On the minimum and maximum selective graph coloring problems in some graph classes

Given a graph together with a partition of its vertex set, the minimum selective coloring problem consists of selecting one vertex per partition set such that the chromatic number of the subgraph induced by the selected vertices is minimum. The contribution of this paper is twofold. First, we investigate the complexity status of the minimum selective coloring problem in some specific graph classes motivated by some models described in Demange et al. (2015). Second, we introduce a new problem that corresponds to the worst situation in the minimum selective coloring; the maximum selective coloring problem aims to select one vertex per partition set such that the chromatic number of the subgraph induced by the selected vertices is maximum. We motivat

Anterolateral ligament reconstruction: a possible option in the therapeutic arsenal for persistent rotatory instability after ACL reconstruction

The results of anterior cruciate ligament reconstruction (ACLR) are widely recognized to be satisfactory on the basis of outcome measures such as the International Knee Documentation Committee (IKDC) and Lysholm scores. However, there is moderate variation among several series of different techniques. For example, Hussein et al showed a range of residual pivot, from 7% to 33%, depending on the technique used. Furthermore, up to 30% of patients in contemporary series can still experience persistent instability, and only 65% to 83% can return to the preinjury level of sport

Orthonormal sequences in L2(Rd)L^2(R^d) and time frequency localization

We study uncertainty principles for orthonormal bases and sequences in $L^2(\R^d)$. As in the classical Heisenberg inequality we focus on the product of the dispersions of a function and its Fourier transform. In particular we prove that there is no orthonormal basis for $L^2(\R)$ for which the time and frequency means as well as the product of dispersions are uniformly bounded. The problem is related to recent results of J. Benedetto, A. Powell, and Ph. Jaming. Our main tool is a time frequency localization inequality for orthonormal sequences in $L^2(\R^d)$. It has various other applications.Comment: 18 page

Biorthogonal quantum mechanics

The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called 'biorthogonal quantum mechanics', is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems. © 2014 IOP Publishing Ltd

Different precursor populations revealed by microscopic studies of bulk damage in KDP and DKDP crystals

We present experimental results aiming to reveal the relationship between damage initiating defect populations in KDP and DKDP crystals under irradiation at different wavelengths. Our results indicate that there is more than one type of defects leading to damage initiation, each defect acting as damage initiators over a different wavelength range. Results showing disparities in the morphology of damage sites from exposure at different wavelengths provides additional evidence for the presence of multiple types of defects responsible for damage initiation

Laser-induced defect reactions governing damage performance in KDP and DKDP crystals

The interaction of damage initiating defect precursors in KDP and DKDP crystals with laser pulses is investigated as a function of laser parameters to obtain experimental results that contain information about the type and nature of the defects. Specifically, the focus is to understand (a) the interaction of the precursors with sub-damage laser pulses leading to improvement to the damage performance (laser conditioning) and (b) the synergetic effects during multi-wavelength irradiation. Our results expose complex behaviors of the defect precursors associated with damage initiation and conditioning at different wavelengths that provide a major step towards revealing the underlying physics

Laser-Induced Damage in DKDP Crystals under Simultaneous Exposure to Laser Harmonics

While KDP and DKDP crystals remain the only viable solution for frequency conversion in large aperture laser systems in the foreseeable future, our understanding of damage behavior in the presence of multiple colors is very limited. Such conditions exist during normal operation where, for third harmonic generation, 1{omega}, 2{omega} and 3{omega} components are present with different energy ratios as they propagate inside the crystal. The objective of this work is to shed light into the damage behavior of frequency conversion crystals during operational conditions as well as probe the fundamental mechanisms of damage initiation. We have performed a series of experiments to quantify the damage performance of pristine (unconditioned) DKDP material under simultaneous exposure to 2{omega} and 3{omega} laser pulses from a 3-ns Nd:YAG laser system as a function of the laser influences at each frequency. Results show that simultaneous dual wavelength exposure leads to a much larger damage density as compared to the total damage resulting from separate exposure at each wavelength. Furthermore, under such excitation conditions, the damage performance is directly related to and can be predicted from the damage behavior of the crystal at each wavelength separately while the mechanism and type of defects responsible for damage initiation are shown to be the same at both 2{omega} and 3{omega} excitation

The effects of age at menarche and first sexual intercourse on reproductive and behavioural outcomes:A Mendelian randomization study

There is substantial variation in the timing of significant reproductive life events such as menarche and first sexual intercourse. Life history theory explains this variation as an adaptive response to an individual's environment and it is important to examine how traits within life history strategies affect each other. Here we applied Mendelian randomization (MR) methods to investigate whether there is a causal effect of variation in age at menarche and age at first sexual intercourse (markers or results of exposure to early life adversity) on outcomes related to reproduction, education and risky behaviour in UK Biobank (N = 114 883-181 255). Our results suggest that earlier age at menarche affects some traits that characterize life history strategies including earlier age at first and last birth, decreased educational attainment, and decreased age at leaving education (for example, we found evidence for a 0.26 year decrease in age at first birth per year decrease in age at menarche, 95% confidence interval: -0.34 to -0.17; p < 0.001). We find no clear evidence of effects of age at menarche on other outcomes, such as risk taking behaviour. Age at first sexual intercourse was also related to many life history outcomes, although there was evidence of horizontal pleiotropy which violates an assumption of MR and we therefore cannot infer causality from this analysis. Taken together, these results highlight how MR can be applied to test predictions of life history theory and to better understand determinants of health and social behaviour

Quantum catastrophes: a case study

The bound-state spectrum of a Hamiltonian H is assumed real in a non-empty domain D of physical values of parameters. This means that for these parameters, H may be called crypto-Hermitian, i.e., made Hermitian via an {\it ad hoc} choice of the inner product in the physical Hilbert space of quantum bound states (i.e., via an {\it ad hoc} construction of the so called metric). The name of quantum catastrophe is then assigned to the N-tuple-exceptional-point crossing, i.e., to the scenario in which we leave domain D along such a path that at the boundary of D, an N-plet of bound state energies degenerates and, subsequently, complexifies. At any fixed $N \geq 2$, this process is simulated via an N by N benchmark effective matrix Hamiltonian H. Finally, it is being assigned such a closed-form metric which is made unique via an N-extrapolation-friendliness requirement.Comment: 23 p

A multi-dimensional investigation of laser conditioning in KDP and DKDP crystals

We present a multi-parametric experimental investigation of laser conditioning efficiency and behavior in KDP and DKDP crystals as a function of laser wavelength, fluence, number of pulses, and conditioning protocol. Our results expose complex behaviors associated with damage initiation and conditioning at different wavelengths that provide a major step towards revealing the underlying physics. In addition, we reveal the key parameters for optimal improvement to the damage performance from laser conditioning