Chemical Vapor Deposition of Molecular Thiolates of Bismuth, Tin and Lead & Multinuclear NMR Studies on Lead Halide Perovskites

The first part of this thesis (Chapters 3 to 5) describes the investigation on molecular single-source precursor and their successful application in the chemical vapor deposition (CVD) of Bi2S3, SnS and PbS. In the second part (Chapter 6) light was shed on the dynamics existent in the precursor solutions (c_solute ≥ 0.4 M) used for the fabrication of APbI3 (A+ = CH3NH3 +, Cs+) lead halide perovskites. Bismuth(III) alkylthiolates, Bi(SR)3 (R= –But (1a); –Pri (1b)) were applied in the CVD process as single-source precursors for both Bi2S3 and Bi. The CVD of Bi(SBut)3 (1a) produced highly oriented and uniformly shaped 2D Bi2S3 platelets. Elemental Bi was obtained from Bi(SPri)3 (1b) in unprecedented morphologies, as the first example of elemental bismuth by non-classical crystallization. Moreover, was the crystal structure of Bi(SBut)3 (1a) determined. The synthesis of the molecular precursor [Sn(SBut)(tfb-dmeda)] (2a) is reported introducing a ‘launch vehicle’-effect, thus remarkably increasing its volatility. (2a) was characterized by single crystal X-ray diffraction analysis, EI-MS, multinuclear (1H, 13C, 19F and 119Sn) and variable-temperature 1D and 2D NMR studies. The precursor (2a) was used to deposit SnS thin films by CVD on different substrates at different temperatures (300℃–450℃) and times (15 min–60 min). The crystal structure and chemical shifts δ207Pb of lead(II) alkylthiolates Pb(SBut)2 (3a) and Pb(SBui)2 (3c) is presented. The application of Pb(SPri)2 (3b) as single-source precursor for the CVD of PbS is reported. The EI-MS analysis of (3b) and (3c) revealed the molecules as monomeric in the gas phase and (3c) also as dinuclear species. The fundamental solution chemistry of PbI2 and PbI2+AI (A+ = Cs+, CH3NH3 +) in DMSO and DMF was elucidated, by means of multinuclear 207Pb-, 133Cs- and 1H-NMR titration and dilution experiments. By establishing the link between solution and solid-state 207Pb-NMR spectroscopy, which was also mirrored in the linewidths of the 133Cs- and 1H-NMR resonances, it could be shown that PbI2 and PbI2 + AI exist in dynamic equilibria in DMSO and DMF solution as polynuclear condensed PbI6-octahedra. Hereby the acceptor property of the solvents was identified as key feature that governs the solute-solvent interactions

A structural approach to kernels for ILPs: Treewidth and Total Unimodularity

Kernelization is a theoretical formalization of efficient preprocessing for NP-hard problems. Empirically, preprocessing is highly successful in practice, for example in state-of-the-art ILP-solvers like CPLEX. Motivated by this, previous work studied the existence of kernelizations for ILP related problems, e.g., for testing feasibility of Ax <= b. In contrast to the observed success of CPLEX, however, the results were largely negative. Intuitively, practical instances have far more useful structure than the worst-case instances used to prove these lower bounds. In the present paper, we study the effect that subsystems with (Gaifman graph of) bounded treewidth or totally unimodularity have on the kernelizability of the ILP feasibility problem. We show that, on the positive side, if these subsystems have a small number of variables on which they interact with the remaining instance, then we can efficiently replace them by smaller subsystems of size polynomial in the domain without changing feasibility. Thus, if large parts of an instance consist of such subsystems, then this yields a substantial size reduction. We complement this by proving that relaxations to the considered structures, e.g., larger boundaries of the subsystems, allow worst-case lower bounds against kernelization. Thus, these relaxed structures can be used to build instance families that cannot be efficiently reduced, by any approach.Comment: Extended abstract in the Proceedings of the 23rd European Symposium on Algorithms (ESA 2015

Efficient algorithms for the minimum cost perfect matching problem on general graphs

Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 1993.Thesis (Master's) -- Bilkent University, 1993Includes bibliographical refences.The minimum cost perfect matching problem is one of the rare combinatorial optimization problems for which polynomial time algorithms exist. Matching algorithms find applications in Postman Problem, Planar Multicommodity Flow Problem, in heuristics to the well known Traveling Salesman Problem, Vehicle Scheduling Problem, Graph Partitioning Problem, Set Partitioning Problem, in VLSI, et cetera. In this thesis, reviewing the existing primal-dual approaches in the literature, we present two efficient algorithms for the minimum cost perfect matching problem on general graphs. In both of the algorithms, we achieved drastic reductions in the total number of time consuming operations such as scanning, updating dual variables and reduced costs. Detailed computational analysis on randomly generated graphs has shown the proposed algorithms to be several times faster than other algorithms in the literature. Hence, we conjecture that employment of the new algorithms in the solution methods of above stated important problems would speed them up significantly.Atamtürk, AlperM.S

Power System State Estimation and Bad Data Detection by Means of Conic Relaxation

This paper is concerned with the power system state estimation problem, which aims to find the unknown operating point of a power network based on a set of available measurements. We design a penalized semidefinite programming (SDP) relaxation whose objective function consists of a surrogate for rank and an l1-norm penalty accounting for noise. Although the proposed method does not rely on initialization, its performance can be improved in presence of an initial guess for the solution. First, a sufficient condition is derived with respect to the closeness of the initial guess to the true solution to guarantee the success of the penalized SDP relaxation in the noiseless case. Second, we show that a limited number of incorrect measurements with arbitrary values have no effect on the recovery of the true solution. Furthermore, we develop a bound for the accuracy of the estimation in the case where a limited number of measurements are corrupted with arbitrarily large values and the remaining measurements are perturbed with modest noise values. The proposed technique is demonstrated on a large-scale 1354-bus European system

On the convex hull of convex quadratic optimization problems with indicators

We consider the convex quadratic optimization problem with indicator variables and arbitrary constraints on the indicators. We show that a convex hull description of the associated mixed-integer set in an extended space with a quadratic number of additional variables consists of a single positive semidefinite constraint (explicitly stated) and linear constraints. In particular, convexification of this class of problems reduces to describing a polyhedral set in an extended formulation. While the vertex representation of this polyhedral set is exponential and an explicit linear inequality description may not be readily available in general, we derive a compact mixed-integer linear formulation whose solutions coincide with the vertices of the polyhedral set. We also give descriptions in the original space of variables: we provide a description based on an infinite number of conic-quadratic inequalities, which are ``finitely generated." In particular, it is possible to characterize whether a given inequality is necessary to describe the convex hull. The new theory presented here unifies several previously established results, and paves the way toward utilizing polyhedral methods to analyze the convex hull of mixed-integer nonlinear sets

State-driven Implicit Modeling for Sparsity and Robustness in Neural Networks

Implicit models are a general class of learning models that forgo the hierarchical layer structure typical in neural networks and instead define the internal states based on an ``equilibrium'' equation, offering competitive performance and reduced memory consumption. However, training such models usually relies on expensive implicit differentiation for backward propagation. In this work, we present a new approach to training implicit models, called State-driven Implicit Modeling (SIM), where we constrain the internal states and outputs to match that of a baseline model, circumventing costly backward computations. The training problem becomes convex by construction and can be solved in a parallel fashion, thanks to its decomposable structure. We demonstrate how the SIM approach can be applied to significantly improve sparsity (parameter reduction) and robustness of baseline models trained on FashionMNIST and CIFAR-100 datasets