Sizes of linear descriptions in combinatorial optimization

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Univ., Dissertation, 2015

Tacit collusion and capacity withholding in repeated uniform price auctions

This paper contributes to the study of tacit collusion by analyzing infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity constrained firms. Under both the Market Clearing and Maximum Accepted Price rules of determining the uniform price, we show that when each firm sets a price-quantity pair specifying the firm's minimum acceptable price and the maximum quantity the firm is willing to sell at this price, there exists a range of discount factors for which the monopoly outcome with equal sharing is sustainable in the uniform price auction, but not in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this out-come. We extend these results to the case where firms may set bids that are arbitrary step functions of price-quantity pairs with any finite number of price steps. Surprisingly, under the Maximum Accepted Price rule, firms need employ no more than two price steps to minimize the value of the discount factor

Unconstrained optimization with MINTOOLKIT for GNU octave

The paper documents MINTOOLKIT for GNU Octave. MINTOOLKIT provides functions for minimization and numeric differentiation. The main algorithms are BFGS, LBFGS, and simulated annealing. Examples are given.

Chaotic dynamics in credit constrained emerging economies

This paper analyzes the role of financial development as a source of endogenous instability in small open economies. By assuming that firms face credit constraints, our model displays a complex dynamic behavior for intermediate values of the parameter representing the level of financial development of the economy. The basic implication of our model is that economies experiencing a process of financial development are more unstable than both very underdeveloped and very developed economies. Our instability concept means that small shocks have a persistent effect on the long run behavior of the model and also that economies can exhibit cycles with a very high period or even chaotic dynamic patterns.

Constrained school choice

Recently, several school districts in the US have adopted or consider adopting the Student-Optimal Stable Mechanism or the Top Trading Cycles Mechanism to assign children to public schools. There is clear evidence that for school districts that employ (variants of) the so-called Boston Mechanism the transition would lead to efficiency gains. The first two mechanisms are strategy-proof, but in practice student assignment procedures impede students to submit a preference list that contains all their acceptable schools. Therefore, any desirable property of the mechanisms is likely toget distorted. We study the non trivial preference revelation game where students can only declare up to a fixed number (quota) of schools to be acceptable. We focus on the stability of the Nash equilibrium outcomes. Our main results identify rather stringent necessary and sufficient conditions on the priorities to guaranteestability. This stands in sharp contrast with the Boston Mechanism which yields stable Nash equilibrium outcomes, independently of the quota. Hence, the transition to any of the two mechanisms is likely to come with a higher risk that students seek legal actionas lower priority students may occupy more preferred schools.

Restriction site-associated DNA sequencing, genotyping error estimation and de novo assembly optimization for population genetic inference.

Restriction site-associated DNA sequencing (RADseq) provides researchers with the ability to record genetic polymorphism across thousands of loci for nonmodel organisms, potentially revolutionizing the field of molecular ecology. However, as with other genotyping methods, RADseq is prone to a number of sources of error that may have consequential effects for population genetic inferences, and these have received only limited attention in terms of the estimation and reporting of genotyping error rates. Here we use individual sample replicates, under the expectation of identical genotypes, to quantify genotyping error in the absence of a reference genome. We then use sample replicates to (i) optimize de novo assembly parameters within the program Stacks, by minimizing error and maximizing the retrieval of informative loci; and (ii) quantify error rates for loci, alleles and single-nucleotide polymorphisms. As an empirical example, we use a double-digest RAD data set of a nonmodel plant species, Berberis alpina, collected from high-altitude mountains in Mexico.

License prices for financially constrained firms

It is often alleged that high auction prices inhibit service deployment. We investigate this claim under the extreme case of financially constrained bidders. If demand is just slightly elastic, auctions maximize consumer surplus if consumer surplus is a convex function of quantity (a common assumption), or if consumer surplus is concave and the proportion of expenditure spent on deployment is greater than one over the elasticity of demand. The latter condition appears to be true for most of the large telecom auctions in the US and Europe. Thus, even if high auction prices inhibit service deployment, auctions appear to be optimal from the consumers' point of view.

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

Constrained school choice: an experimental study

The literature on school choice assumes that families can submit a preference list over all the schools they want to be assigned to. However, in many real-life instances families are only allowed to submit a list containing a limited number of schools. Subjects' incentives are drastically affected, as more individuals manipulate their preferences. Including a safety school in the constrained list explains most manipulations. Competitiveness across schools play an important role. Constraining choices increases segregation and affects the stability and efficiency of the final allocation. Remarkably, the constraint reduces significantly the proportion of subjects playing a dominated strategy.

Non-Cooperative Asymptotic Oligopoly in Economies with Infinitely Many Commodities

In this paper, we extend the non-cooperative analysis of oligopoly to exchange economics with infinitely many commodities by using strategic market games. This setting can be interpreted as a model of oligopoly with differentiated commodities by using the Hotelling line. We prove the existence of an "active" Cournot-Nash equilibrium and show that, when traders are replicated, the price vector and the allocation converge to the Walras equilibrium. We examine how the notion of oligopoly extends to our setting with a countable infinity of commodities by distinguishing between asymptotic oligopolists and asymptotic price-takes. We illustrate these notions via a number of examples.

Diffusion-weighted MR imaging of the spine at 3-T: feasibility, optimization of b-value and utility to differentiate benign from pathological vertebral compression fractures

Purpose: To evaluate the feasibility, determine the optimal b-value, and assess the utility of 3-T diffusion-weighted MR imaging (DWI) of the spine in differentiating benign from pathologic vertebral compression fractures.Methods and Materials: Twenty patients with 38 vertebral compression fractures (24 benign, 14 pathologic) and 20 controls (total: 23 men, 17 women, mean age 56.2years) were included from December 2010 to May 2011 in this IRB-approved prospective study. MR imaging of the spine was performed on a 3-T unit with T1-w, fat-suppressed T2-w, gadolinium-enhanced fat-suppressed T1-w and zoomed-EPI (2D RF excitation pulse combined with reduced field-of-view single-shot echo-planar readout) diffusion-w (b-values: 0, 300, 500 and 700s/mm2) sequences. Two radiologists independently assessed zoomed-EPI image quality in random order using a 4-point scale: 1=excellent to 4=poor. They subsequently measured apparent diffusion coefficients (ADCs) in normal vertebral bodies and compression fractures, in consensus.Results: Lower b-values correlated with better image quality scores, with significant differences between b=300 (mean±SD=2.6±0.8), b=500 (3.0±0.7) and b=700 (3.6±0.6) (all p<0.001). Mean ADCs of normal vertebral bodies (n=162) were 0.23, 0.17 and 0.11×10-3mm2/s with b=300, 500 and 700s/mm2, respectively. In contrast, mean ADCs were 0.89, 0.70 and 0.59×10-3mm2/s for benign vertebral compression fractures and 0.79, 0.66 and 0.51×10-3mm2/s for pathologic fractures with b=300, 500 and 700s/mm2, respectively. No significant difference was found between ADCs of benign and pathologic fractures.Conclusion: 3-T DWI of the spine is feasible and lower b-values (300s/mm2) are recommended. However, our preliminary results show no advantage of DWI in differentiating benign from pathologic vertebral compression fractures.

Optimization and inhibition of the adherent ability of Plasmodium falciparum-infected erythrocytes

The vast majority of the 1-2 million malaria associated deaths that occur each year are due to anemia and cerebral malaria (the attachment of erythrocytes containing mature forms of Plasmodium falciparum to the endothelial cells that line the vascular beds of the brain). A "model" system"for the study of cerebral malaria employs amelanotic melanoma cells as the "target"cells in an vitro cytoadherence assay. Using this model system we determined that the optimum pH for adherence is 6.6 to 6.8, that high concentrations of Ca²* (50mM) result in increased levels of binding, and that the type of buffer used influences adherence (Bis Tris > MOPS > HEPES > PIPES). We also observed that the ability of infected erythrocytes to cytoadhere varied from (erythrocyte) donor to donor. We have produced murine monoclonal antibodies against P. falciparum-infected red cells which recognized modified forms of human band 3; these inhibit the adherence of infected erythrocytes to melanoma cells in a doso responsive fashion. Antimalarials (chloroquine, quinacrine, mefloquine, artemisinin), on the other hand, affected adherence in an indirect fashion i.e. since cytoadherence is due, in part to the presence of knobs on the surface of the infected erythrocyte, and knob formation is dependent on intracellular parasite growth, when plasmodial development is inhibited so is knob production, and consequently adherence is ablated.

Budget constrained expenditure multipliers

We show that standard expenditure multipliers capture economy-wide effects of new government projects only when financing constraints are not binding. In actual policy making, however, new projects usually need financing. Under liquidity constraints, new projects are subject to two opposite effects: an income effect and a set of spending substitution effects. The former is the traditional, unrestricted, multiplier effect; the latter is the result of expenditure reallocation to upheld effective financing constraints. Unrestricted multipliers will therefore be, as a general rule, upward biased and policy designs based upon them should be reassessed in the light of the countervailing substitution effects.

Optimization of a mouse immunization protocol with Paracoccidioides brasiliensis antigens

The objectives of the present study were to optimize the protocol of mouse immunization with Paracoccidioides brasiliensis antigens (Rifkind's protocol) and to test the modulation effect of cyclophosphamide (Cy) on the delayed hypersensitivity response (DHR) of immunized animals. Experiments were carried out using one to four immunizing doses of either crude particulate P. brasiliensis antigen or yeast-cell antigen, followed by DHR test four or seven days after the last immunizing dose. The data demonstrated that an immunizing dose already elicited response; higher DHR indices were obtained with two or three immunizing doses; there were no differences between DHR indices of animals challenged four or seven days after the last dose. Overall the inoculation of two or three doses of the yeast-cell antigen, which is easier to prepare, and DHR test at day 4 simplify the original Rifkind's immunization protocol and shorten the duration of the experiments. The modulation effect of Cy on DHR was assayed with administration of 2.5, 20 and 100 mg/kg weight at seven day intervals starting from day 4 prior to the first immunizing dose. Only the treatment with 2.5 mg Cy increased the DHR indices. Treatment with 100 mg Cy inhibited the DHR, whereas 20 mg Cy did not affect the DHR indices. Results suggest an immunostimulating effect of low dose of Cy on the DHR of mice immunized with P. brasiliensis antigens.