Some aspects of the cenozoic geology of the Moawhango River region, in the Army training area in Waiouru, North Island, New Zealand : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Quaternary Geology at Massey University

Late Tertiary marine strata of the Waiouru Formation were unconformably deposited on a dissected Late Cretaceous peneplain surface of unusually high relief formed on Torlesse Supergroup greywacke at Waiouru. Central North Island, New Zealand. Waiouru is uniquely located on the southern boundary of the Taupo Volcanic Zone and the northern margin of the Wanganui Basin, an infilled Pliocene basin now subject to Plio-Pleistocene uplift. Two transgressive episodes are identified. The first involved submergence of the peneplain in the Neogene, when Kapitean mudstone was deposited. Then a general marine shallowing occurred around the New Zealand landmass which saw uplift of Waiouru towards the end of the Kapitean Stage, followed by a period of sub-aerial erosion. The second transgressive episode was initiated by subsidence of the Wanganui Basin in the Pliocene, which led to onlap of coarse shallow-water sandstones during the Opoitian Stage. Basement subsidence tended to result in vertical rather than horizontal migration of the shoreline. No evidence has been found for previously recognised eustatic sealevel cycles, due possibly to masking by strong tidal conditions throughout the Opoitian sequence; Waiouru being located on the northern edge of the Pliocene Kuripapango Strait. Eventually, shallow seas supported a faunal population sufficient to produce widespread carbonate skeletal fragments that formed extensive shell limestone beds at the top of the Waiouru Formation. Rapid lateral and vertical changes in the facies are interpreted as due to rapidly changing local depositional conditions. These were caused by the submerging basement initially forming a steep coast with at least two offshore islands. Marine infilling occurred within former incised river valleys 3 km wide and over 300 m in depth. Erosion of local greywacke contributed to the Opoitian sedimentation, as did a granitic source, probably in North-west Nelson, with materials transported from this latter source by currents propagating through the Kuripapango Strait. The presence of abundant granite-derived micas in Opoitian strata, yet their absence in the Kapitean strata provide a limiting age for the arrival of micas in Wanganui Basin strata. As the Wanganui Basin depocentre moved southwards, offlap and emergence occurred with Plio-Pleistocene uplift. The paleo-Moawhango River established its course in the newly uplifted strata, forming superimposed gorges where it cut into exposed basement. Except for initially deposited basal strata, dips in the Neogene marine strata are almost all uniformly consistent with the regional dip. Mapping of the shell limestone beds has shown post-Opoitian development of a small scale (<2 km wide) anticline and a minor associated fault. To the south of the study area, the Waipipian age Taihape Mudstone overlies the Waiouru Formation. The contact between the two is interpreted to be the Opoitian-Waipipian boundary and thus the Waiouru Formation was deposited within the Opoitian Stage

Improved Parameterized Algorithms for Constraint Satisfaction

For many constraint satisfaction problems, the algorithm which chooses a random assignment achieves the best possible approximation ratio. For instance, a simple random assignment for {\sc Max-E3-Sat} allows 7/8-approximation and for every \eps >0 there is no polynomial-time (7/8+\eps)-approximation unless P=NP. Another example is the {\sc Permutation CSP} of bounded arity. Given the expected fraction $\rho$ of the constraints satisfied by a random assignment (i.e. permutation), there is no (\rho+\eps)-approximation algorithm for every \eps >0, assuming the Unique Games Conjecture (UGC). In this work, we consider the following parameterization of constraint satisfaction problems. Given a set of $m$ constraints of constant arity, can we satisfy at least $\rho m +k$ constraint, where $\rho$ is the expected fraction of constraints satisfied by a random assignment? {\sc Constraint Satisfaction Problems above Average} have been posed in different forms in the literature \cite{Niedermeier2006,MahajanRamanSikdar09}. We present a faster parameterized algorithm for deciding whether $m/2+k/2$ equations can be simultaneously satisfied over ${\mathbb F}_2$. As a consequence, we obtain $O(k)$-variable bikernels for {\sc boolean CSPs} of arity $c$ for every fixed $c$, and for {\sc permutation CSPs} of arity 3. This implies linear bikernels for many problems under the "above average" parameterization, such as {\sc Max-$c$-Sat}, {\sc Set-Splitting}, {\sc Betweenness} and {\sc Max Acyclic Subgraph}. As a result, all the parameterized problems we consider in this paper admit $2^{O(k)}$-time algorithms. We also obtain non-trivial hybrid algorithms for every Max $c$-CSP: for every instance $I$, we can either approximate $I$ beyond the random assignment threshold in polynomial time, or we can find an optimal solution to $I$ in subexponential time.Comment: A preliminary version of this paper has been accepted for IPEC 201

Coevolutionary dynamics on scale-free networks

We investigate Bak-Sneppen coevolution models on scale-free networks with various degree exponents $\gamma$ including random networks. For $\gamma >3$, the critical fitness value $f_c$ approaches to a nonzero finite value in the limit $N \to \infty$, whereas $f_c$ approaches to zero as $2<\gamma \le 3$. These results are explained by showing analytically $f_c(N) \simeq A/_N$ on the networks with size $N$. The avalanche size distribution $P(s)$ shows the normal power-law behavior for $\gamma >3$. In contrast, $P(s)$ for $2 <\gamma \le 3$ has two power-law regimes. One is a short regime for small $s$ with a large exponent $\tau_1$ and the other is a long regime for large $s$ with a small exponent $\tau_2$ ($\tau_1 > \tau_2$). The origin of the two power-regimes is explained by the dynamics on an artificially-made star-linked network.Comment: 5 pages, 5 figure

Kaon and Hyperon Form Factors in Kaon Electroproduction on the Nucleon

The electromagnetic form factors of strange mesons and baryons are studied by means of kaon electroproduction on the nucleon. The response functions that are sensitive to the K0, Lambda, Sigma, and KK*\gamma transition form factors are systematically explored. The effects of these form factors on several response functions are discussed.Comment: 10 pages, Latex2e, 12 postscript figures. Invited talk given at the International Conference on Hypernuclear and Strange Particle Physics (HYP97), Brookhaven National Laboratory, USA, October 13-18, 1997. To be published in Nucl. Phys.

Who Can Win a Single-Elimination Tournament?

A single-elimination (SE) tournament is a popular way to select a winner in both sports competitions and in elections. A natural and well-studied question is the tournament fixing problem (TFP): given the set of all pairwise match outcomes, can a tournament organizer rig an SE tournament by adjusting the initial seeding so that their favorite player wins? We prove new sufficient conditions on the pairwise match outcome information and the favorite player, under which there is guaranteed to be a seeding where the player wins the tournament. Our results greatly generalize previous results. We also investigate the relationship between the set of players that can win an SE tournament under some seeding (so called SE winners) and other traditional tournament solutions. In addition, we generalize and strengthen prior work on probabilistic models for generating tournaments. For instance, we show that \emph{every} player in an $n$ player tournament generated by the Condorcet Random Model will be an SE winner even when the noise is as small as possible, $p=\Theta(\ln n/n)$; prior work only had such results for $p\geq \Omega(\sqrt{\ln n/n})$. We also establish new results for significantly more general generative models.Comment: A preliminary version appeared in Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI), 201

Quantum Bound States in Yang-Mills-Higgs Theory

We give rigorous proofs for the existence of infinitely many (non-BPS) bound states for two linear operators associated with the Yang-Mills-Higgs equations at vanishing Higgs self-coupling and for gauge group SU(2): the operator obtained by linearising the Yang-Mills-Higgs equations around a charge one monopole and the Laplace operator on the Atiyah-Hitchin moduli space of centred charge two monopoles. For the linearised system we use the Riesz-Galerkin approximation to compute upper bounds on the lowest 20 eigenvalues. We discuss the similarities in the spectrum of the linearised system and the Laplace operator, and interpret them in the light of electric-magnetic duality conjectures.Comment: minor corrections implemented; to appear in Communications in Mathematical Physic

Measured and simulated performance of a ceramic micromechanical beam steering device at 94 GHz

We report the first experimental demonstration of a transmission-mode micromechanical beam steering device for use in standoff terahertz imaging and spectroscopy. The device was constructed by laminating laser-cut 96% alumina sheets to form two plates with interlocking rectangular gratings of 762 μm period and was characterized at 94 GHz in a free-space measurement setup with an automated elevation scan. Plate tilts as great as 6° deflected the transmitted beam by 6° for the transverse electric (TE) polarization and by 4° for the transverse magnetic polarization. Finite-difference time-domain simulations of the TE performance were in good agreement with the measurements