QPTAS and Subexponential Algorithm for Maximum Clique on Disk Graphs

A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for Maximum Clique on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics '90]. Since then, it has been an intriguing open question whether or not tractability can be extended to general disk graphs. We show the rather surprising structural result that a disjoint union of cycles is the complement of a disk graph if and only if at most one of those cycles is of odd length. From that, we derive the first QPTAS and subexponential algorithm running in time 2^{O~(n^{2/3})} for Maximum Clique on disk graphs. In stark contrast, Maximum Clique on intersection graphs of filled ellipses or filled triangles is unlikely to have such algorithms, even when the ellipses are close to unit disks. Indeed, we show that there is a constant ratio of approximation which cannot be attained even in time 2^{n^{1-epsilon}}, unless the Exponential Time Hypothesis fails

The eclipsing bursting X-ray binary EXO 0748-676 revisited by XMM-Newton

The bright eclipsing and bursting low-mass X-ray binary EXO 0748-676 has been observed at several occasions by XMM-Newton during the initial calibration and performance verification (CAL/PV) phase. We present here the results obtained from observations with the EPIC cameras. Apart from several type-I X-ray bursts, the source shows a high degree of variability with the presence of soft flares. The wide energy coverage and high sensitivity of XMM-Newton allows for the first time a detailed description of the spectral variability. The source is found to be the superposition of a central (~2 10^8 cm) Comptonized emission, most probably a corona surrounding the inner edge of an accretion disk, associated with a more extended (~3 10^10 cm) thermal halo at a typical temperature of ~0.6 keV with an indication of non-solar abundances. Most of the variations of the source can be accounted for by a variable absorption affecting only the central comptonized component and reaching up to NH ~1.3 10^23 cm^{-2}. The characteristics of the surrounding halo are found compatible with an irradiated atmosphere of an accretion disc which intercepts the central emission due to the system high inclination.Comment: 6 pages, 4 figures, accepted for publication in A&A Letters, XMM special issu

Structural relationship between link proteins and proteoglycan monomers

AbstractStructural homologies between link proteins and proteoglycan monomers are demonstrated. A possible redundancy in the proteoglycan monomers structure is discussed and the link proteins domains homologous to other proteins are specified

Memory Effects in the Standard Model for Glasses

The standard model of glasses is an ensemble of two-level systems interacting with a thermal bath. The general origin of memory effects in this model is a quasi-stationary but non-equilibrium state of a single two-level system, which is realized due to a finite-rate cooling and very slow thermally activated relaxation. We show that single particle memory effects, such as negativity of the specific heat under reheating, vanish for a sufficiently disordered ensemble. In contrast, a disordered ensemble displays a collective memory effect [similar to that described by Kovacs for glassy polymers], where non-equilibrium features of the ensemble are monitored via a macroscopic observable. An experimental realization of the effect can be used to further assess the consistency of the model.Comment: 4 pages, 6 figure

Designing RNA secondary structures is hard

An RNA sequence is a word over an alphabet on four elements {A, C, G, U} called bases. RNA sequences fold into secondary structures where some bases match one another while others remain unpaired. Pseudoknot-free secondary structures can be represented as well-parenthesized expressions with additional dots, where pairs of matching parentheses symbolize paired bases and dots, unpaired bases. The two fundamental problems in RNA algorithmic are to predict how sequences fold within some model of energy and to design sequences of bases which will fold into targeted secondary structures. Predicting how a given RNA sequence folds into a pseudoknot-free secondary structure is known to be solvable in cubic time since the eighties and in truly subcubic time by a recent result of Bringmann et al. (FOCS 2016), whereas Lyngsø has shown it is NP-complete if pseudoknots are allowed (ICALP 2004). As a stark contrast, it is unknown whether or not designing a given RNA secondary structure is a tractable task; this has been raised as a challenging open question by Anne Condon (ICALP 2003). Because of its crucial importance in a number of fields such as pharmaceutical research and biochemistry, there are dozens of heuristics and software libraries dedicated to RNA secondary structure design. It is therefore rather surprising that the computational complexity of this central problem in bioinformatics has been unsettled for decades. In this paper we show that, in the simplest model of energy which is the Watson-Crick model the design of secondary structures is NP-complete if one adds natural constraints of the form: index i of the sequence has to be labeled by base b. This negative result suggests that the same lower bound holds for more realistic models of energy. It is noteworthy that the additional constraints are by no means artificial: they are provided by all the RNA design pieces of software and they do correspond to the actual practice (see for example the instances of the EteRNA project). Our reduction from a variant of 3-Sat has as main ingredients: arches of parentheses of different widths, a linear order interleaving variables and clauses, and an intended rematching strategy which increases the number of pairs iff the three literals of a same clause are not satisfied. The correctness of the construction is also quite intricate; it relies on the polynomial algorithm for the design of saturated structures – secondary structures without dots – by Haleš et al. (Algorithmica 2016), counting arguments, and a concise case analysis