115 research outputs found
Problems on Matchings and Independent Sets of a Graph
Let be a finite simple graph. For , the difference of
, where is the neighborhood of and is called the critical difference of . is
called a critical set if equals the critical difference and ker is
the intersection of all critical sets. It is known that ker is an
independent (vertex) set of . diadem is the union of all critical
independent sets. An independent set is an inclusion minimal set with if no proper subset of has positive difference.
A graph is called K\"onig-Egerv\'ary if the sum of its independence
number () and matching number () equals . It is
known that bipartite graphs are K\"onig-Egerv\'ary.
In this paper, we study independent sets with positive difference for which
every proper subset has a smaller difference and prove a result conjectured by
Levit and Mandrescu in 2013. The conjecture states that for any graph, the
number of inclusion minimal sets with is at least the critical
difference of the graph. We also give a short proof of the inequality
kerdiadem (proved by Short in 2016).
A characterization of unicyclic non-K\"onig-Egerv\'ary graphs is also
presented and a conjecture which states that for such a graph , the critical
difference equals , is proved.
We also make an observation about ker using Edmonds-Gallai Structure
Theorem as a concluding remark.Comment: 18 pages, 2 figure
Can LIGO Detect Asymmetric Dark Matter?
Dark matter from the galactic halo can accumulate in neutron stars and
transmute them into sub-2.5 black holes if the dark matter particles
are heavy, stable, and have interactions with nucleons. We show that
non-detection of gravitational waves from mergers of such low-mass black holes
can constrain the interactions of asymmetric dark matter particles with
nucleons. We find benchmark constraints with LIGO O3 data, viz., cm for bosonic DM with PeV (or
GeV, if they can Bose-condense) and
cm for fermionic DM with PeV. These bounds depend on the
priors on DM parameters and on the currently uncertain binary neutron star
merger rate density. However, if null-detection continues with increased
exposure over the next decade, LIGO will set remarkable constraints. We find
the forecasted sensitivity to heavy asymmetric dark matter to be world-leading,
viz., dipping many orders of magnitude below the neutrino floor and completely
testing the dark matter solution to missing pulsars in the Galactic center, and
demonstrate a windfall science-case for gravitational wave detectors.Comment: 14 pages, 6 figures. Comments welcom
Machine learning approach to genome of two-dimensional materials with flat electronic bands
Many-body physics of electron-electron correlations plays a central role in
condensed mater physics, it governs a wide range of phenomena, stretching from
superconductivity to magnetism, and is behind numerous technological
applications. To explore this rich interaction-driven physics, two-dimensional
(2D) materials with flat electronic bands provide a natural playground thanks
to their highly localised electrons. Currently, thousands of 2D materials with
computed electronic bands are available in open science databases, awaiting
such exploration. Here we used a new machine learning algorithm combining both
supervised and unsupervised machine intelligence to automate the otherwise
daunting task of materials search and classification, to build a genome of 2D
materials hosting flat electronic bands. To this end, a feedforward artificial
neural network was employed to identify 2D flat band materials, which were then
classified by a bilayer unsupervised learning algorithm. Such a hybrid approach
of exploring materials databases allowed us to reveal completely new material
classes outside the known flat band paradigms, offering new systems for
in-depth study on their electronic interactions
Impact of diabetes mellitus on ventricular structure, arterial stiffness, and pulsatile hemodynamics in heart failure with preserved ejection fraction
Background-Heterogeneity in the underlying processes that contribute to heart failure with preserved ejection fraction (HFpEF) is increasingly recognized. Diabetes mellitus is a frequent comorbidity in HFpEF, but its impact on left ventricular and arterial structure and function in HFpEF is unknown. Methods and Results-Weassessed the impact of diabetesmellitus on left ventricular cellular and interstitial hypertrophy (assessedwith cardiacmagnetic resonance imaging, including T1mapping pregadolinium and postgadolinium administration), arterial stiffness (assessed with arterial tonometry), and pulsatile arterial hemodynamics (assessed with in-office pressure-flow analyses and 24-hour ambulatory monitoring) among 53 subjects with HFpEF (32 diabetic and 21 nondiabetic subjects). Despite few differences in clinical characteristics, diabetic subjects with HFpEF exhibited a markedly greater left ventricular mass index (78.1 [95% CI, 70.4-85.9] g versus 63.6 [95% CI, 55.8-71.3] g; P=0.0093) and indexed extracellular volume (23.6 [95% CI, 21.2-26.1] mL/m(2) versus 16.2 [95% CI, 13.1-19.4] mL/m(2); P=0.0008). Pronounced aortic stiffening was also observed in the diabetic group (carotid-femoral pulse wave velocity, 11.86 [95% CI, 10.4-13.1] m/s versus 8.8 [95% CI, 7.5-10.1] m/s; P=0.0027), with an adverse pulsatile hemodynamic profile characterized by increased oscillatory power (315 [95% CI, 258-373] mWversus 190 [95% CI, 144-236] mW; P=0.0007), aortic characteristic impedance (0.154 [95% CI, 0.124-0.183] mmHg/mL per second versus 0.096 [95% CI, 0.072-0.121] mm Hg/mL per second; P=0.0024), and forward (59.5 [95% CI, 52.8-66.1] mm Hg versus 40.1 [95% CI, 31.6-48.6] mm Hg; P=0.0010) and backward (19.6 [95% CI, 16.2-22.9] mm Hg versus 14.1 [95% CI, 10.9-17.3] mm Hg; P=0.0169) wave amplitude. Abnormal pulsatile hemodynamics were also evident in 24-hour ambulatory monitoring, despite the absence of significant differences in 24-hour systolic blood pressure between the groups. Conclusions-Diabetes mellitus is a key determinant of left ventricular remodeling, arterial stiffness, adverse pulsatile hemodynamics, and ventricular-arterial interactions in HFpEF
Strain driven emergence of topological non-triviality in YPdBi thin films
Half-Heusler compounds exhibit a remarkable variety of emergent properties
such as heavy-fermion behaviour, unconventional superconductivity and
magnetism. Several of these compounds have been predicted to host topologically
non-trivial electronic structures. Remarkably, recent theoretical studies have
indicated the possibility to induce non-trivial topological surface states in
an otherwise trivial half-Heusler system by strain engineering. Here, using
magneto-transport measurements and first principles DFT-based simulations, we
demonstrate topological surface states on strained [110] oriented thin films of
YPdBi grown on (100) MgO. These topological surface states arise in an
otherwise trivial semi-metal purely driven by strain. Furthermore, we observe
the onset of superconductivity in these strained films highlighting the
possibility of engineering a topological superconducting state. Our results
demonstrate the critical role played by strain in engineering novel topological
states in thin film systems for developing next-generation spintronic devices.Comment: 20 pages, 5 Figure
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