are verified with Complete Interval Property Checking (C-IPC) under environment constraints.
At present, there is a trend that more of the functionality in SoCs is shifted from the hardware to the hardware-dependent software (HWDS), which is a crucial component in an SoC, since other software layers, such as the operating systems are built on it. Therefore there is an increasing need to apply formal verification to HWDS, especially for safety-critical systems.
The interactions between HW and HWDS are often reactive, and happen in a temporal order. This requires new property languages to specify the reactive behavior at the HW and SW interfaces.
This thesis introduces a new property language, called Reactive Software Property Language (RSPL), to specify the reactive interactions between the HW and the HWDS.
Furthermore, a method for checking the completeness of software properties, which are specified by using RSPL, is presented in this thesis. This method is motivated by the approach of checking the completeness of hardware properties.

This thesis presents research studies on the fundamental interplay of diatomic molecules with transition metal compounds under cryogenic conditions. The utilized setup offers a multitude of opportunities to study isolated ions: The ions can either be generated by an ElectroSpray Ionization (ESI) source or a Laser VAPorization (LVAP) cluster ion source. The setup facilitates kinetic investigations of the ions with different reaction gases under well-defined isothermal conditions. Moreover it enables cryo InfraRed (Multiple) Photon Dissociation (IR-(M)PD) spectroscopy in combination with tunable OPO/OPA laser systems. In conjunction with density functional theory (DFT) modelling, the IR(M)-PD spectra allow for an assignment of geometric minimum structures. Furthermore DFT modelling helps to identify possible reaction pathways. Altogether the presented methods allow to gain fundamental insights into molecular structures and reactivity of the investigated systems.
The first part of this thesis focuses on the interplay of N2 with different transition metal clusters (Con+, Nin+, and Fen+) by cryo IR spectroscopy and cryo kinetics. In conjunction with DFT modelling the N2 coordination was elucidated (Con+), structures were assigned (Nin+), the concept of structure related surface adsorption behavior was introduced (Nin+), and the a first explanation for the inertness if Fe17+ was given (Fen+). Furthermore this thesis provides for a case study on the coadsorption of H2 and N2 on Ru8+ that elucidates the H migration on the Ru cluster. The last part of the thesis addresses the IR spectra of in vacuo generated [Hemin]+ complexes with N2, O2, and CO. Structures and spin states were assigned with the help of DFT modelling.

In the present work, the interaction of diatomic molecules with charged transition metal clusters and complexes was investigated. Temperature controlled isothermal kinetic studies served to elucidate the adsorption behavior of transition metal clusters. Infrared multiple photon dissociation (IR-MPD) experiments in conjunction with density functional theory (DFT) computations enabled the analysis of adsorbate induced changes on the structure and spin multiplicity of transition metal cores. A tandem cryo trap setup was used for the kinetic and spectroscopic investigations of the given compounds as isolated species in the gas phase. The presented investigations enabled insight into the metal-adsorbate bonding and provided cluster size and adsorbate coverage dependent information on cluster surface morphologies.

Computational simulations run on large supercomputers balance their outputs with the need of the scientist and the capability of the machine. Persistent storage is typically expensive and slow, its peformance grows at a slower rate than the processing power of the machine. This forces scientists to be practical about the size and frequency of the simulation outputs that can be later analyzed to understand the simulation states. Flexibility in the trade-offs of flexibilty and accessibility of the outputs of the simulations are critical the success of scientists using the supercomputers to understand their science. In situ transformations of the simulation state to be persistently stored is the focus of this dissertation.
The extreme size and parallelism of simulations can cause challenges for visualization and data analysis. This is coupled with the need to accept pre partitioned data into the analysis algorithms, which is not always well oriented toward existing software infrastructures. The work in this dissertation is focused on improving current work flows and software to accept data as it is, and efficiently produce smaller, more information rich data, for persistent storage that is easily consumed by end-user scientists. I attack this problem from both a theoretical and practical basis, by managing completely raw data to quantities of information dense visualizations and study methods for managing both the creation and persistence of data products from large scale simulations.

In current practices of system-on-chip (SoC) design a trend can be observed to integrate more and more low-level software components into the system hardware at different levels of granularity. The implementation of important control functions and communication structures is frequently shifted from the SoC’s hardware into its firmware. As a result, the tight coupling of hardware and software at a low level of granularity raises substantial verification challenges since the conventional practice of verifying hardware and software independently is no longer sufficient. This calls for new methods for verification based on a joint analysis of hardware and software.
This thesis proposes hardware-dependent models of low-level software for performing formal verification. The proposed models are conceived to represent the software integrated with its hardware environment according to the current SoC design practices. Two hardware/software integration scenarios are addressed in this thesis, namely, speed-independent communication of the processor with its hardware periphery and cycle-accurate integration of firmware into an SoC module. For speed-independent hardware/software integration an approach for equivalence checking of hardware-dependent software is proposed and an evaluated. For the case of cycle-accurate hardware/software integration, a model for hardware/software co-verification has been developed and experimentally evaluated by applying it to property checking.