Combed 3-Manifolds with Concave Boundary, Framed Links, and Pseudo-Legendrian Links

We provide combinatorial realizations, according to the usual objects/moves scheme, of the following three topological categories: (1) pairs (M,v) where M is a 3-manifold (up to diffeomorphism) and v is a (non-singular vector) field, up to homotopy; here possibly the boundary of M is non-empty and v may be tangent to the boundary, but only in a concave fashion, and homotopy should preserve tangency type; (2) framed links L in M, up to framed isotopy; (3) triples (M,v,L), with (M,v) as above and L transversal to v, up to pseudo-Legendrian isotopy (transversality-preserving simultaneous homotopy of v and isotopy of L). All realizations are based on the notion of branched standard spine, and build on results previously obtained. Links are encoded by means of diagrams on branched spines, where the diagram is smooth with respect to the branching. Several motivations for being interested in combinatorial realizations of the topological categories considered in this paper are given in the introduction. The encoding of links is suitable for the comparison of the framed and the pseudo-Legendrian categories, and some applications are given in connection with contact structures, torsion and finite-order invariants. An estension of Trace's notion of winding number of a knot diagram is introduced and discussed.Comment: 38 pages, 33 figure

Impact of a XENONnT Signal on LHC Dijet Searches

It is well-known that dark matter (DM) direct detection experiments and the LHC are complementary, since they probe physical processes occurring at different energy scales. And yet, there are aspects of this complementarity which are still not fully understood, or exploited. For example, what is the impact that the discovery of DM at XENONnT would have on present and future searches for DM in LHC final states involving a pair of hadronic jets? In this work we investigate the impact of a XENONnT signal on the interpretation of current dijet searches at the LHC, and on the prospects for dijet signal discovery at the High-Luminosity (HL) LHC in the framework of simplified models. Specifically, we focus on a general class of simplified models where DM can have spin 0, 1/2 or 1, and interacts with quarks through the exchange of a scalar, pseudo-scalar, vector, or pseudo-vector mediator. We find that exclusion limits on the mediator's mass and its coupling to quarks from dijet searches at the LHC are significantly affected by a signal at XENONnT, and that $\mathcal{O}(100)$ signal events at XENONnT would drastically narrow the region in the parameter space of simplified models where a dijet signal can be discovered at $5\sigma$ C.L. at the HL-LHC.Comment: 23 pages, 3 figures, 3 tables, version accepted by JHE

Why not a di-NUT? or Gravitational duality and rotating solutions

We study how gravitational duality acts on rotating solutions, using the Kerr-NUT black hole as an example. After properly reconsidering how to take into account both electric (i.e. mass-like) and magnetic (i.e. NUT-like) sources in the equations of general relativity, we propose a set of definitions for the dual Lorentz charges. We then show that the Kerr-NUT solution has non-trivial such charges. Further, we clarify in which respect Kerr's source can be seen as a mass M with a dipole of NUT charges.Comment: 20 pages. v2: minor clarifications in section 4, version to appear in PR

Determining Dark Matter properties with a XENONnT/LZ signal and LHC-Run3 mono-jet searches

We develop a method to forecast the outcome of the LHC Run 3 based on the hypothetical detection of $\mathcal{O}(100)$ signal events at XENONnT. Our method relies on a systematic classification of renormalisable single-mediator models for dark matter-quark interactions, and is valid for dark matter candidates of spin less than or equal to one. Applying our method to simulated data, we find that at the end of the LHC Run 3 only two mutually exclusive scenarios would be compatible with the detection of $\mathcal{O}(100)$ signal events at XENONnT. In a first scenario, the energy distribution of the signal events is featureless, as for canonical spin-independent interactions. In this case, if a mono-jet signal is detected at the LHC, dark matter must have spin 1/2 and interact with nucleons through a unique velocity-dependent operator. If a mono-jet signal is not detected, dark matter interacts with nucleons through canonical spin-independent interactions. In a second scenario, the spectral distribution of the signal events exhibits a bump at non zero recoil energies. In this second case, a mono-jet signal can be detected at the LHC Run 3, dark matter must have spin 1/2 and interact with nucleons through a unique momentum-dependent operator. We therefore conclude that the observation of $\mathcal{O}(100)$ signal events at XENONnT combined with the detection, or the lack of detection, of a mono-jet signal at the LHC Run 3 would significantly narrow the range of possible dark matter-nucleon interactions. As we argued above, it can also provide key information on the dark matter particle spin.Comment: 17 pages, 8 figures, updated operator coefficients and figures, version accepted by PR

Conformational profiling of a G-rich sequence within the c-KIT promoter

G-quadruplexes (G4) within oncogene promoters are considered to be promising anticancer targets. However, often they undergo complex structural rearrangements that preclude a precise description of the optimal target. Moreover, even when solved structures are available, they refer to the thermodynamically stable forms but little or no information is supplied about their complex multistep folding pathway. To shed light on this issue, we systematically followed the kinetic behavior of a G-rich sequence located within the c-KIT proximal promoter (kit2) in the presence of monovalent cations K + and Na + . A very short-lived intermediate was observed to start the G4 folding process in both salt conditions. Subsequently, the two pathways diverge to produce distinct thermodynamically stable species (parallel and antiparallel G-quadruplex in K + and Na + , respectively). Remarkably, in K + -containing solution a branched pathway is required to drive the wild type sequence to distribute between a monomeric and dimeric G-quadruplex. Our approach has allowed us to identify transient forms whose relative abundance is regulated by the environment; some of them were characterized by a half-life within the timescale of physiological DNA processing events and thus may represent possible unexpected targets for ligands recognition

Imaging high-speed friction at the nanometer scale

Friction is a complicated phenomenon involving nonlinear dynamics at different length and time scales[1, 2]. The microscopic origin of friction is poorly understood, due in part to a lack of methods for measuring the force on a nanometer-scale asperity sliding at velocity of the order of cm/s.[3, 4] Despite enormous advance in experimental techniques[5], this combination of small length scale and high velocity remained illusive. Here we present a technique for rapidly measuring the frictional forces on a single asperity (an AFM tip) over a velocity range from zero to several cm/s. At each image pixel we obtain the velocity dependence of both conservative and dissipative forces, revealing the transition from stick-slip to a smooth sliding friction[1, 6]. We explain measurements on graphite using a modified Prandtl-Tomlinson model that takes into account the damped elastic deformation of the asperity. With its greatly improved force sensitivity and very small sliding amplitude, our method enables rapid and detailed surface mapping of the full velocity-dependence of frictional forces with less than 10~nm spatial resolution.Comment: 7 pages, 4 figure

Structural assessment of the 16th century coastal watchtowers in the defense system of the Pontifical state

Since medieval times the Mediterranean area and in particular its coasts have witnessed a series of clashes for economic and cultural domination, partially concluded, with the Battle of Lepanto in 1571. The resulting state of uncertainty and endless terror among the population pushed military engineers to develop organized coastal defense systems consisting of a network of strongholds such as watchtowers, castles and fortresses whose structural and functional characteristics changed sensitively during the centuries. The result is a vast, heterogeneous and almost unexplored part of our built heritage. This paper focuses on the description of the coastal defensive system of the Pontifical State, concentrating on the geometrical, material and constructive characteristics of a particular structural typology: the 16th century watchtower. The aim is to establish an idealized model validated by historical information and in-situ surveys. A structural analysis is carried out, including a simple index analysis, linear dynamic and nonlinear static analyses. These analyses provide preliminary insights on the global mechanisms of failure and on the real behavior of the structure. Conclusions are drawn concerning the necessity of interventions in the perspective of an appropriate reuse of the towers which could endorse the restoration and maintenance bringing them to a new life.(undefined