A poset structure on quasifibonacci partitions

In this paper, we study partitions of positive integers into distinct quasifibonacci numbers. A digraph and poset structure is constructed on the set of such partitions. Furthermore, we discuss the symmetric and recursive relations between these posets. Finally, we prove a strong generalization of Robbins' result on the coefficients of a quasifibonacci power series.Comment: 16 pages, 6 figure

Economywide impact of avian flu in Ghana: A dynamic CGE model analysis

"We use a dynamic CGE model to quantitatively assess the economywide impact of HPAI in Ghana. The likely effect of an avian flu outbreak is modeled as demand or supply shocks to the poultry sector. Our analysis shows that, while chicken is a quite small sector of the Ghanaian economy, the shock in chicken demand due to consumers' anxieties is the dominant factor in causing chicken production to fall. The indirect effect on soybean and maize that are used as chicken feed is also large. Under the worst-case scenario, soybean production will fall by 37 percent and maize by 6.4 percent. However, the economywide impact on both AgGDP and GDP is very small. In the worst-case scenario, in which chicken production falls by 70 percent in 2011, AgGDP falls by only 0.4 percent and GDP is almost unchanged. However, the livelihood impacts of a HPAI outbreak could be significant for some sections of the population in Ghana particularly those involved in the poultry sector. Micro-level analysis of chicken producers' livelihood, therefore, is necessary." from authors' abstractAvian influenza Developing countries, General equilibrium model, Computable general equilibrium (CGE) modeling, Food safety, Water quality, Water policies,

The Eigencurve is Proper

We prove that the Coleman-Mazur eigencurve is proper over the weight space for any prime p and tame level N.Comment: Final refereed version; to appear in Duke mathematical Journa

Probability Theory of Random Polygons from the Quaternionic Viewpoint

We build a new probability measure on closed space and plane polygons. The key construction is a map, given by Knutson and Hausmann using the Hopf map on quaternions, from the complex Stiefel manifold of 2-frames in n-space to the space of closed n-gons in 3-space of total length 2. Our probability measure on polygon space is defined by pushing forward Haar measure on the Stiefel manifold by this map. A similar construction yields a probability measure on plane polygons which comes from a real Stiefel manifold. The edgelengths of polygons sampled according to our measures obey beta distributions. This makes our polygon measures different from those usually studied, which have Gaussian or fixed edgelengths. One advantage of our measures is that we can explicitly compute expectations and moments for chordlengths and radii of gyration. Another is that direct sampling according to our measures is fast (linear in the number of edges) and easy to code. Some of our methods will be of independent interest in studying other probability measures on polygon spaces. We define an edge set ensemble (ESE) to be the set of polygons created by rearranging a given set of n edges. A key theorem gives a formula for the average over an ESE of the squared lengths of chords skipping k vertices in terms of k, n, and the edgelengths of the ensemble. This allows one to easily compute expected values of squared chordlengths and radii of gyration for any probability measure on polygon space invariant under rearrangements of edges.Comment: Some small typos fixed, added a calculation for the covariance of edgelengths, added pseudocode for the random polygon sampling algorithm. To appear in Communications on Pure and Applied Mathematics (CPAM

Quantum Multi-object Search Algorithm with the Availability of Partial Information

Consider the unstructured search of an unknown number l of items in a large unsorted database of size N. The multi-object quantum search algorithm consists of two parts. The first part of the algorithm is to generalize Grover's single-object search algorithm to the multi-object case and the second part is to solve a counting problem to determine l. In this paper, we study the multi-object quantum search algorithm (in continuous time), but in a more structured way by taking into account the availability of partial information. The modeling of available partial information is done simply by the combination of several prescribed, possibly overlapping, information sets with varying weights to signify the reliability of each set. The associated statistics is estimated and the algorithm efficiency and complexity are analyzed. Our analysis shows that the search algorithm described here may not be more efficient than the unstructured (generalized) multi-object Grover search if there is ``misplaced confidence''. However, if the information sets have a ``basic confidence'' property in the sense that each information set contains at least one search item, then a quadratic speedup holds on a much smaller data space, which further expedite the quantum search for the first item.Comment: 17 pages, 1 figur

New Synthetic Cannabinoids Metabolism and Strategies to Best Identify Optimal Marker Metabolites.

Synthetic cannabinoids (SCs) were initially developed as pharmacological tools to probe the endocannabinoid system and as novel pharmacotherapies, but are now highly abused. This is a serious public health and social problem throughout the world and it is highly challenging to identify which SC was consumed by the drug abusers, a necessary step to tie adverse health effects to the new drug\u27s toxicity. Two intrinsic properties complicate SC identification, their often rapid and extensive metabolism, and their generally high potency relative to the natural psychoactive Δ 9 -tetrahydrocannabinol in cannabis. Additional challenges are the lack of reference standards for the major urinary metabolites needed for forensic verification, and the sometimes differing illicit and licit status and, in some cases, identical metabolites produced by closely related SC pairs, i.e., JWH-018/AM-2201, THJ-018/THJ-2201, and BB-22/MDMB-CHMICA/ADB-CHMICA. We review current SC prevalence, establish the necessity for SC metabolism investigation and contrast the advantages and disadvantages of multiple metabolic approaches. The human hepatocyte incubation model for determining a new SC\u27s metabolism is highly recommended after comparison to human liver microsomes incubation, in silico prediction, rat in vivo, zebrafish, and fungus Cunninghamella elegans models. We evaluate SC metabolic patterns, and devise a practical strategy to select optimal urinary marker metabolites for SCs. New SCs are incubated first with human hepatocytes and major metabolites are then identified by high-resolution mass spectrometry. Although initially difficult to obtain, authentic human urine samples following the specified SC exposure are hydrolyzed and analyzed by high-resolution mass spectrometry to verify identified major metabolites. Since some SCs produce the same major urinary metabolites, documentation of the specific SC consumed may require identification of the SC parent itself in either blood or oral fluid. An encouraging trend is the recent reduction in the number of new SC introduced per year. With global collaboration and communication, we can improve education of the public about the toxicity of new SC and our response to their introduction