Factorable Monoids : Resolutions and Homology via Discrete Morse Theory

We study groups and monoids that are equipped with an extra structure called factorability. A factorable group can be thought of as a group G together with the choice of a generating set S and a particularly well-behaved normal form map G → S*, where S* denotes the free group over S. This is related to the theory of complete rewriting systems, collapsing schemes and discrete Morse theory. Given a factorable monoid M, we construct new resolutions of Z over the monoid ring ZM. These resolutions are often considerably smaller than the bar resolution E*M. As an example, we show that a large class of generalized Thompson groups and monoids fits into the framework of factorability and compute their homology groups. In particular, we provide a purely combinatorial way of computing the homology of Thompson's group F

Insulin-like growth factor 1 stimulates the angiogenic activity of adipose tissue-derived microvascular fragments

Angiogenesis in adipose tissue is promoted by insulin-like growth factor 1 signaling. We analyzed whether this regulatory mechanism also improves the angiogenic activity of adipose tissue-derived microvascular fragments. Murine adipose tissue-derived microvascular fragments were cultivated for 24 h in the University of Wisconsin (UW) solution supplemented with vehicle, insulin-like growth factor 1, or a combination of insulin-like growth factor 1 and insulin-like growth factor-binding protein 4. Subsequently, we assessed their cellular composition, viability, proliferation, and growth factor expression. Moreover, cultivated adipose tissue-derived microvascular fragments were seeded onto collagen-glycosaminoglycan scaffolds, which were implanted into dorsal skinfold chambers to study their vascularization and incorporation. Insulin-like growth factor 1 increased the viability and growth factor expression of adipose tissue-derived microvascular fragments without affecting their cellular composition and proliferation. Accordingly, scaffolds containing insulin-like growth factor 1-stimulated adipose tissue-derived microvascular fragments exhibited an enhanced in vivo vascularization and incorporation. These positive insulin-like growth factor 1 effects were reversed by additional exposure of adipose tissue-derived microvascular fragments to insulin-like growth factor-binding protein 4. Our findings indicate that insulin-like growth factor 1 stimulation of adipose tissue-derived microvascular fragments is suitable to improve their vascularization capacity

Cosmic variance of the local Hubble flow in large-scale cosmological simulations

The increasing precision in the determination of the Hubble parameter has reached a per cent level at which large-scale cosmic flows induced by inhomogeneities of the matter distribution become non-negligible. Here, we use large-scale cosmological N-body simulations to study statistical properties of the local Hubble parameter as measured by local observers. We show that the distribution of the local Hubble parameter depends not only on the scale of inhomogeneities, but also on how one defines the positions of observers in the cosmic web and what reference frame is used. Observers located in random dark matter haloes measure on average lower expansion rates than those at random positions in space or in the centres of cosmic voids, and this effect is stronger from the halo rest frames compared to the cosmic microwave background (CMB) rest frame. We compare the predictions for the local Hubble parameter with observational constraints based on Type Ia supernova (SNIa) and CMB observations. Due to cosmic variance, for observers located in random haloes we show that the Hubble constant determined from nearby SNIa may differ from that measured from the CMB by ±0.8 per cent at 1σ statistical significance. This scatter is too small to significantly alleviate a recently claimed discrepancy between current measurements assuming a flat Λ cold dark matter (ΛCDM) model. However, for observers located in the centres of the largest voids permitted by the standard ΛCDM model, we find that Hubble constant measurements from SNIa would be biased high by 5 per cent, rendering this tension non-existent in this extreme case

Challenges in QCD matter physics - The Compressed Baryonic Matter experiment at FAIR

Substantial experimental and theoretical efforts worldwide are devoted to explore the phase diagram of strongly interacting matter. At LHC and top RHIC energies, QCD matter is studied at very high temperatures and nearly vanishing net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was created at experiments at RHIC and LHC. The transition from the QGP back to the hadron gas is found to be a smooth cross over. For larger net-baryon densities and lower temperatures, it is expected that the QCD phase diagram exhibits a rich structure, such as a first-order phase transition between hadronic and partonic matter which terminates in a critical point, or exotic phases like quarkyonic matter. The discovery of these landmarks would be a breakthrough in our understanding of the strong interaction and is therefore in the focus of various high-energy heavy-ion research programs. The Compressed Baryonic Matter (CBM) experiment at FAIR will play a unique role in the exploration of the QCD phase diagram in the region of high net-baryon densities, because it is designed to run at unprecedented interaction rates. High-rate operation is the key prerequisite for high-precision measurements of multi-differential observables and of rare diagnostic probes which are sensitive to the dense phase of the nuclear fireball. The goal of the CBM experiment at SIS100 (sqrt(s_NN) = 2.7 - 4.9 GeV) is to discover fundamental properties of QCD matter: the phase structure at large baryon-chemical potentials (mu_B > 500 MeV), effects of chiral symmetry, and the equation-of-state at high density as it is expected to occur in the core of neutron stars. In this article, we review the motivation for and the physics programme of CBM, including activities before the start of data taking in 2022, in the context of the worldwide efforts to explore high-density QCD matter.Comment: 15 pages, 11 figures. Published in European Physical Journal

Observation of two new Ξb−\Xi_b^- baryon resonances

Two structures are observed close to the kinematic threshold in the $\Xi_b^0 \pi^-$ mass spectrum in a sample of proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb$^{-1}$ recorded by the LHCb experiment. In the quark model, two baryonic resonances with quark content $bds$ are expected in this mass region: the spin-parity $J^P = \frac{1}{2}^+$ and $J^P=\frac{3}{2}^+$ states, denoted $\Xi_b^{\prime -}$ and $\Xi_b^{*-}$. Interpreting the structures as these resonances, we measure the mass differences and the width of the heavier state to be $m(\Xi_b^{\prime -}) - m(\Xi_b^0) - m(\pi^{-}) = 3.653 \pm 0.018 \pm 0.006$ MeV$/c^2$, $m(\Xi_b^{*-}) - m(\Xi_b^0) - m(\pi^{-}) = 23.96 \pm 0.12 \pm 0.06$ MeV$/c^2$, $\Gamma(\Xi_b^{*-}) = 1.65 \pm 0.31 \pm 0.10$ MeV, where the first and second uncertainties are statistical and systematic, respectively. The width of the lighter state is consistent with zero, and we place an upper limit of $\Gamma(\Xi_b^{\prime -}) < 0.08$ MeV at 95% confidence level. Relative production rates of these states are also reported.Comment: 17 pages, 2 figure

Search for the lepton-flavor-violating decays Bs0→e±μ∓ and B0→e±μ∓

A search for the lepton-flavor-violating decays Bs0→e±μ∓ and B0→e±μ∓ is performed with a data sample, corresponding to an integrated luminosity of 1.0  fb-1 of pp collisions at √s=7  TeV, collected by the LHCb experiment. The observed number of Bs0→e±μ∓ and B0→e±μ∓ candidates is consistent with background expectations. Upper limits on the branching fractions of both decays are determined to be B(Bs0→e±μ∓)101  TeV/c2 and MLQ(B0→e±μ∓)>126  TeV/c2 at 95% C.L., and are a factor of 2 higher than the previous bounds

Observation of the decay Bc→J/ψK+K−π+B_c \rightarrow J/\psi K^+ K^- \pi^+

The decay $B_c\rightarrow J/\psi K^+ K^- \pi^+$ is observed for the first time, using proton-proton collisions collected with the LHCb detector corresponding to an integrated luminosity of 3fb$^{-1}$. A signal yield of $78\pm14$ decays is reported with a significance of 6.2 standard deviations. The ratio of the branching fraction of \B_c \rightarrow J/\psi K^+ K^- \pi^+ decays to that of $B_c \rightarrow J/\psi \pi^+$ decays is measured to be $0.53\pm 0.10\pm0.05$, where the first uncertainty is statistical and the second is systematic.Comment: 18 pages, 2 figure