Finding a Second Hamiltonian cycle in Barnette Graphs

We study the following two problems: (1) finding a second room-partitioning of an oik, and (2) finding a second Hamiltonian cycle in cubic graphs. The existence of solution for both problems is guaranteed by a parity argument. For the first problem we prove that deciding whether a 2-oik has a room-partitioning is NP-hard, even if the 2-oik corresponds to a planar triangulation. For the problem of finding a second Hamiltonian cycle, we state the following conjecture: for every cubic planar bipartite graph finding a second Hamiltonian cycle can be found in time linear in the number of vertices via a standard pivoting algorithm. We fail to settle the conjecture, but we prove it for cubic planar bipartite WH(6)-minor free graphs

Frustration in Biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with a finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of "frustration" in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and how structure connects to function. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding, how a large part of the biological functions of proteins are related to subtle local frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. We hope to illustrate how Frustration is a fundamental concept in relating function to structural biology.Comment: 97 pages, 30 figure

Experimental statistical channel modelling for advanced wireless communication systems in indoor environments

Draadloze communicatiesystemen voor mobiele telefonie en draadloos internet zijn onmisbaar geworden in het dagelijkse leven. De grootste troef van draadloze communicatie over bedrade communicatie is de toegenomen mobiliteit. Draadloze communicatie heeft evenwel ook één groot nadeel, namelijk de onzekerheid over de kwaliteit van de link tussen zender en ontvanger. Waar bedrade communicatie een doorgedreven ontwerp van het kanaal tussen zender en ontvanger (d.i. de kabel) toelaat, is het ontwerp van het draadloze kanaal (d.i. de omgeving) bijna onmogelijk. Desondanks kunnen wel modellen van de propagatie van draadloze signalen opgesteld worden voor verschillende types omgevingen. Deze modellen laten toe om de betrouwbaarheid en de performantie van een draadloze link in te schatten. Modellering van draadloze propagatie voor indooromgevingen is het algemeen onderwerp van dit proefschrift. De propagatiemodellering in dit proefschrift betreft drie types indooromgevingen, nl. industriële en kantooromgevingen, en de omgeving binnen in een voertuig. De modellering bestaat uit statistische modellen gebaseerd op veldmetingen in deze omgevingen. Verschillende parameters van draadloze signalen worden onderzocht, zoals de variabiliteit van het signaalvermogen met de afstand en in de tijd, het signaalbereik, de dispersie in het tijdsdomein, de dispersie in het spatiaal domein en het vermogensverlies bij propagatie van buiten naar binnen een voertuig

Synthesis and NMR-based network structure analysis of cationic hydrogels for seawater applications

Superabsorbent polymers (SAPs) are hydrophilic polymer networks (i. e., hydrogels) that contain charged monomer units along the polymer backbone. Poly(sodium acrylate) (PSA), which has negatively charged carboxylate groups, is the most prominent chemical structure of SAPs. Recent studies have shown that PSA can be used as a separation medium for the desalination of salt water. This approach, however, is limited to NaCl solutions because the divalent Mg$^{2+}$ and Ca$^{2+}$ cations in seawater interact electrostatically with the anionic polymer backbone of PSA, inducing thereby a network collapse. To overcome this limitation, this dissertation explores the swelling and desalination capacity of cationic SAPs in seawater. Two cationic SAP model systems with distinct functional groups were synthesized. The first one is based on a poly(acrylamide) (PAM) derivative with a trimethyl quaternary ammonium group as the positively charged monomer unit. The second model system is based on poly(vinyl amine) (PVAm) bearing positively charged ammonium groups. Swelling capacity measurements reveal that divalent SO$_{4}^{2-}$ anions in seawater induce a network collapse of PVAm similar to the PSA analogue. In contrast, the swelling behavior of PAM hydrogels is fully unaffected by seawater, suggesting that the quaternary ammonium moiety is essential to provide seawater resistant swelling properties of SAPs. In addition to swelling capacity studies, this dissertation aims to advance our understanding of the intriguing interplay between macroscopic, mechanical properties and molecular dynamics of the hydrogel network. Due to the inherent multi-length scale structural complexity of hydrogels, the quantitative correlation of mechanical properties with molecular dynamics remains a longstanding challenge. An advanced rheometer setup consisting of a portable low-field NMR unit that is integrated into a rheometer was used to study the gelation kinetics of acrylic acid (AAc) hydrogels. The elastic modulus G′ was studied by small amplitude oscillatory time sweeps whereas the local molecular mobility of polymer network chains was probed by T$_{2}$ relaxation measurements. From the in-situ G′ and T$_{2}$ correlation plots, it can be concluded that the elastic plateau modulus is inversely proportional to the T$_{2}$ relaxation time of the hydrogel. Consequently, the mechanical strength of hydrogels can be predicted based on the segmental mobility of polymer network chains, which has important implications for the further development of non-invasive and forceless mechanical characterization techniques

An NMR Study of Helium-3 Adsorbed on Hexagonal Boron Nitride

A Pulse-NMR study of helium-3 adsorbed on hexagonal boron-nitride (BN) powder has been performed. Structurally very similar to graphite, the exposed basalplanes present a very smooth, ideal adsorbing surface and lack its undesirable strong anisotropic diamagnetism. The relaxation times T1 and T2 of helium-3 have been measured as a function of coverage, temperature and frequency. A variety of two dimensional phases have been observed including: a fluid, commensurate solid, incommensurate solid plus a separate crystallite edge film. 2D melting in the incommensurate solid and an order-disorder transition in the commensurate solid have been observed. Evidence for a low temperature, low coverage fluid+commensurate solid coexistence which transforms to a single phase at higher temperatures plus a possible domain-wall phase at higher coverages has been identified. Coupled magnetic relaxation between the helium-3 film and substrate boron-11 spins has been noted. Boron-11 relaxation times have been measured against coverage and temperature. Heteronuclear relaxation is particularly important in the commensurate phases where it can dominate homonuclear spin-lattice relaxation, providing a powerful new probe of the low coverage phases. Based on the detailed theory of coupled magnetic dipolar relaxation a model has been developed which quantitatively describes all the important features of the data many of which are unique to the BN/3He system. Presented separately in chapter 8, it concludes the magnetic properties of registered helium 3 spins are dominated by 14N�� 3He cross relaxation processes, mediated by the €14N quadrupole splitting at FQ(14N) and driven by exchange motion in the film. Using a computer for unattended, real-time experimental control has allowed substantial quantities of high quality relaxation data to be taken. Off-line, automated, numerical analysis of raw spin-echo and processed data has been extensively used. Modelling relaxation data with a stretched-exponential function, h(t) = h(0) exp(ta/T1,2) has provided a exceptionally sensitive indicator of physical changes in the film