Design concepts for a high-impedance narrow-band 42 GHz power TWT using a fundamental/forward ladder-based circuit

A low-cost, narrowband, millimeter wave space communications TWT design was studied. Cold test interaction structure scale models were investigated and analyses were undertaken to predict the electrical and thermal response of the hypothetical 200 W TWT at 42 GHz and 21 kV beam voltage. An intentionally narrow instantaneous bandwidth (1%, with the possibility of electronic tuning of the center frequency over several percent) was sought with a highly dispersive, high impedance "forward wave' interaction structure based on a ladder (for economy in fabrication) and nonspace harmonic interaction, for a high gain rate and a short, economically focused tube. The "TunneLadder' interaction structure devised combines ladder properties with accommodation for a pencil beam. Except for the impedance and bandwidth, there is much in common with the millimeter wave helix TWTs which provided the ideal of diamond support rods. The benefits of these are enhanced in the TunneLadder case because of spatial separation of beam interception and RF current heating

State taxation of Fifth District banks

Federal Reserve District, 5th ; Banks and banking - Taxation

Quantum adiabatic optimization and combinatorial landscapes

In this paper we analyze the performance of the Quantum Adiabatic Evolution algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, $\gamma=M/N$. We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (versus only energy) is used, and are able to show the existence of a dynamic threshold $\gamma=\gamma_d$ starting with some value of K -- the number of variables in each clause. Beyond dynamic threshold, the algorithm should take exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz. We have been able to map the ensemble of random graphs onto another ensemble with fluctuations significantly reduced. This enabled us to obtain tight upper bounds on satisfiability transition and to recompute the dynamical transition using the extended set of landscapes.Comment: 41 pages, 10 figures; added a paragraph on paper's organization to the introduction, fixed reference

LIFETIME LEVERAGE CHOICE FOR PROPRIETARY FARMERS IN A DYNAMIC STOCHASTIC ENVIRONMENT

This article reviews various models that may be used to explain optimal leverage choice for the proprietary farmer in a stochastic dynamic environment and develops a new model that highlights the risk of failure rather than the usual concept of risk as the variability of wealth. The model suggests that in addition to the usual factors, farm financial leverage is affected by age, wealth, and the opportunity cost of farming.Farm Management,

On Randomized Algorithms for Matching in the Online Preemptive Model

We investigate the power of randomized algorithms for the maximum cardinality matching (MCM) and the maximum weight matching (MWM) problems in the online preemptive model. In this model, the edges of a graph are revealed one by one and the algorithm is required to always maintain a valid matching. On seeing an edge, the algorithm has to either accept or reject the edge. If accepted, then the adjacent edges are discarded. The complexity of the problem is settled for deterministic algorithms. Almost nothing is known for randomized algorithms. A lower bound of $1.693$ is known for MCM with a trivial upper bound of $2$. An upper bound of $5.356$ is known for MWM. We initiate a systematic study of the same in this paper with an aim to isolate and understand the difficulty. We begin with a primal-dual analysis of the deterministic algorithm due to McGregor. All deterministic lower bounds are on instances which are trees at every step. For this class of (unweighted) graphs we present a randomized algorithm which is $\frac{28}{15}$-competitive. The analysis is a considerable extension of the (simple) primal-dual analysis for the deterministic case. The key new technique is that the distribution of primal charge to dual variables depends on the "neighborhood" and needs to be done after having seen the entire input. The assignment is asymmetric: in that edges may assign different charges to the two end-points. Also the proof depends on a non-trivial structural statement on the performance of the algorithm on the input tree. The other main result of this paper is an extension of the deterministic lower bound of Varadaraja to a natural class of randomized algorithms which decide whether to accept a new edge or not using independent random choices

Hypes, hurdles and hopes: Energy and biofuels from biomass

The world is heading towards a crisis in providing sufficient food, water and fuel for a rapidly expanding population, while also conserving biodiversity and mitigating climate change. Through photosynthesis, plants could provide multiple solutions, helping to secure future supplies of not only food, but also energy, chemicals and materials. These roles have to be balanced to reduce conflict over the limited land resources available for cultivation. In particular, the current use of some food crop products for fuel should be superseded by the use of non-food biomass. To achieve this, the recalcitrance of lignocellulose to break down needs to be overcome and improvements in crop composition and cell walls are required to provide more optimized feedstocks for processing and conversion though biological or thermochemical routes. Research should also focus on improving energy yields of biomass crops on resource-limited land that is less suitable for food-based agriculture. Finally, the exploitation of high-value products is also needed to extract maximum value from biomass through the development of integrated biorefinery systems. In this article, brief highlights are provided of progress already achieved towards some of these goals. Such endeavours provide opportunities for biochemists to join forces with crop geneticists, biotechnologists and engineers to provide more sustainable fuels and chemicals for the future

Sum-of-squares lower bounds for planted clique

Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size k is planted in a random G(n, 1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for k ~ sqrt(n). In this paper we study the complexity of the planted clique problem under algorithms from the Sum-of-squares hierarchy. We prove the first average case lower bound for this model: for almost all graphs in G(n,1/2), r rounds of the SOS hierarchy cannot find a planted k-clique unless k > n^{1/2r} (up to logarithmic factors). Thus, for any constant number of rounds planted cliques of size n^{o(1)} cannot be found by this powerful class of algorithms. This is shown via an integrability gap for the natural formulation of maximum clique problem on random graphs for SOS and Lasserre hierarchies, which in turn follow from degree lower bounds for the Positivestellensatz proof system. We follow the usual recipe for such proofs. First, we introduce a natural "dual certificate" (also known as a "vector-solution" or "pseudo-expectation") for the given system of polynomial equations representing the problem for every fixed input graph. Then we show that the matrix associated with this dual certificate is PSD (positive semi-definite) with high probability over the choice of the input graph.This requires the use of certain tools. One is the theory of association schemes, and in particular the eigenspaces and eigenvalues of the Johnson scheme. Another is a combinatorial method we develop to compute (via traces) norm bounds for certain random matrices whose entries are highly dependent; we hope this method will be useful elsewhere