On reconfiguration of disks in the plane and related problems

We revisit two natural reconfiguration models for systems of disjoint objects in the plane: translation and sliding. Consider a set of n pairwise interior-disjoint objects in the plane that need to be brought from a given start (initial) configuration S into a desired goal (target) configuration T, without causing collisions. In the translation model, in one move an object is translated along a fixed direction to another position in the plane. In the sliding model, one move is sliding an object to another location in the plane by means of an arbitrarily complex continuous motion (that could involve rotations). We obtain various combinatorial and computational results for these two models: (I) For systems of n congruent disks in the translation model, Abellanas et al. showed that 2n − 1 moves always suffice and ⌊8n/5 ⌋ moves are sometimes necessary for transforming the start configuration into the target configuration. Here we further improve the lower bound to ⌊5n/3 ⌋ − 1, and thereby give a partial answer to one of their open problems. (II) We show that the reconfiguration problem with congruent disks in the translation model is NPhard, in both the labeled and unlabeled variants. This answers another open problem of Abellanas et al. (III) We also show that the reconfiguration problem with congruent disks in the sliding model is NP-hard, in both the labeled and unlabeled variants. (IV) For the reconfiguration with translations of n arbitrary convex bodies in the plane, 2n moves are always sufficient and sometimes necessary

Hardness and approximation for the geodetic set problem in some graph classes

In this paper, we study the computational complexity of finding the \emph{geodetic number} of graphs. A set of vertices $S$ of a graph $G$ is a \emph{geodetic set} if any vertex of $G$ lies in some shortest path between some pair of vertices from $S$. The \textsc{Minimum Geodetic Set (MGS)} problem is to find a geodetic set with minimum cardinality. In this paper, we prove that solving the \textsc{MGS} problem is NP-hard on planar graphs with a maximum degree six and line graphs. We also show that unless $P=NP$, there is no polynomial time algorithm to solve the \textsc{MGS} problem with sublogarithmic approximation factor (in terms of the number of vertices) even on graphs with diameter $2$. On the positive side, we give an $O\left(\sqrt[3]{n}\log n\right)$-approximation algorithm for the \textsc{MGS} problem on general graphs of order $n$. We also give a $3$-approximation algorithm for the \textsc{MGS} problem on the family of solid grid graphs which is a subclass of planar graphs

‘Dark Tourism’ and the ‘Kitschification’ of 9/11

This paper aims to interrogate the framing of New York’s Ground Zero as a ‘dark tourist’ destination, with particular reference to the entanglement of notions of kitsch in academic discussions of the events of September 11th 2001. What makes Ground Zero contentious, even scandalous, for many scholars is the presence of a conspicuous commodity culture around the site in the form of tourist souvenirs, leading to accusations of kitschification of memory and the constitution of visitors as ‘tourists of history’. Drawing upon theoretical ideas of Jacques Ranciere, Bruno Latour and W. J. T. Mitchell around image politics, the alignment of kitsch with the figure of the tourist will be questioned, along with the conviction that the so-called ‘teddy-bearification’ of 9/11 threatens the formation of dangerous political subjectivities. In attempting to rid the debates of their default settings, and reliance on essentialist notions of kitsch, it is hoped that that the way will be cleared for the sociological, ethnographic and empirical work necessary to considering the cultural and political significance of the Ground Zero souvenir economy

On the Discrete Unit Disk Cover Problem

Abstract. Given a set P of n points and a set D of m unit disks on a 2-dimensional plane, the discrete unit disk cover (DUDC) problem is (i) to check whether each point in P is covered by at least one disk in D or not and (ii) if so, then find a minimum cardinality subset D ∗ ⊆ D such that unit disks in D ∗ cover all the points in P. The discrete unit disk cover problem is a geometric version of the general set cover problem which is NP-hard [14]. The general set cover problem is not approx-imable within c log |P|, for some constant c, but the DUDC problem was shown to admit a constant factor approximation. In this paper, we pro-vide an algorithm with constant approximation factor 18. The running time of the proposed algorithm is O(n log n+m logm+mn). The previ-ous best known tractable solution for the same problem was a 22-factor approximation algorithm with running time O(m2n4).

A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems

International audienceSzeliski et al. published an influential study in 2006 on energy minimization methods for Markov Random Fields (MRF). This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the phenomenal success of random field models means that the kinds of inference problems that have to be solved changed significantly. Specifically , the models today often include higher order interactions, flexible connectivity structures, large label-spaces of different car-dinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of more than 27 state-of-the-art optimization techniques on a corpus of 2,453 energy minimization instances from diverse applications in computer vision. To ensure reproducibility, we evaluate all methods in the OpenGM 2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types

Normal and intruder configurations in Si- 34 populated in the beta(-) decay of Mg-34 and Al-34

The structure of Si-34 was studied through gamma spectroscopy separately in the beta(-) decays of Mg-34 and Al-34 at the ISOLDE facility of CERN. Different configurations in Si-34 were populated independently from the two recently identified beta-decaying states in Al-34 having spin-parity assignments J(pi) = 4(-) dominated by the normal configuration pi(d(5/2))(-1) circle times nu(f(7/2)) and J(pi) = 1(+) by the intruder configuration pi(d(5/2))(-1) circle times nu(d(3/2))(-1) (f(7/2))(2). The paper reports on spectroscopic properties of Si-34 such as an extended level scheme, spin and parity assignments based on log(ft) values and gamma-ray branching ratios, absolute beta feeding intensities, and neutron emission probabilities. A total of 11 newly identified levels and 26 transitions were added to the previously known level scheme of Si-34. Large scale shell-model calculations using the SDPF-U-MIX interaction, able to treat higher order intruder configurations, are compared with the new results and conclusions are drawn concerning the predictive power of SDPF-U-MIX, the N = 20 shell gap, the level of mixing between normal and intruder configurations for the 0(1)(+), 0(2)(+), and 2(1)(+) states, and the absence of triaxial deformation in Si-3(4).Peer reviewe

Mutation of two key aspartate residues alters stoichiometry of the NhaB Na⁺/H⁺ exchanger from Klebsiella pneumoniae

Bacterial NhaB Na+/H+ exchangers belonging to the Ion Transporter superfamily are poorly characterized in contrast to Na+/H+ exchangers of the Cation Proton Antiporter superfamily which have NhaA from Escherichia coli as a prominent member. For a more detailed understanding of the intricacies of the exchanger's transport mechanism, mutational studies are essential. Therefore, we mutated two protonatable residues present in the putative transmembrane region of NhaB from Klebsiella pneumoniae (KpNhaB), which could serve as substrate binding sites, Asp146 and Asp404, to either glutamate or alanine and analyzed transport function and stability of the mutants using electrophysiological and fluorimetric techniques. While mutation of either Asp residue to Glu only had slight to moderate effects on the transport activity of the exchanger, the mutations D404A and D146A, in particular, had more profound effects on the transport function. Furthermore, a double mutant, D146A/D404A, exhibited a remarkable behavior at alkaline pH, where recorded electrical currents changed polarity, showing steady-state transport with a stoichiometry of H+:Na+ +:Na+ {> 1 stoichiometry of the WT. Thus, we showed that Asp146 and Asp404 are part of the substrate binding site(s) of KpNhaB and engineered a Na+/H+ exchanger with a variable stoichiometry

Replacement of Lys-300 with a glutamine in the NhaA Na⁺/H⁺ antiporter of Escherichia coli yields a functional electrogenic transporter

Much of the research on Na+/H+ exchange has been done in prokaryotic models, mainly on the NhaA Na+/H+-exchanger from Escherichia coli (EcNhaA). Two conserved aspartate residues, Asp-163 and Asp-164, are essential for transport and are candidates for possible binding sites for the two H+ that are exchanged for one Na+ to make the overall transport process electrogenic. More recently, a proposed mechanism of transport for EcNhaA has suggested direct binding of one of the transported H+ to the conserved Lys-300 residue, a salt bridge partner of Asp-163. This contention is supported by a study reporting that substitution of the equivalent residue, Lys-305, of a relatedNa+/H+ antiporter, NapA from Thermus thermophilus, renders the transporter electroneutral. In this work, we sought to establish whether the Lys-300 residue and its partner Asp-163 are essential for the electrogenicity of EcNhaA. To that end, we replaced Lys-300 with Gln, either alone or together with the simultaneous substitution of Asp-163 with Asn, and characterized these transporter variants in electrophysiological experiments combined with H+ transport measurements and stability analysis. We found that K300Q EcNhaA can still support electrogenic Na+/H+ antiport in EcNhaA, but has reduced thermal stability. A parallel electrophysiological investigation of the K305Q variant of TtNapA revealed that it is also electrogenic. Furthermore, replacement of both salt bridge partners in the ion-binding site of EcNhaA produced an electrogenic variant (D163N/K300Q). Our findings indicate that alternative mechanisms sustain EcNhaA activity in the absence of canonical ion-binding residues and that the conserved lysines confer structural stability

Electrogenic Cation Binding in the Electroneutral Na⁺/H⁺ Antiporter of Pyrococcus abyssi

Na+H+ antiporters in the CPA1 branch of the cation proton antiporter family drive the electroneutral exchange of H+ against Na+ ions and ensure pH homeostasis in eukaryotic and prokaryotic organisms. Although their transport cycle is overall electroneutral, specific partial reactions are electrogenic. Here, we present an electrophysiological study of the PaNhaP Na+H+ antiporter from Pyrococcus abyssi reconstituted into liposomes. Positive transient currents were recorded upon addition of Na+ to PaNhaP proteoliposomes, indicating a reaction where positive charge is rapidly displaced into the proteoliposomes with a rate constant of k > 200 s-1. We attribute the recorded currents to an electrogenic reaction that includes Na+ binding and possibly occlusion. Subsequently, positive charge is transported out of the cell during H+ binding, so that the overall reaction is electroneutral. We show that the differences in pH profile and Na+ affinity of PaNhaP and the related MjNhaP1 from Methanocaldococcus jannaschii can be attributed to an additional negatively charged glutamate residue in PaNhaP. The results are discussed in the context of the physiological function of PaNhaP and other microbial Na+H+ exchangers. We propose that both, electroneutral and electrogenic Na+H+ antiporters, represent a carefully tuned self-regulatory system, which drives the cytoplasmic pH back to neutral after any deviation