Growth, entropy and commutativity of algebras satisfying prescribed relations

In 1964, Golod and Shafarevich found that, provided that the number of relations of each degree satisfy some bounds, there exist infinitely dimensional algebras satisfying the relations. These algebras are called Golod-Shafarevich algebras. This paper provides bounds for the growth function on images of Golod-Shafarevich algebras based upon the number of defining relations. This extends results from [32], [33]. Lower bounds of growth for constructed algebras are also obtained, permitting the construction of algebras with various growth functions of various entropies. In particular, the paper answers a question by Drensky [7] by constructing algebras with subexponential growth satisfying given relations, under mild assumption on the number of generating relations of each degree. Examples of nil algebras with neither polynomial nor exponential growth over uncountable fields are also constructed, answering a question by Zelmanov [40]. Recently, several open questions concerning the commutativity of algebras satisfying a prescribed number of defining relations have arisen from the study of noncommutative singularities. Additionally, this paper solves one such question, posed by Donovan and Wemyss in [8].Comment: arXiv admin note: text overlap with arXiv:1207.650

The sudden change phenomenon of quantum discord

Even if the parameters determining a system's state are varied smoothly, the behavior of quantum correlations alike to quantum discord, and of its classical counterparts, can be very peculiar, with the appearance of non-analyticities in its rate of change. Here we review this sudden change phenomenon (SCP) discussing some important points related to it: Its uncovering, interpretations, and experimental verifications, its use in the context of the emergence of the pointer basis in a quantum measurement process, its appearance and universality under Markovian and non-Markovian dynamics, its theoretical and experimental investigation in some other physical scenarios, and the related phenomenon of double sudden change of trace distance discord. Several open questions are identified, and we envisage that in answering them we will gain significant further insight about the relation between the SCP and the symmetry-geometric aspects of the quantum state space.Comment: Lectures on General Quantum Correlations and their Applications, F. F. Fanchini, D. O. Soares Pinto, and G. Adesso (Eds.), Springer (2017), pp 309-33

fMRI Evidence for a Dual Process Account of the Speed-Accuracy Tradeoff in Decision-Making

Background: The speed and accuracy of decision-making have a well-known trading relationship: hasty decisions are more prone to errors while careful, accurate judgments take more time. Despite the pervasiveness of this speed-accuracy tradeoff (SAT) in decision-making, its neural basis is still unknown. Methodology/Principal Findings: Using functional magnetic resonance imaging (fMRI) we show that emphasizing the speed of a perceptual decision at the expense of its accuracy lowers the amount of evidence-related activity in lateral prefrontal cortex. Moreover, this speed-accuracy difference in lateral prefrontal cortex activity correlates with the speedaccuracy difference in the decision criterion metric of signal detection theory. We also show that the same instructions increase baseline activity in a dorso-medial cortical area involved in the internal generation of actions. Conclusions/Significance: These findings suggest that the SAT is neurally implemented by modulating not only the amount of externally-derived sensory evidence used to make a decision, but also the internal urge to make a response. We propose that these processes combine to control the temporal dynamics of the speed-accuracy trade-off in decisionmaking

Distinct Effector Memory CD4+ T Cell Signatures in Latent Mycobacterium tuberculosis Infection, BCG Vaccination and Clinically Resolved Tuberculosis

Two billion people worldwide are estimated to be latently infected with Mycobacterium tuberculosis (Mtb) and are at risk for developing active tuberculosis since Mtb can reactivate to cause TB disease in immune-compromised hosts. Individuals with latent Mtb infection (LTBI) and BCG-vaccinated individuals who are uninfected with Mtb, harbor antigen-specific memory CD4+ T cells. However, the differences between long-lived memory CD4+ T cells induced by latent Mtb infection (LTBI) versus BCG vaccination are unclear. In this study, we characterized the immune phenotype and functionality of antigen-specific memory CD4+ T cells in healthy BCG-vaccinated individuals who were either infected (LTBI) or uninfected (BCG) with Mtb. Individuals were classified into LTBI and BCG groups based on IFN-γ ELISPOT using cell wall antigens and ESAT-6/CFP-10 peptides. We show that LTBI individuals harbored high frequencies of late-stage differentiated (CD45RA−CD27−) antigen-specific effector memory CD4+ T cells that expressed PD-1. In contrast, BCG individuals had primarily early-stage (CD45RA−CD27+) cells with low PD-1 expression. CD27+ and CD27− as well as PD-1+ and PD-1− antigen-specific subsets were polyfunctional, suggesting that loss of CD27 expression and up-regulation of PD-1 did not compromise their capacity to produce IFN-γ, TNF-α and IL-2. PD-1 was preferentially expressed on CD27− antigen-specific CD4+ T cells, indicating that PD-1 is associated with the stage of differentiation. Using statistical models, we determined that CD27 and PD-1 predicted LTBI versus BCG status in healthy individuals and distinguished LTBI individuals from those who had clinically resolved Mtb infection after anti-tuberculosis treatment. This study shows that CD4+ memory responses induced by latent Mtb infection, BCG vaccination and clinically resolved Mtb infection are immunologically distinct. Our data suggest that differentiation into CD27−PD-1+ subsets in LTBI is driven by Mtb antigenic stimulation in vivo and that CD27 and PD-1 have the potential to improve our ability to evaluate true LTBI status

Binary systems and their nuclear explosions

Peer ReviewedPreprin

Observation of Two New Excited Ξb0 States Decaying to Λb0 K-π+

Two narrow resonant states are observed in the Λb0K-π+ mass spectrum using a data sample of proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the LHCb experiment and corresponding to an integrated luminosity of 6 fb-1. The minimal quark content of the Λb0K-π+ system indicates that these are excited Ξb0 baryons. The masses of the Ξb(6327)0 and Ξb(6333)0 states are m[Ξb(6327)0]=6327.28-0.21+0.23±0.12±0.24 and m[Ξb(6333)0]=6332.69-0.18+0.17±0.03±0.22 MeV, respectively, with a mass splitting of Δm=5.41-0.27+0.26±0.12 MeV, where the uncertainties are statistical, systematic, and due to the Λb0 mass measurement. The measured natural widths of these states are consistent with zero, with upper limits of Γ[Ξb(6327)0]<2.20(2.56) and Γ[Ξb(6333)0]<1.60(1.92) MeV at a 90% (95%) credibility level. The significance of the two-peak hypothesis is larger than nine (five) Gaussian standard deviations compared to the no-peak (one-peak) hypothesis. The masses, widths, and resonant structure of the new states are in good agreement with the expectations for a doublet of 1D Ξb0 resonances

Test of lepton universality in b→sℓ+ℓ−b \rightarrow s \ell^+ \ell^- decays

The first simultaneous test of muon-electron universality using $B^{+}\rightarrow K^{+}\ell^{+}\ell^{-}$ and $B^{0}\rightarrow K^{*0}\ell^{+}\ell^{-}$ decays is performed, in two ranges of the dilepton invariant-mass squared, $q^{2}$. The analysis uses beauty mesons produced in proton-proton collisions collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9 $\mathrm{fb}^{-1}$. Each of the four lepton universality measurements reported is either the first in the given $q^{2}$ interval or supersedes previous LHCb measurements. The results are compatible with the predictions of the Standard Model.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-046.html (LHCb public pages