This article presents measurements of inclusive $J/ψ$ production at midrapidity ($\left|y\right| <$ 1.0) in Au+Au collisions at $\sqrt{s_\mathrm{NN}} = 54.4$ GeV with the STAR detector at the Relativistic Heavy Ion Collider. A suppression of the $J/ψ$ yield, quantified using the nuclear modification factors ($R_{\mathrm{AA}}$, $R_{\mathrm{CP}}$), is observed with respect to the scaled production in $p$+$p$ collisions. The dependence of $R_{\mathrm{AA}}$ on collision centrality and $J/ψ$ transverse momentum is measured with improved precision compared to previous measurements at 39 and 62.4 GeV, while the centrality dependence of $R_{\mathrm{CP}}$ is measured and compared to the same results at 39, 62.4, and 200 GeV. In central collisions, no significant collision energy dependence of $R_{\mathrm{AA}}$ is found within uncertainties for collision energies between 17.3 and 200 GeV. Two transport model calculations that include dissociation and regeneration contributions are consistent with the experimental results within uncertainties. Although no significant collision energy dependence of the $J/ψ$ suppression in high energy heavy-ion collisions up to $\sqrt{s_\mathrm{NN}} = 200$ GeV is observed within uncertainties, the newly measured results at 54.4 GeV Au+Au collisions provide additional constraints on theoretical calculations of the hot medium evolution and cold nuclear matter effects.

We introduce QuiverTools, a new software package, available in both a SageMath and Julia version, to study quivers and their moduli spaces of representations. Its key features are the computation of general subdimension vectors, leading to canonical decompositions, and checking the existence of (semi)stable representations, as well as the enumeration of Harder-Narasimhan types and related calculations for Teleman quantization. Computations related to intersection theory on quiver moduli are also implemented.

This is an introduction to advanced linear algebra, with emphasis on geometric aspects, and with some applications included too. We first review basic linear algebra, notably with the spectral theorem in its general form, and with the theory of the resultant and discriminant. Then we discuss the Jordan form and its basic applications to physics, and other advanced decomposition results for the matrices. We then go into positivity topics, involving matrices and bilinear forms, and with a look into curved space-time, and discrete Laplacians. Finally, we discuss the various groups of matrices, with a look at reflection groups, Lie groups, spin matrices and random matrices.

The origin of cosmic rays remains an unresolved fundamental problem in astrophysics. The synergy of multiple observational probes, including the energy spectra, the mass composition, and anisotropy is a viable way to jointly uncover this mystery. In this work, we propose that the energy-dependent of those observables in a wide energy range, from $O(10)$ GeV to ultrahigh energies of $10^{11}$ GeV, share quite a few correlated features, indicating a strong co-evolution which could be a consequence of the underlying origin of different source populations. We decipher these structures with a four-component model, i.e., the ensemble of Galactic sources, a local source close to the solar system, and the ensemble of two extra-galactic source populations. In this scenario, the $O(10^2)$ GV hardening and $O(10)$ TV bump is due to the contribution of the local source, the knee is due to the maximum acceleration energy of protons by the Galactic source population, the second knee is due to the maximum acceleration energy of iron nuclei by Galactic sources, the dip feature between the two knees is due to the appearance of the extra-galactic component, the ankle comes from the transition from one extra-galactic component to the other, and the spectral suppression at the highest energies arises from the acceleration limit of the second extra-galactic component. The transition from Galactic to extra-galactic origin of cosmic rays occurs around $O(10^8)$ GeV, which is smaller than the ankle energy.

In this paper we highlight a few open problems concerning maximal sum-free sets in abelian groups. In addition, for most even order abelian groups $G$ we asymptotically determine the number of maximal distinct sum-free subsets in $G$. Our proof makes use of the container method.

It is well-known that the tensor product of two bialgebras constitutes the binary product in the category of cocommutative bialgebras and morphisms of bialgebras between them. In this paper, we extend this result to triangular bialgebras and twisted morphisms of triangular bialgebras. We do so by adopting the framework of 2-categories and the proper notion of binary product, as well as by employing a description of twists on the tensor product bialgebra, specifically developed for this purpose. We apply this extension to provide a new interpretation of the twisted tensor products of triangular bialgebras in terms of binary products.

We consider a type I superconducting body that contains one or more holes in its interior that undergoes a transition between normal and superconducting states in the presence of a magnetic field. We argue that unlike other thermodynamic systems that undergo first order phase transitions the system cannot reach its equilibrium thermodynamic state, and that this sheds new light on the physics of the Meissner effect. How the Meissner effect occurs has not been addressed within the conventional theory of superconductivity, BCS. The situation considered in this paper indicates that expulsion of magnetic field requires physical elements absent from Hamiltonians assumed to describe superconductors within BCS theory. These physical elements are essential components of the alternative theory of hole superconductivity.

Complexity has gained recent attention in machine learning for its ability to extract synthetic information from large datasets. Complex dynamical systems are characterized by temporal complexity associated with intermittent birth-death events of self-organizing behavior. These rapid transition events (RTEs) can be modelled as a stochastic point process on the time axis, with inter-event times (IETs) revealing rich dynamics. In particular, IETs with power-law distribution mark a departure from the Poisson statistics and indicate the presence of nontrivial complexity that is quantified by the power-law exponent $μ$ of the IET distribution. However, detection of RTEs in noisy signals remains a challenge, since false positives can obscure the statistical structure of the underlying process. In this paper, we address the problem of quantifying the effect of the event detection tool on the accuracy of complexity estimation. This is reached through a systematic evaluation of the Event-Driven Diffusion Scaling (EDDiS) algorithm, a tool exploiting event-driven diffusion to estimate temporal complexity.After introducing the event detection method RTE-Finder (RTEF), we assess the performance of the RTEF-EDDiS pipeline using event-driven synthetic signals. The reliability of the RTEF is found to strongly depend on parameters such as the percentile and the number of false positives can be much higher than the number of genuine complex events. Despite this, we found that the complexity estimation is quite robust with respect to the rate of false positives. For the power-law distributed IETs with $μ\le2.5$, the second moment scaling $H$ appears to even improve as the rate of false positives increases, reaching estimation errors of about 4-7%.

The signature of a path is a non-commutative power series whose coefficients are given by certain iterated integrals over the path coordinates. This series almost uniquely characterizes the path up to translation and reparameterization. Taking only fixed degree parts of these series yields signature tensors. We introduce the Macaulay2 package $\texttt{PathSignatures}$ to simplify the study of these interesting objects for piecewise polynomial paths. It allows for the creation and manipulation of parametrized families of paths and provides methods for computing their signature tensors and their associated algebraic varieties.

Given $a,b\ge 0$ and $t>0$, let $ρ=\{ ρ_{s}\} _{0\le s\le t}$ be a three-dimensional Bessel bridge from $a$ to $b$ over $[0,t]$. In this paper, based on a conditional identity in law between Brownian bridges stemming from Pitman's theorem, we show in particular that the process given by \begin{align*} ρ_{s}+\Bigl| b-a+ \min _{0\le u\le s}ρ_{u}-\min _{s\le u\le t}ρ_{u} \Bigr| -\Bigl| \min _{0\le u\le s}ρ_{u}-\min _{s\le u\le t}ρ_{u} \Bigr| ,\quad 0\le s\le t, \end{align*} has the same law as the time reversal $\{ ρ_{t-s}\} _{0\le s\le t}$ of $ρ$. As an immediate application, letting $R=\{ R_{s}\} _{s\ge 0}$ be a three-dimensional Bessel process starting from $a$, we obtain the following time-reversal and time-inversion results on $R$: $\{ R_{t-s}\} _{0\le s\le t}$ is identical in law with the process given by \begin{align*} R_{s}+R_{t}-2\min _{s\le u\le t}R_{u},\quad 0\le s\le t, \end{align*} when $a=0$, and $\{ sR_{1/s}\} _{s>0}$ is identical in law with the process given by \begin{align*} R_{s}-2(1+s)\min _{0\le u\le s}\frac{R_{u}}{1+u}+a(1+s),\quad s>0, \end{align*} for every $a\ge 0$.

For a fixed exponent $0 < θ\leq 1$, it is expected that we have the prime number theorem in short intervals $\sum_{x \leq n < x+x^θ} Λ(n) \sim x^θ$ as $x \to \infty$. From the recent zero density estimates of Guth and Maynard, this result is known for all $x$ for $θ> \frac{17}{30}$ and for almost all $x$ for $θ> \frac{2}{15}$. Prior to this work, Bazzanella and Perelli obtained some upper bounds on the size of the exceptional set where the prime number theorem in short intervals fails. We give an explicit relation between zero density estimates and exceptional set bounds, allowing for the most recent zero density estimates to be directly applied to give upper bounds on the exceptional set via a small amount of computer assistance.

We use Hodge theory to relate poles of the Archimedean zeta function $Z_f$ of a holomorphic function $f$ with several invariants of singularities. First, we prove that the largest nontrivial pole of $Z_f$ is the negative of the minimal exponent of $f$, whose order is determined by the multiplicity of the corresponding root of the Bernstein--Sato polynomial $b_f(s)$, resolving in a strong sense a question of Mustaţă--Popa. This simultaneously generalizes a result of Loeser for isolated singularities and of Kollár--Litchin for the log canonical threshold, and improves them by accounting for the multiplicity. On the other hand, we give an example of $f$ where a root of $b_f(s)$ is not a pole of $Z_f$, answering a question of Loeser from 1985 in the negative. As a byproduct, we give a positive answer to a question of Budur--Walther in the case of the minimal exponent. In general, we determine poles of $Z_f$ from the Hodge filtration on vanishing cycles, sharpening a result of Barlet. Finally, we obtain analytic descriptions of the $V$-filtration of Kashiwara and Malgrange, Hodge and higher multiplier ideals, addressing another question of Mustaţă--Popa. The proofs mainly rely on a positivity property of the polarization on the lowest piece of the Hodge filtration on a complex Hodge module in the sense of Sabbah--Schnell.

The intricate interplay between flat bands, Dirac cones, and magnetism in kagome materials has recently attracted significant attention from materials scientists, particularly in compounds belonging to the RMn6Sn6 family (R = Sc, Y, rare earths), due to their inherent magnetic frustration. Here, we present a detailed investigation of the ferromagnetic (FM) kagome magnet ScMn6(Sn0.78Ga0.22)6 using angle-resolved photoemission spectroscopy (ARPES), magnetotransport measurements, and density functional theory (DFT) calculations. Our findings reveal a paramagnetic-to-FM transition at 375 K, with the in-plane direction serving as the easy magnetization axis. Notably, ARPES measurements reveal a Dirac cone near the Fermi energy, while the Hall resistivity exhibits a substantial contribution from the anomalous Hall effect. Additionally, we observe a flat band spanning a substantial portion of the Brillouin zone, arising from the destructive interference of wave functions in the Mn kagome lattice. Theoretical calculations reveal that the gap in the Dirac cone can be modulated by altering the orientation of the magnetic moment. An out-of-plane orientation produces a gap of approximately 15 meV, while an in-plane alignment leads to a gapless state, as corroborated by ARPES measurements. This comprehensive analysis provides valuable insights into the electronic structure of magnetic kagome materials and paves the way for exploring novel topological phases in this material class.

We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and associated graded rings. We emphasize both long-standing problems and more recent questions and developments.

Free-stream preservation is an essential property for numerical solvers on curvilinear grids. Key to this property is that the metric terms of the curvilinear mapping satisfy discrete metric identities, i.e., have zero divergence. Divergence-free metric terms are furthermore essential for entropy stability on curvilinear grids. We present a new way to compute the metric terms for discontinuous Galerkin spectral element methods (DGSEMs) that guarantees they are divergence-free. Our proposed mimetic approach uses projections that fit within the de Rham Cohomology.

Pila and Tsimerman proved in 2017 that for every $k$ there exists at most finitely many $k$-tuples $(x_1,\ldots, x_k)$ of distinct non-zero singular moduli with the property "$x_1, \ldots,x_k$ are multiplicatively dependent, but any proper subset of them is multiplicatively independent". The proof was non-effective, using Siegel's lower bound for the Class Number. In 2019 Riffaut obtained an effective version of this result for $k=2$. Moreover, he determined all the instances of $x^my^n\in \mathbb Q^\times$, where $x,y$ are distinct singular moduli and $m,n$ non-zero integers. In this article we obtain a similar result for $k=3$. We show that $x^my^nz^r\in \mathbb Q^\times$ (where $x,y,z$ are distinct singular moduli and $m,n,r$ non-zero integers) implies that the discriminants of $x,y,z$ do not exceed $10^{10}$.

Pairwise velocities of the large-scale structure encode valuable information about the growth of structure. They can be observed indirectly through redshift-space distortions and the kinetic Sunyaev-Zeldovich effect. Whether it is Gaussian or non-Gaussian, pairwise velocity has a broad distribution, but the cosmologically useful information lies primarily in the mean - the streaming velocities; the dispersion around the mean is often treated as a nuisance and marginalized over. This conventional approach reduces the constraining power of our observations. Here, we show that this does not have to be the case, provided the physics behind the dispersion is understood. We demonstrate that by splitting the halo/galaxy samples according to their density environments and measuring the streaming velocities separately, the total signal-to-noise is several times greater than in conventional global measurements of the pairwise velocity distribution (PVD). This improvement arises because the global PVD is a composite of a series of near-Gaussian distributions with different means and dispersions, each determined by its local density environment. Around underdense and overdense regions, the mean streaming velocities are positive and negative, respectively. By splitting the data, we avoid cancellation between these opposing velocities, effectively turning what would be considered dispersion in the global PVD into a signal. Our findings indicate substantial potential for improving the analysis of PVD observations using the kinetic Sunyaev-Zeldovich effect and redshift-space distortions.

It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum systems to produce an equal superposition of eigenstates. The quantum phase estimation subroutine then allows for the computations of functions of the input operator, leading to a variety of methods in linear algebra. The algorithm circumvents the need for elaborate wavefunction preparation on the quantum computer to find the solution of the linear algebra problem in poly-logarithmic time.

This article is devoted to analytic (in the sense of Boutet de Monvel-Sjöstrand) estimates in $\hbar$, of the Bohr-Sommerfeld expansion of the eigenvalues of self-adjoint pseudodifferential operators acting on $L^2(R)$ in the regular case. We consider an interval of energies in which the spectrum of P is discrete and such that the energy sets are regular connected curves. Under some assumptions on the holomorphy of the symbol p, we will use the isometry between $L^2(R)$ and the Bargmann space to obtain an exponentially sharp description of the spectrum in the energy window . More precisely it is possible to build exponentially sharp WKB quasimodes in the Bargmann space. A precise examination of the principal symbols will provide an interpretation to the Maslov correction $π\hbar$ in the Bargmann space.

We answer in the negative the long-standing open question of whether biholomorphic equivalence implies algebraic equivalence for germs of real algebraic manifolds in $\mathbb C^n$. More precisely we give an example of two germs of real algebraic surfaces in $\mathbb C^2$ that are biholomorphic, but not by means of an algebraic biholomorphism.

In this work we solve, for given bounded operators $B,C$ and Hilbert-Schmidt operator $M$ acting on potentially infinite-dimensional separable Hilbert spaces, the reduced rank approximation problem, $\min\{\lVert M-BXC\rVert_{L_2}:\ \text{dim ran}\ X\leq r\}.$ This extends the result of Sondermann (Statistische Hefte, 1986) and Friedland and Torokhti (SIAM J. Matrix Analysis and Applications, 2007), which studies this problem in the case of matrices $M$, $B$, $C$, $X$, and the analysis involves the Moore-Penrose inverse. In classical approximation problems that can be solved by the singular value decomposition or Moore-Penrose inverse, the solution satisfies a minimal norm property. Friedland and Torokhti state such a minimal norm property of the solution. We show that this minimal norm property does not hold in general and give a modified minimality property that does hold. We show that the solution may be discontinuous in infinite-dimensional settings. We give conditions for continuity of the solutions and construct continuous approximations when such conditions are not met. Finally, we study problems from signal processing, reduced rank regression and linear operator learning under a rank constraint. Our theoretical results enable us to explicitly find solutions to these problems and to characterise their existence, uniqueness and minimality property.

We study a variant of the Generalized Excited Random Walk (GERW) on $\mathbb{Z}^d$ introduced by Menshikov, Popov, Ramírez and Vachkovskaia in [Ann. Probab. 40 (5), 2012]. It consists of a particular version of the model studied in [arXiv preprint arXiv:2211.05715, 2022] where excitation may or may not occur according to a time-dependent probability. Specifically, given $\{p_n\}_{n \ge 1}$, $p_n \in (0, 1]$ for all $n \ge 1$, whenever the process visits a site at time $n$ for the first time, with probability $p_n$ it gains a drift in a fixed direction. Otherwise, it behaves as a $d$-martingale with zero-mean vector. We refer to the model as $p_n$-GERW. Assuming bounded jumps and $p_n \approx n^{-β}$, we show a series of results for the $p_n$-\Name{} depending on the value of $β$ and on the dimension $d$. Specifically, for every $β\in(0,1]$ and $d=2$ or $d>h(β)$, with $h$ a decreasing function of $β$, we prove a SLLN for the range, while for $β<1/2$ we prove a sub-ballistic SLLN for the process whenever the SLLN for the range holds. We also study the $p_n$-\Name{} under diffusive scaling, and we obtain a Functional Central Limit Theorem for $β> 1/2$ and $d\geq 2$, or $β=1/2$ and $d=2$. Finally, for $β=1/2$ and $d \ge 11$ we show that the diffusively rescaled $p_n$-\Name{} converges in distribution to a Brownian Motion plus a multiple of the square root of time.

Let $H_g$ denote the 4-dimensional handlebody of genus $g$ and $U_g$ its boundary. We show that for all $g \ge 0$ the map from $B Homeo(H_g)$ to $B Homeo(U_g)$ induced by restriction to the boundary admits a section.

Recent improvements in energy efficiency and renewable energy integration have increased the relative importance of embodied carbon in data centers, motivating improved provisioning strategies. Conventional approaches primarily minimize operational energy, but this perspective is increasingly insufficient for sustainability. In this paper, we propose carbon depreciation models to encourage longer hardware lifetimes. Carbon depreciation assigns a larger portion of embodied carbon to newly provisioned servers, discouraging unnecessary deployment of new hardware. As a result, new servers are provisioned mainly for jobs with strict quality-of-service (QoS) constraints, while older servers, whose embodied carbon has largely been recovered, are used for other workloads. We further argue that both embodied carbon and operational carbon from server idle time should be recovered during active jobs, encouraging provisioning strategies that maintain high utilization. We show that prior carbon accounting strategies can be counterproductive: under a greedy scheduler minimizing carbon under QoS constraints, jobs are priced as 25% cheaper on new hardware than on older hardware. In contrast, our approach uses a greedy scheduler that prioritizes older hardware through non-linear carbon depreciation, promoting sustainable provisioning. Experimental results show carbon reductions of 28-57%, depending on server lifetime assumptions.

An attempt has been made to estimate the minimum size of the de-confined matter of Quark-Gluon Plasma (QGP) in small systems like p-Pb system that could be satisfactorily modeled with low-order hydrodynamics. The variation of second order transport coefficient of second order relativistic viscous hydrodynamics, the shear relaxation time has been utilized to study the sensitivity of experimental observables like elliptic flow coefficient. A representative system of p-Pb collisions at $\sqrt{s_{NN}} =$ 5.02 TeV, simulated with the state-of-art framework of JETSCAPE event generator was used to study the variation of elliptic flow coefficient for peripheral collisions. The soft sector dynamics was simulated using an initial condition, a pre-equilibrium stage, hydrodynamics and a hadron afterburner. The transverse momentum spectra and rapidity distribution was obtained for light flavored hadrons and compared with the experimental data. The increase in elliptic flow fluctuations indicate breakdown of fluid behavior at $dN/dy \approx 14$ for p-Pb collision at $\sqrt{s_{NN}} =$ 5.02 TeV.

The study of gapless phases with categorical (or so-called non-invertible) symmetries is a formidable task, in particular in higher than two space-time dimensions. In this paper we build on previous works arXiv:2408.05266 and arXiv:2502.20440 on gapped phases in (2+1)d and provide a systematic framework to study phase transitions with categorical symmetries. The Symmetry Topological Field Theory (SymTFT) is, as often in these matters, the central tool. Applied to gapless theories, we need to consider the extension of the SymTFT to interfaces between topological orders, so-called ``club sandwiches", which realize generalizations of so-called Kennedy-Tasaki (KT) transformations. This requires an input phase transition for a smaller symmetry, such as the Ising transition for $\mathbb{Z}_2$, and the SymTFT constructs a transformation to a gapless phase with a larger categorical symmetry. We carry this out for categorical symmetries whose SymTFT is a (3+1)d Dijkgraaf-Witten (DW) theory for a finite group $G$ with twist -- so-called all bosonic fusion 2-categories. We classify such interfaces using a physically motivated picture of generalized gauging, as well as with a complementary analysis using (bi-)module 2-categories.This is exemplified in numerous abelian and non-abelian DW theories, giving rise to interesting gapless phases such as intrinsically gapless symmetry protected phases (igSPTs) and spontaneous symmetry breaking phases (igSSBs) from abelian, $S_3$, and $D_8$ DW theories.

The Kolmogorov-Smirnov statistic is usually introduced as a supremum, but its finite-sample behavior is governed by a more local question: where does the empirical process first cross a boundary? This letter gives a partial answer through a finite-sample crossing ledger. The ledger rewrites the Smirnov- Birnbaum-Tingey one-sample formula as an explicit hitting-time law and yields a stable log-scale tail evaluator. For two samples, it gives one-wall and two-wall exact lattice recursions for arbitrary sample sizes, with the balanced reflection formula appearing as a special closed form. The same viewpoint explains the Dvoretzky-Kiefer-Wolfowitz-Massart inequality as an exponential compression of exact crossing sums and shows where exact distribution-free counting stops: under a composite null, fitted parameters change the path itself. Simulations and two small data diagnostics illustrate the resulting calibration warning.

We study convective stability of a two-front superposition in a reaction-diffusion system. Due to the instability of the connecting equilibrium, long-range semi-strong interaction is expected between the two waves. When restricting to the linear dynamic, we indeed identify that convective stability of superposed waves occurs for fewer propagation speeds than for the corresponding single waves. It reflects the interaction that monostable waves have over long distances. Our method relies on numerical range estimates, that imply time-uniform resolvent bounds.

In the recent paper (Phys.Rev.Lett. 133 (2024) 12, 121601), a higher-order phase transition between the planar, charged, 5-dimensional Reissner-Nordström-Anti-de Sitter black hole and a hairy black hole solution of the type IIB supergravity was investigated. Here, following a bottom-up approach, we set out to investigate these two phases of the theory by means of the holographic probe that describes a quark-antiquark in the dual gauge theory. We ask ourselves whether studying the quark-antiquark potential suffices to detect the change of behavior at different values of the parameter that controls the phase transition, this parameter being the ratio between the chemical potential and the temperature. We show that, while evaluating the probe on both phases leads to the same value at the point where the transition takes place, there is always one phase that dominates over the other with regard to this observable. The same can be said about higher-dimensional probes such as those involved in the computation of holographic entanglement entropy.

We introduce a new algorithm to solve constrained nonlinear optimal control problem, with an emphasis on low-thrust trajectory in highly nonlinear dynamics. The algorithm, dubbed Pontryagin-Bellman Differential Dynamic Programming (PDDP), is the result of the incorporation of Pontryagin Minimum Principle (PMP) into the Differential Dynamic Programming (DDP) formulation. Unlike traditional indirect methods that rely on first-order shooting techniques to determine the optimal costate, PDDP optimizes the costates using a null-space trust-region method, solving a series of quadratic subproblems derived from first- and second-order sensitivities. Terminal equality constraints are handled via a general augmented Lagrangian method, while state-path constraints are enforced using a quadratic penalty approach. The resulting solution method represents a significant improvement over classical indirect methods, which are known to be ineffective for state-constrained problems. The use of DDP to optimize the costate partially reduces the inherent sensitivities of indirect methods, thereby improving the robustness to poor initial guess. Finally, the incorporation of PMP within the DDP formulation enables the design of long-duration, multi-spiral low-thrust trajectories with fewer optimization variables compared to classical DDP formulations. Although the paper emphasizes the spacecraft low-thrust trajectory optimization problem, the theoretical foundations are general and applicable to any control-affine optimal control problem.