Quasiconformal variation of slit domains

We use quasiconformal variations to study Riemann mappings onto variable single slit domains when the slit is the tail of an appropriately smooth Jordan arc. In the real analytic case our results answer a question of Dieter Gaier and show that the function κ in Löwner's differential equation is real analytic

On Colorful Bin Packing Games

We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of $m\geq 2$ colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance

Lower bounds for several online variants of bin packing

We consider several previously studied online variants of bin packing and prove new and improved lower bounds on the asymptotic competitive ratios for them. For that, we use a method of fully adaptive constructions. In particular, we improve the lower bound for the asymptotic competitive ratio of online square packing significantly, raising it from roughly 1.68 to above 1.75.Comment: WAOA 201

Merger Simulation: A Simplified Approach with New Applications

Merger simulation is growing in importance as a tool to evaluate the unilateral competitive effects of mergers. This paper offers a relatively non-technical description of the principles of merger simulation. In addition, it introduces PCAIDS, a new and highly flexible "calibrated-demand" merger simulation methodology that is based on a simplified version of AIDS. PCAIDS can be implemented using market shares and two price elasticities; scanner or transaction-level data are not required. The paper offers some applications of merger simulation with PCAIDS that include comparisons with other simulation models. It also shows how PCAIDS can be applied to the analysis of efficiencies, divestiture, and product repositioning/entry. Finally, the paper offers an analysis of the Merger Guidelines safeharbors. A detailed mathematical appendix is included.

Merger Simulation with Brand-Level Margin: Extending PCAIDS with Nests

We present a method to calibrate empirically the demand parameters in a merger simulation model by using brand-level profit margin data. While the approach can be generalized, we develop these ideas within a particular framework the PCAIDS (proportionality- calibrated AIDS) model. We show that the brand-level margins effectively define product "nests" (products that are especially close substitutes) and substantially increase the flexibility of PCAIDS for modeling critical own- and cross-price elasticities. The model is particularly valuable for transactions at the wholesale level (where scanner data do not exist) and for geographic markets that span national borders (where comparable data may not be available), since other methods to derive elasticities, particularly those based on econometric estimation, may not be possible or may not be reliable.

A Robust AFPTAS for Online Bin Packing with Polynomial Migration

In this paper we develop general LP and ILP techniques to find an approximate solution with improved objective value close to an existing solution. The task of improving an approximate solution is closely related to a classical theorem of Cook et al. in the sensitivity analysis for LPs and ILPs. This result is often applied in designing robust algorithms for online problems. We apply our new techniques to the online bin packing problem, where it is allowed to reassign a certain number of items, measured by the migration factor. The migration factor is defined by the total size of reassigned items divided by the size of the arriving item. We obtain a robust asymptotic fully polynomial time approximation scheme (AFPTAS) for the online bin packing problem with migration factor bounded by a polynomial in $\frac{1}{\epsilon}$. This answers an open question stated by Epstein and Levin in the affirmative. As a byproduct we prove an approximate variant of the sensitivity theorem by Cook at el. for linear programs

The Dual Feminisation of HIV/AIDS

This is an Accepted Manuscript of an article published by Taylor & Francis in Globalizations on 2011, available online: http://wwww.tandfonline.com/10.1080/14747731.2010.49302

Frontostriatal Maturation Predicts Cognitive Control Failure to Appetitive Cues in Adolescents

Adolescent risk-taking is a public health issue that increases the odds of poor lifetime outcomes. One factor thought to influence adolescents' propensity for risk-taking is an enhanced sensitivity to appetitive cues, relative to an immature capacity to exert sufficient cognitive control. We tested this hypothesis by characterizing interactions among ventral striatal, dorsal striatal, and prefrontal cortical regions with varying appetitive load using fMRI scanning. Child, teen, and adult participants performed a go/no-go task with appetitive (happy faces) and neutral cues (calm faces). Impulse control to neutral cues showed linear improvement with age, whereas teens showed a nonlinear reduction in impulse control to appetitive cues. This performance decrement in teens was paralleled by enhanced activity in the ventral striatum. Prefrontal cortical recruitment correlated with overall accuracy and showed a linear response with age for no-go versus go trials. Connectivity analyses identified a ventral frontostriatal circuit including the inferior frontal gyrus and dorsal striatum during no-go versus go trials. Examining recruitment developmentally showed that teens had greater between-subject ventral-dorsal striatal coactivation relative to children and adults for happy no-go versus go trials. These findings implicate exaggerated ventral striatal representation of appetitive cues in adolescents relative to an intermediary cognitive control response. Connectivity and coactivity data suggest these systems communicate at the level of the dorsal striatum differentially across development. Biased responding in this system is one possible mechanism underlying heightened risk-taking during adolescence

The Allan Hills Meteorite Icefield-An alternative view

More than 1300 meteorites have been found on the surface of blue icefields in North Victorialand, Antarctica. The Allan Hills Icefield (about 100 km^2) has exceptionally high meteorite concentrations while other icefields to the West have much smaller concentrations. Measurements of the rates of ablation and of horizontal displacement of the ice surface near the Allan Hills have been conducted since 1978 at a 20 station triangulation network. These data show that the horizontal ice velocity at the most active stations is about one m/yr and less at the high meteorite concentration site. Ablation of the ice surface averages about 4.2 em/yr. Measurements of the oxygen isotopic composition of surface ice along the triangulation network show a rather large scatter of about 8δ^(18)O‰. This indicates that the ice comes from different areas or possibly is different in age. The terrestrial ages of Allan Hills meteorites are between 0 and 700,000 years, with only a few older than 400,000 years. A model for the appearance of meteorites on blue ice surfaces in Antarctica is that specimens are carried within the moving ice sheet to stagnant areas where they are uncovered by the ablation process (see e.g. Bull and Lipschutz, 1982). These areas ("emergent zones") are fed by ice that originally accumulated as snow at the source regions of the ice. This model accounts for the general occurrence of meteorites on blue ice fields but an additional mechanism is needed to explain the high concentrations found at the Allan Hills. It is suggested that this icefield has concentrated meteorites primarily by horizontal movement of the ice from the emergent zones located to the west of the concentration zone. These meteorites are transported by surface compressive flow of the ice into the Allan Hills Meteorite Icefield and left stranded in an area where ice is only lost by the ablation process. This model seems to be in agreement with all field and laboratory observations

Energy Density-Flux Correlations in an Unusual Quantum State and in the Vacuum

In this paper we consider the question of the degree to which negative and positive energy are intertwined. We examine in more detail a previously studied quantum state of the massless minimally coupled scalar field, which we call a ``Helfer state''. This is a state in which the energy density can be made arbitrarily negative over an arbitrarily large region of space, but only at one instant in time. In the Helfer state, the negative energy density is accompanied by rapidly time-varying energy fluxes. It is the latter feature which allows the quantum inequalities, bounds which restrict the magnitude and duration of negative energy, to hold for this class of states. An observer who initially passes through the negative energy region will quickly encounter fluxes of positive energy which subsequently enter the region. We examine in detail the correlation between the energy density and flux in the Helfer state in terms of their expectation values. We then study the correlation function between energy density and flux in the Minkowski vacuum state, for a massless minimally coupled scalar field in both two and four dimensions. In this latter analysis we examine correlation functions rather than expectation values. Remarkably, we see qualitatively similar behavior to that in the Helfer state. More specifically, an initial negative energy vacuum fluctuation in some region of space is correlated with a subsequent flux fluctuation of positive energy into the region. We speculate that the mechanism which ensures that the quantum inequalities hold in the Helfer state, as well as in other quantum states associated with negative energy, is, at least in some sense, already ``encoded'' in the fluctuations of the vacuum.Comment: 21 pages, 7 figures; published version with typos corrected and one added referenc