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Raman measurements performed on dense H2, D2 and H2+D2 in a wide pressure-temperature range reveal the presence of the ΔJ=0 rotational excitation. In the gas/fluid state this excitation has zero Raman shift, but in the solid, the crystal field drive s it away from the zero value e.g. 75 cm-1 at around 50 GPa and 10 K for both isotopes and their mixture. In the case of deuterium, the ΔJ=0 mode splits upon entering phase II suggesting a very complex molecular environment of the broken symmetry phase (BSP). In the fluid state and phases I and II the frequencies (energies) of the ΔJ=0 transition for H2 and D2 do not scale either as rotational (by factor of 2) nor vibrational (by square 2) modes and appear to be completely isotope independent. This independence on mass marks this transition as unique and a fundamentally different type of excitation from the commonly considered harmonic oscillator and quantum rotor.

The goal of this article is to prove that the Grothendieck-Teichmüller group $\widehat{GT}$ acts on $\widehatΓ_{g,0}$ and $\widehatΓ_{g,1}$,the (full) profinite genus $g$ mapping class group with $0$ or $1$ marked point, for every $g>0$.

In this supplementary note, we study the traces of multiple SLE(0) systems with two or more additional marked points. For general chordal configurations, the traces correspond to the real locus of real rational functions; in the radial case, they correspond to the horizontal trajectories of residue-free quadratic differentials. In both settings, we establish the regularity of the trajectories near singularities: no spiraling occurs, and no two trajectories asymptotically converge to the same direction. Moreover, in the radial case with non-zero spin at the marked interior point, we show that the spin induces a spiraling behavior at the marked interior point. However, this regularity breaks down when multiple interior marked points are present. In such cases, trajectories may asymptotically approach the same direction, and spiraling can occur even in the absence of spin. We present explicit counterexamples generated using MATLAB, with code provided for reference.

We give criteria for determining the positivity of line bundles coming from vertex operator algebras (VOAs) on the moduli space $\overline{\mathrm{M}}_{0,n}$ of rational curves with $n$ marked points. The criteria use the multiplicative structure of VOA representations encoded in the fusion ring. Using them, we construct positive line bundles on $\overline{\mathrm{M}}_{0,n}$ from certain parafermion VOAs. These give the first examples of commutant VOAs producing positive line bundles.

Borger's theory of $Λ$-spaces imbues algebraic spaces, which include schemes, with an additional structure defined by an extension of the Witt vector functor. Motivated by $\mathbb{F}_1$-geometry, we prove the existence of a weak resolution of singularities in the category of $Λ$-schemes. Our arguments are based on standard arguments in characteristic $0$ using the order reduction of an ideal marked with $Λ$-equivariant data. This paper is based on work from the author's PhD thesis.

The game of i-Mark is an impartial combinatorial game introduced by Sopena (2016). The game is parametrized by two sets of positive integers $S$, $D$, where $\min D\ge 2$. From position $n\ge 0$ one can move to any position $n-s$, $s\in S$, as long as $n-s\ge 0$, as well as to any position $n/d$, $d\in D$, as long as $n>0$ and $d$ divides $n$. The game ends when no more moves are possible, and the last player to move is the winner. Sopena, and subsequently Friman and Nivasch (2021), characterized the Sprague-Grundy sequences of many cases of i-Mark$(S,D)$ with $|D|=1$. Friman and Nivasch also obtained some partial results for the case i-Mark$(\{1\},\{2,3\})$. In this paper we present a convergence technique that gives polynomial-time algorithms for the Sprague-Grundy sequence of many instances of i-Mark with $|D|>1$. In particular, we prove our technique works for all games i-Mark$(\{1\},\{d_1,d_2\})$. Keywords: Combinatorial game, impartial game, Sprague-Grundy function, convergence, dynamic programming.

Recent measurements by various experiments in ultra-peripheral collisions have observed spin-interference in $ρ^{0}$ photoproduction, marking a breakthrough in Fermi-scale quantum interference experiments. Building on this, STAR extended the measurement to hadronic heavy-ion collisions, where significant rescattering effects on $ρ^{0}$ mesons were expected. In this study, we investigate how these rescattering effects influence the measurement of spin-interference. By embedding $ρ^{0}$ mesons produced via photoproduction, modeled by the Vector Meson Dominance model, into the Ultrarelativistic Quantum Molecular Dynamics framework, we estimate the impact on the $\cos2φ$ and $\cos4φ$ modulations, where $φ$ is the angle between $ρ^{0}$ and one of the daughters' ($π^{\pm}$) transverse momentum. The results indicate a significant suppression of the $\cos2φ$ modulation, while the $\cos4φ$ modulation remains largely unaffected, which provides insight for understanding the difference due to rescattering effects between experimental measurements and theoretical predictions for $ρ^{0}$ photoproduction in heavy-ion collisions.

We study the spectral rigidity problem for Sinai billiards with finite horizon, specifically asking whether the geometry of the billiard table can be recovered from the lengths of its (marked) periodic trajectories. To address this, we introduce an enriched marked length spectrum EL and prove that two Sinai billiards sharing the same EL must be isometric. Our approach involves approximating the billiard flow using geodesic flows on smooth Riemannian surfaces. In the limit, these flows converge to CAT(0) spaces, which encode both the lengths of periodic orbits and the geometry of the boundary. We adapt Otal's original method -- developed for marked length spectrum rigidity in negatively curved surfaces -- to this new setting. Here, the lack of curvature control is offset by metric comparison estimates. By integrating the analysis of geodesic flows with perturbative techniques for periodic orbits, we establish a rigidity theorem for Sinai billiards with finite horizon. These results extend the classical theory of marked length spectrum rigidity beyond the Riemannian setting, demonstrating that even in discontinuous dynamical systems, geometric information is rigidly encoded in spectr

Based on a data sample of $(10087 \pm 44) \times 10^6$ $J/ψ$ events taken with the BESIII detector, we search for the flavor-changing neutral current charmonium decay $J/ψ\to D^{0} μ^{+} μ^{-} + \text{c.c.}$. No significant signal above the background is observed, and the upper limit on its branching fraction is set to be $\mathcal{B}(J/ψ\to D^{0}μ^{+}μ^{-} + \text{c.c.} ) < 1.1 \times 10^{-7}$ at the 90% confidence level. This marks the first search for a flavor-changing neutral current charmonium decay involving muons in the final state.

Over any field of characteristic $0$, we prove that the homotopy exact sequence of algebraic fundamental groups for the universal curve with unordered marked points does not split. The same nonsplitting holds for the universal hyperelliptic curve. Our approach extends Chen's topological result to the profinite setting and relies on the use of relative and continuous relative completions to detect the nonexistence of algebraic sections.

We describe a family $\textrm{Cyc}_p(\mathcal{F})$ of marked cycle curves that parameterize the cycles of period $p$ of a given family $\mathcal{F}$ of dynamical systems. We produce algorithms to compute a canonical cell decomposition for the marked cycle curves over the family $\textrm{Per}_1(0)$ of quadratic polynomials as well as over the family $\textrm{Per}_2(0)$ of quadratic rational maps with a critical 2-cycle. We obtain formulas for the number of $d$-cells in these decompositions, giving rise to e.g. a formula for their genus.

We develop a theory of multiple radial SLE(0) -- a smooth system of curves in a simply connected domain $Ω$ with marked boundary points $z_1, \ldots, z_n \in \partial Ω$ and a marked interior point $q$ -- arising as the deterministic limit of random multiple radial SLE($κ$) systems. We construct multiple radial SLE(0) systems by starting from the stationary relations, which arise heuristically as the $κ\to 0$ limit of partition functions. By constructing the field integrals of motion for the Loewner dynamics, we show that the traces of multiple radial SLE(0) systems are the horizontal trajectories of an equivalence class of quadratic differentials. These trajectories have limiting ends at the boundary points $\{z_1, z_2, \ldots, z_n\}$. The stationary relations connect the classification of multiple radial SLE(0) systems to the enumeration of critical points of the master function of trigonometric Knizhnik--Zamolodchikov (KZ) equations. In the deterministic case $κ= 0$, we show that the Loewner dynamics with a common parametrization of capacity form a special class of classical Calogero--Sutherland systems, restricted to a submanifold of phase space defined by the Lax matrix.

The charge neutrality point of bilayer graphene, denoted as ν = 0 state, manifests competing phases marked by spontaneously broken isospin (spin/valley/layer) symmetries under external magnetic and electric fields. However, due to their electrically insulating nature, identifying these phases through electrical conductance measurements remains challenging. A recent theoretical proposal introduces a novel approach, employing thermal transport measurements to detect these competing phases. Here, we experimentally explore the bulk thermal transport of the ν = 0 state in bilayer graphene to investigate its ground states and collective excitations associated with isospin. While the theory anticipates a finite thermal conductance in the ν = 0 state, our findings unveil an absence of detectable thermal conductance. Through variations in the external electric field and temperature-dependent measurements, our results suggest towards gapped collective excitations at ν = 0 state. Our findings underscore the necessity for further investigations into the nature of ν = 0.

In hierarchical structure formation, correlations between galaxy properties and their environments reveal important clues about galaxy evolution, emphasizing the importance of measuring these relationships. We probe the environmental dependence of Lyman-break galaxy (LBG) properties in the redshift range of $3$ to $5$ using marked correlation function statistics with galaxy samples from the Hyper Suprime-Cam Subaru Strategic Program and the Canada--France--Hawaii Telescope U-band surveys. We find that the UV magnitude and color of magnitude-selected LBG samples are strongly correlated with their environment, making these properties effective tracers of it. In contrast, the star formation rate and stellar mass of LBGs exhibit a weak environmental dependence. For UV magnitudes and color, the correlation is stronger in brighter galaxy samples across all redshifts and extends to scales far beyond the size of typical dark matter halos. This suggests that within a given sample, LBGs with high UV magnitudes or colors are more likely to form pairs at these scales than predicted by the two-point angular correlation function. Moreover, the amplitude of the marked correlation function is gene

We show that for any surface of genus at least 3 equipped with any choice of framing, the graph of non-separating curves with winding number 0 with respect to the framing is hierarchically hyperbolic but not Gromov hyperbolic. We also describe how to build analogues of the curve graph for marked strata of abelian differentials that capture the combinatorics of their boundaries, analogous to how the curve graph captures the combinatorics of the augmented Teichmueller space. These curve graph analogues are also shown to be hierarchically, but not Gromov, hyperbolic.

This paper contains some results about the topology of $\M_{0,n+1}/Σ_n$, where $\M_{0,n+1}$ is the moduli space of genus zero Riemann surfaces with marked points. We show that $\M_{0,n+1}/Σ_n$ is not a topological manifold for $n\geq 4$, and it is simply connected for any $n\in\N$. We also present some homology computations: for example we show that $\M_{0,p+1}/Σ_p$ has no $p$ torsion, where $p$ is a prime. Lastly we compute $H_*(\M_{0,n+1}/Σ_n;\Z)$ for small values of $n$, proving that $\M_{0,n+1}/Σ_n$ is contractible for $n\leq 5$ while $\M_{0,7}/Σ_6$ is not.

We present the first $Λ$CDM cosmological analysis performed on a galaxy survey using marked power spectra. The marked power spectrum is the two-point function of a marked field, where galaxies are weighted by a function that depends on their local density. The presence of the mark leads these statistics to contain higher-order information of the original galaxy field, making them a good candidate to exploit the non-Gaussian information of a galaxy catalog. In this work we make use of \simbig, a forward modeling framework for galaxy clustering analyses, and perform simulation-based inference using normalizing flows to infer the posterior distribution of the $Λ$CDM cosmological parameters. We consider different mark configurations (ways to weight the galaxy field) and deploy them in the \simbig~pipeline to analyze the corresponding marked power spectra measured from a subset of the BOSS galaxy sample. We analyze the redshift-space mark power spectra decomposed in $\ell = 0, 2, 4$ multipoles and include scales up to the non-linear regime. Among the various mark configurations considered, the ones that give the most stringent cosmological constraints produce posterior median and $68\%$

We compare the marked length spectra of some pairs of proper and cocompact cubical actions of a non-virtually cyclic group on $\text{CAT}(0)$ cube complexes. The cubulations are required to be virtually co-special, have the same sets of convex-cocompact subgroups, and admit a contracting element. There are many groups for which these conditions are always fulfilled for any pair of cubulations, including non-elementary cubulable hyperbolic groups, many cubulable relatively hyperbolic groups, and many right-angled Artin and Coxeter groups. For these pairs of cubulations, we study the Manhattan curve associated to their combinatorial metrics. We prove that this curve is analytic and convex, and a straight line if and only if the marked length spectra are homothetic. The same result holds if we consider invariant combinatorial metrics in which the lengths of the edges are not necessarily one. In addition, for their standard combinatorial metrics, we prove a large deviation theorem with shrinking intervals for their marked length spectra. We deduce the same result for pairs of word metrics on hyperbolic groups. The main tool is the construction of a finite-state automaton that simultane

In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times that have its intensity driven by a diffusion, with the associated marks also depending upon the diffusion process. We assume that one must resort to time-discretizing the diffusion process and develop particle and multilevel particle filters to recursively approximate the filter. In particular, we prove that our multilevel particle filter can achieve a mean square error (MSE) of $\mathcal{O}(ε^2)$ ($ε>0$ and arbitrary) with a cost of $\mathcal{O}(ε^{-2.5})$ versus using a particle filter which has a cost of $\mathcal{O}(ε^{-3})$ to achieve the same MSE. We then show how this methodology can be extended to give unbiased (that is with no time-discretization error) estimators of the filter, which are proved to have finite variance and with high-probability have finite cost. Finally, we extend our methodology to the problem of online static-parameter estimation.