Optimization over Young diagrams

Journal of Algebraic Combinatorics - We consider the problem of finding a Young diagram minimizing the sum of evaluations of a given pair of functions on the parts of the associated pair of...     

On the vanishing of homology in random Čech complexes

We compute the homology of random ?ech complexes over a homogeneous Poisson process on the d‐dimensional torus, and show that there are, coarsely, two phase transitions. The first transition is analogous to the Erd?s ‐Rényi phase transition, where the ?ech complex becomes connected. The second transition is where all the other homology groups are computed correctly (almost simultaneously). Our calculations also suggest a finer measurement of scales, where there is a further refinement to this picture and separation between different homology groups. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 14–51, 2017     

Thermal Effects and Structural Changes of Photosynthetic Reaction Centers Characterized by Wide Frequency Band Hydrophone: Effects of Carotenoids and Terbutryn

Photothermal characteristics and light‐induced structural (volume) changes of carotenoid‐containing and noncontaining photosynthetic reaction centers (RCs) were investigated by wide frequency band hydrophone. We found that the presence of carotenoid either does not play considerable role in the light‐induced conformational movements, or these rearrangements are too slow for inducing a photoacoustic (PA) signal. The kinetic component with a few tens of microseconds, exhibited by the carotenoid‐less RCs, appears to be similar to that of triplet state lifetimes, identified by other methods. The binding of terbutryn to the acceptor side is shown to affect the dynamics of the RC. Our results do not confirm large displacements or volume changes induced by the charge movements and by the charge relaxation processes in the RCs in few hundreds of microseconds time scale that accompanies the electron transfer between the primary and secondary electron acceptor quinones.     

Modular Symbols and the Topological Nonrigidity of Arithmetic Manifolds

In this paper we address the existence of smooth manifolds proper homotopy equivalent to nonuniform arithmetic manifolds M = Γ\G/K that are not homeomorphic to it. While the manifolds M are properly rigid if rank_ℚ(Γ) ≤ 2, we show that the so‐called virtual structure group has infinite rank as a ℚ‐vector space if rank_ℚ(Γ) ≥ 4.© 2015 Wiley Periodicals, Inc.     

Thermo-XRD-analysis of montmorillonite treated with 1,4-diaminoanthraquinone

Charcoals formed during the thermo-XRD-analysis of montmorillonite (MONT) complexes with the dye 1,4-diaminoanthraquinone (DAAQ) were investigated by using curve-fitting calculations. Five saturated dye solutions were prepared (i) in distilled water and (ii–v) in 0.1, 0.5, 1.0, and 2.0 molar HCl. Two series of dye-clay complexes were prepared by using clay suspensions of 0.6 %and of 0.006 % labeled first and second series, respectively. Five dye-clay complexes were prepared of each series by adding 25 mL of dye solution to 25 mL of clay suspension. There is no free dye in complexes of the first series, but those of the second series, which were synthesized with a high ratio between dye and clay, contain non-adsorbed dye even after five washings. Complexes of the first series are loaded with very small amounts of molecular and protonated DAAQ (5–24 mmol DAAQ per 100 g clay), and their spacings are 1.25–1.54 nm suggesting the presence of tactoids with protonated or molecular DAAQ lying parallel to the clay layers. No carbon analyses were performed to the second series complexes. In addition to tactoids with spacing of 1.32 nm, they contain tactoids with spacings of 1.81–1.96 nm, suggesting that intercalated DAAQ are lying perpendicular to the clay layers. Three types of intercalated charcoal are identified in both series during the thermal analysis, one type with a low thermal stability and two types with high thermal stabilities. Charcoals of the second series complexes preserve the geometry of the original complexes up to high temperatures.     

A polynomial oracle-time algorithm for convex integer minimization

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex N-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex N-fold integer minimization problems for which our approach provides polynomial time solution algorithms.     

N-fold integer programming and nonlinear multi-transshipment

The multi-transshipment problem is NP-hard already for two commodities over bipartite networks. Nonetheless, using our recent theory of n-fold integer programming and extensions developed herein, we are able to establish the polynomial time solvability of the problem in two broad situations. First, for any fixed number of commodities and number of suppliers, we solve the problem over bipartite networks with variable number of consumers in polynomial time. This is very natural in operations research applications where few facilities serve many customers. Second, for every fixed network, we solve the problem with variable number of commodities in polynomial time.