On various types of nilpotency of the structure monoid and group of a set-theoretic solution of the Yang--Baxter equation

Given a finite bijective non-degenerate set-theoretic solution $(X,r)$ of the Yang--Baxter equation we characterize when its structure monoid $M(X,r)$ is Malcev nilpotent. Applying this characterization to solutions coming from racks, we rediscover some results obtained recently by Lebed and Mortier, and by Lebed and Vendramin on the description of finite abelian racks and quandles. We also investigate bijective non-degenerate multipermutation (not necessarily finite) solutions $(X,r)$ and show, for example, that this property is equivalent to the solution associated to the structure monoid $M(X,r)$ (respectively structure group $G(X,r)$) being a multipermuation solution and that $G=G(X,r)$ is solvable of derived length not exceeding the multipermutation level of $(X,r)$ enlarged by one, generalizing results of Gateva-Ivanova and Cameron obtained in the involutive case. Moreover, we also prove that if $X$ is finite and $G=G(X,r)$ is nilpotent, then the torsion part of the group $G$ is finite, it coincides with the commutator subgroup $[G,G]_+$ of the additive structure of the skew left brace $G$ and $G/[G,G]_+$ is a trivial left brace.Comment: 35 page

Double-Antiprism Central Configurations of the 3n-Body Problem

Abstract In this paper we study numerically a new type of central configurations of the 3n-body problem with equal masses which consist of three n-gons contained in three planes z = 0 and z = ±β = 0. The n-gon on z = 0 is scaled by a factor α and it is rotated by an angle of π/n with respect to the ones on z = ±β. In this kind of configurations, the masses on the planes z = 0 and z = β are at the vertices of an antiprism with bases of different size. The same occurs with the masses on z = 0 and z = −β. We call this kind of central configurations double-antiprism central configurations. We will show the existence of central configurations of this type

Pharmacologic activation of LXR alters the expression profile of tumor-associated macrophages and the abundance of regulatory T cells in the tumor microenvironment

Liver X receptors (LXR) are transcription factors from the nuclear receptor family that are activated by oxysterols and synthetic high-affinity agonists. In this study, we assessed the antitumor effects of synthetic LXR agonist TO901317 in a murine model of syngeneic Lewis Lung carcinoma. Treatment with TO901317 inhibited tumor growth in wild-type, but not in LXR-deficient mice, indicating that the antitumor effects of the agonist depends on functional LXR activity in host cells. Pharmacologic activation of the LXR pathway reduced the intratumoral abundance of regulatory T cells (Treg) and the expression of the Treg-attracting chemokine Ccl17 by MHCIIhigh tumor-associated macrophages (TAM). Moreover, gene expression profiling indicated a broad negative impact of the LXR agonist on other mechanisms used by TAM for the maintenance of an immunosuppressive environment. In studies exploring the macrophage response to GM-CSF or IL4, activated LXR repressed IRF4 expression, resulting in subsequent downregulation of IRF4-dependent genes including Ccl17. Taken together, this work reveals the combined actions of the LXR pathway in the control of TAM responses that contribute to the antitumoral effects of pharmacologic LXR activation. Moreover, these data provide new insights for the development of novel therapeutic options for the treatment of cancer.This work was supported by the following grants: Spanish Ministry of Economy and Competitivity (MINECO) grants SAF2017-89510-R and SAF2014-57856-P [to A.F. Valledor and C. Caelles; SAF2014-56819-R to A. Castrillo; SAF2017-90604-REDT and SAF2015-71878-REDT to the NuRCaMeIn network (to A.F. Valledor, C. Caelles, and A. Castrillo); Spanish Ministry of Science and Innovation (MICINN) grants SAF2011-23402 and SAF2010-14989 (to A.F. Valledor); Fundacio La Marato de TV3 grant 080930 (to A.F. Valledor); grants DFG HU 1824/5-1, 1824/7-1, and 1824/9-1 (to M. Huber); the European Cooperation in Science and Technology (COST) Action BM1404 Mye-EUNITER (http://www.mye-euniter. eu/; to A.F. Valledor, J.A. Van Ginderachter); and Instituto de Salud Carlos III and FEDER “Una manera de hacer Europa” grant FIS 16/00139 (to J.C. Escola-Gil). CIBERDEM is an Instituto de Salud Carlos III project. J.M. C received a fellowship from the University of Barcelona (APIF) and J. Font-Díaz received a fellowship from the Spanish Ministry of Science, Innovation and Universities (FPI, PRE2018-085579)

Celestial Mechanics, Conformal Structures, and Gravitational Waves

The equations of motion for $N$ non-relativistic particles attracting according to Newton's law are shown to correspond to the equations for null geodesics in a $(3N+2)$-dimensional Lorentzian, Ricci-flat, spacetime with a covariantly constant null vector. Such a spacetime admits a Bargmann structure and corresponds physically to a generalized pp-wave. Bargmann electromagnetism in five dimensions comprises the two Galilean electro-magnetic theories (Le Bellac and L\'evy-Leblond). At the quantum level, the $N$-body Schr\"odinger equation retains the form of a massless wave equation. We exploit the conformal symmetries of such spacetimes to discuss some properties of the Newtonian $N$-body problem: homographic solutions, the virial theorem, Kepler's third law, the Lagrange-Laplace-Runge-Lenz vector arising from three conformal Killing 2-tensors, and motions under inverse square law forces with a gravitational constant $G(t)$ varying inversely as time (Dirac). The latter problem is reduced to one with time independent forces for a rescaled position vector and a new time variable; this transformation (Vinti and Lynden-Bell) arises from a conformal transformation preserving the Ricci-flatness (Brinkmann). A Ricci-flat metric representing $N$ non-relativistic gravitational dyons is also pointed out. Our results for general time-dependent $G(t)$ are applicable to the motion of point particles in an expanding universe. Finally we extend these results to the quantum regime.Comment: 26 pages, LaTe

Pharmacological activation of LXR alters the expression profile of tumor-associated macrophages and the abundance of regulatory T cells in the tumor microenvironment

Liver X receptors (LXR) are transcription factors from the nuclear receptor family that are activated by oxysterols and synthetic high-affinity agonists. In this study, we assessed the anti-tumor effects of synthetic LXR agonist TO901317 in a murine model of syngeneic Lewis Lung carcinoma. Treatment with TO901317 inhibited tumor growth in wild-type but not in LXR-deficient mice, indicating that the anti-tumor effects of the agonist depends on functional LXR activity in host cells. Pharmacological activation of the LXR pathway reduced the intratumoral abundance of regulatory T cells (Treg) and the expression of the Treg-attracting chemokine Ccl17 by MHCIIhigh tumor-associated macrophages (TAM). Moreover, gene expression profiling indicated a broad negative impact of the LXR agonist on other mechanisms used by TAM for the maintenance of an immunosuppressive environment. In studies exploring the macrophage response to GM-CSF or IL-4, activated LXR repressed IRF4 expression, resulting in subsequent downregulation of IRF4-dependent genes including Ccl17. Taken together, this work reveals the combined actions of the LXR pathway in the control of TAM responses that contribute to the anti-tumoral effects of pharmacological LXR activation. Moreover, these data provide new insights for the development of novel therapeutic options for the treatment of cancer

ApoA-I mimetic administration, but not increased apoA-I-containing HDL, inhibits tumour growth in a mouse model of inherited breast cancer

Low levels of high-density lipoprotein cholesterol (HDLc) have been associated with breast cancer risk, but several epidemiologic studies have reported contradictory results with regard to the relationship between apolipoprotein (apo) A-I and breast cancer. We aimed to determine the effects of human apoA-I overexpression and administration of specific apoA-I mimetic peptide (D-4F) on tumour progression by using mammary tumour virus-polyoma middle T-antigen transgenic (PyMT) mice as a model of inherited breast cancer. Expression of human apoA-I in the mice did not affect tumour onset and growth in PyMT transgenic mice, despite an increase in the HDLc level. In contrast, D-4F treatment significantly increased tumour latency and inhibited the development of tumours. The effects of D-4F on tumour development were independent of 27-hydroxycholesterol. However, D-4F treatment reduced the plasma oxidized low-density lipoprotein (oxLDL) levels in mice and prevented oxLDL-mediated proliferative response in human breast adenocarcinoma MCF-7 cells. In conclusion, our study shows that D-4F, but not apoA-I-containing HDL, hinders tumour growth in mice with inherited breast cancer in association with a higher protection against LDL oxidative modification

ApoA-I Mimetic administration, but not increased apoA-I-containing HDL, inhibits tumour growth in a mouse model of inherited breast cancer.

Low levels of high-density lipoprotein cholesterol (HDLc) have been associated with breast cancer risk, but several epidemiologic studies have reported contradictory results with regard to the relationship between apolipoprotein (apo) A-I and breast cancer. We aimed to determine the effects of human apoA-I overexpression and administration of specific apoA-I mimetic peptide (D-4F) on tumour progression by using mammary tumour virus-polyoma middle T-antigen transgenic (PyMT) mice as a model of inherited breast cancer. Expression of human apoA-I in the mice did not affect tumour onset and growth in PyMT transgenic mice, despite an increase in the HDLc level. In contrast, D-4F treatment significantly increased tumour latency and inhibited the development of tumours. The effects of D-4F on tumour development were independent of 27-hydroxycholesterol. However, D-4F treatment reduced the plasma oxidized low-density lipoprotein (oxLDL) levels in mice and prevented oxLDL-mediated proliferative response in human breast adenocarcinoma MCF-7 cells. In conclusion, our study shows that D-4F, but not apoA-I-containing HDL, hinders tumour growth in mice with inherited breast cancer in association with a higher protection against LDL oxidative modificatio