Consensus-Halving: Does It Ever Get Easier?

In the $\varepsilon$-Consensus-Halving problem, a fundamental problem in fair division, there are $n$ agents with valuations over the interval $[0,1]$, and the goal is to divide the interval into pieces and assign a label "$+$" or "$-$" to each piece, such that every agent values the total amount of "$+$" and the total amount of "$-$" almost equally. The problem was recently proven by Filos-Ratsikas and Goldberg [2019] to be the first "natural" complete problem for the computational class PPA, answering a decade-old open question. In this paper, we examine the extent to which the problem becomes easy to solve, if one restricts the class of valuation functions. To this end, we provide the following contributions. First, we obtain a strengthening of the PPA-hardness result of [Filos-Ratsikas and Goldberg, 2019], to the case when agents have piecewise uniform valuations with only two blocks. We obtain this result via a new reduction, which is in fact conceptually much simpler than the corresponding one in [Filos-Ratsikas and Goldberg, 2019]. Then, we consider the case of single-block (uniform) valuations and provide a parameterized polynomial time algorithm for solving $\varepsilon$-Consensus-Halving for any $\varepsilon$, as well as a polynomial-time algorithm for $\varepsilon=1/2$; these are the first algorithmic results for the problem. Finally, an important application of our new techniques is the first hardness result for a generalization of Consensus-Halving, the Consensus-$1/k$-Division problem. In particular, we prove that $\varepsilon$-Consensus-$1/3$-Division is PPAD-hard

Student\u27s Encyclopedia of Great American Writers (5 volumes)

https://digitalcommons.usu.edu/usufaculty_monographs/1028/thumbnail.jp

Tradeoff between coverage and capacity in dynamic optimization of 3g cellular networks

Abstract — For 3G cellular networks, capacity is an important objective, along with coverage, when characterizing the performance of high-data-rate services. In live networks, the effective network capacity heavily depends on the degree that the traffic load is balanced over all cells, so changing traffic patterns demand dynamic network reconfiguration to maintain good performance. Using a four-cell sample network, and antenna tilt, cell power level and pilot fraction as adjustment variables, we study the competitive character of network coverage and capacity in such a network optimization process, and how it compares to the CDMA-intrinsic coverage-capacity tradeoff driven by interference. We find that each set of variables provides its distinct coverage-capacity tradeoff behavior with widely varying and application-dependent performance gains. The study shows that the impact of dynamic load balancing highly depends on the choice of the tuning variable as well as the particular tradeoff range of operation

Evidence for involvement of a hydrophobic patch in framework region 1 of human V4-34-encoded Igs in recognition of the red blood cell I antigen

The monoclonal IgM cold agglutinins that bind to the I/i carbohydrate Ags on the surface of RBCs all have Ig H chains encoded by the V4-34 gene segment. This mandatory use indicates that distinctive amino acid sequences may be involved in recognition. Critical amino acids exist in framework region 1 (FR1) of V4-34-encoded Ig, and these generate a specific Id determinant which apparently lies close to the I binding site. However, I binding by Id-expressing Ig can be modulated by sequences in complementarity-determining region (CDR)H3. Examination of the crystal structure of an anti-I cold agglutinin has revealed a hydrophobic patch in FR1 involving residue W7 on {beta}-strand A and the AVY motif (residues 23–25) on {beta}-strand B. In this study we used mutagenesis to show that each of the strand components of the hydrophobic patch is required for binding the I carbohydrate Ag. In addition, the crystal structure reveals that amino acids in the carboxyl-terminal region of CDRH3 form a surface region adjacent to the hydrophobic patch. We propose that the I carbohydrate Ag interacts simultaneously with the entire hydrophobic patch in FR1 and with the outside surface of CDRH3. This interaction could leave most of the conventional binding site available for binding other Ags.<br/

A novel immunoglobulin superfamily receptor (19A) related to CD2 is expressed on activated lymphocytes and promotes homotypic B-cell adhesion.

A novel lymphocyte-specific immunoglobulin superfamily protein (19A) has been cloned. The predicted 335-amino-acid sequence of 19A represents a Type 1 membrane protein with homology with the CD2 family of receptors. A molecular model of the two predicted extracellular immunoglobulin-like domains of 19A has been generated using the crystal structure of CD2 as a template. In isolated lymphocytes, expression of 19A is induced by various activation stimuli, and enforced expression of the 19A gene promotes homotypic cell adhesion in a B-cell-line model. Collectively these data imply that the 19A protein plays a role in regulation of lymphocyte adhesion