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This paper is a write-up of the ideas that were presented, developed and discussed at the fourth International Workshop on QCD Challenges from pp to AA, which took place in February 2023 in Padua, Italy. The goal of the workshop was to focus on some of the open questions in the field of high-energy heavy-ion physics and to stimulate the formulation of concrete suggestions for making progresses on both the experimental and theoretical sides. The paper gives a brief introduction to each topic and then summarizes the primary results.

In the present paper, we investigate both the global exponential stability and the existence of a periodic solution of a general differential equation with unbounded distributed delays. The main stability criterion depends on the dominance of the non-delay terms over the delay terms. The criterion for the existence of a periodic solution is obtained with the application of the coincide degree theorem. We use the main results to get criteria for the existence and global exponential stability of periodic solutions of a generalized higher-order periodic Cohen-Grossberg neural network model with discrete-time varying delays and infinite distributed delays. Additionally, we provide a comparison with the results in the literature and a numerical simulation to illustrate the effectiveness of some of our results., Comment: 30 pages

In this paper, a new global exponential stability criterion is obtained for a general multidimensional delay difference equation using induction arguments. In the cases that the difference equation is periodic, we prove the existence of a periodic solution by constructing a type of Poincar\'e map. The results are used to obtain stability criteria for a general discrete-time neural network model with a delay in the leakage terms. As particular cases, we obtain new stability criteria for neural network models recently studied in the literature, in particular for low-order and high-order Hopfield and Bidirectional Associative Memory(BAM)., Comment: 20 pages, 3 figures

The future Electron-Ion Collider (EIC) will utilize a series of high-luminosity high-energy electron+proton ($e+p$) and electron+nucleus ($e+A$) collisions to explore the inner structure of nucleon and nucleus and the matter formation process. Heavy flavor hadron and jet measurements at the EIC will play an essential role in determining the nucleon/nucleus parton distribution function and heavy quark hadronization process in not well constrained kinematic regions. A high granularity and low material budget forward silicon tracker will enable precise forward heavy flavor measurements at the EIC, which have enhanced sensitivities to access these kinematic extremes. A Forward Silicon Tracker (FST) detector is under design and R$\&$D for the EIC. Two advanced silicon technologies, the Depleted Monolithic Active Pixel Sensor (DMAPS) and the AC coupled Low Gain Avalanche Diode (AC-LGAD), which can provide fine spatial and timing resolutions, have been considered as candidates for the EIC silicon tracking detector. Progresses and results about the FST conceptual design and ongoing DMAPS and LGAD detector R$\&$D will be presented. The path towards an integrated EIC detector will be discussed as well., Comment: 7 pages, 5 figures, proceeding for 41st International Conference on High Energy Physics - ICHEP2022, accepted by PoS

For linear nonautonomous differential equations we introduce a new family of spectrums defined with general nonuniform dichotomies: for a given growth rate $\mu$ in a large family of growth rates, we consider a notion of spectrum, named nonuniform $\mu$-dichotomy spectrum. This family of spectrums contain the nonuniform dichotomy spectrum as the very particular case of exponential growth rates. For each growth rate $\mu$, we describe all possible forms of the nonuniform $\mu$-dichotomy spectrum, relate its connected components with adapted notions of Lyapunov exponents, and use it to obtain a reducibility result for nonautonomous linear differential equations. We also give an illustrative examples where the spectrum is obtained, including a situation where a normal form is obtained for polynomial behavior., Comment: 32 pages

We prove that Sarnak's conjecture holds for any infinite measure symbolic rank-one map. We further extended Bourgain-Sarnak's result, which says that the M\"{o}bius function is a good weight for the ergodic theorem, to maps acting on $\sigma$-finite measure spaces. We also discuss and extend Bourgain's theorem by establishing that there is a class of maps for which the M\"{o}bius disjointness property holds for any continuous bounded function. Our proof allows us to obtain an extension of Bourgain's theorem on M\"{o}bius disjointness for bounded rank one maps and a simple and self-contained proof of this fact., Comment: 20 pages. Scientific comments are welcome

In the last decade, a great effort has been employed in the study of Hybrid Unmanned Aerial Underwater Vehicles, robots that can easily fly and dive into the water with different levels of mechanical adaptation. However, most of this literature is concentrated on physical design, practical issues of construction, and, more recently, low-level control strategies. Little has been done in the context of high-level intelligence, such as motion planning and interactions with the real world. Therefore, we proposed in this paper a trajectory planning approach that allows collision avoidance against unknown obstacles and smooth transitions between aerial and aquatic media. Our method is based on a variant of the classic Rapidly-exploring Random Tree, whose main advantages are the capability to deal with obstacles, complex nonlinear dynamics, model uncertainties, and external disturbances. The approach uses the dynamic model of the \hydrone, a hybrid vehicle proposed with high underwater performance, but we believe it can be easily generalized to other types of aerial/aquatic platforms. In the experimental section, we present simulated results in environments filled with obstacles, where the robot is commanded to perform different media movements, demonstrating the applicability of our strategy., Comment: Accepted to the Journal of Intelligent & Robotic Systems

Prospects for quarkonium-production studies accessible during the upcoming high-luminosity phases of the CERN Large Hadron Collider operation after 2021 are reviewed. Current experimental and theoretical open issues in the field are assessed together with the potential for future studies in quarkonium-related physics. This will be possible through the exploitation of the huge data samples to be collected in proton-proton, proton-nucleus and nucleus-nucleus collisions, both in the collider and fixed-target modes. Such investigations include, among others, those of: (i) J/psi and Upsilon produced in association with other hard particles; (ii) chi(c,b) and eta(c,b) down to small transverse momenta; (iii) the constraints brought in by quarkonia on gluon PDFs, nuclear PDFs, TMDs, GPDs and GTMDs, as well as on the low-x parton dynamics; (iv) the gluon Sivers effect in polarised-nucleon collisions; (v) the properties of the quark-gluon plasma produced in ultra-relativistic heavy-ion collisions and of collective partonic effects in general; and (vi) double and triple parton scatterings., Comment: Latex, 115 pages, 55 figures, 4 tables. v2: Review published in Progress in Particle and Nuclear Physics

We obtain characterizations of nonuniform dichotomies, defined by general growth rates, based on admissibility conditions. Additionally, we use the obtained characterizations to derive robustness results for the considered dichotomies. As particular cases, we recover several results in the literature concerning nonuniform exponential dichotomies and nonuniform polynomial dichotomies as well as new results for nonuniform dichotomies with logarithmic growth., Comment: 26 pages

We study two properties of nonsingular and infinite measure-preserving ergodic systems: weak double ergodicity, and ergodicity with isometric coefficients. We show that there exist infinite measure-preserving transformations that are ergodic with isometric coefficients but are not weakly doubly ergodic. We also give type $\text{III}_\lambda$ examples of such systems, $0<\lambda\leq 1$. We prove that under certain hypotheses, systems that are weakly mixing are ergodic with isometric coefficients and along the way we give an example of a uniformly rigid topological dynamical system along the sequence $(n_i)$ that is not measure theoretically rigid along $(n_i)$ for any nonsingular ergodic finite measure., Comment: Made sure third co-author (BH) appears in heading

We define a notion of rank for words and subshifts that we call spacer rank, extending the notion of rank-one symbolic shifts of Gao and Hill. We construct infinite words of each finite spacer rank, of unbounded spacer rank, and show there exist words that do not have a spacer rank construction. We consider words that are fixed points of substitutions and give explicit conditions for the word to have an at most spacer rank two construction, and not to be rank one. We prove that finite spacer rank subshifts have topological entropy zero, and that there are zero entropy subshifts not defined by a word with a finite spacer rank construction. We also study shift systems associated with infinite words, including those associated to Sturmian sequences, which we show are spacer rank-two systems., Comment: Changed the title to now use "spacer rank". Updated the abstract. Added some references. Small corrections. Shortened parts of sections 3 and 4 (please refer to older version for omitted details)

The future Electron-Ion Collider (EIC) will explore several fundamental questions in a broad Bjorken-x ($x_{BJ}$) and $Q^{2}$ phase space. Heavy flavor and jet products are ideal probes to precisely study the tomography of nucleon/nuclei structure, help solve the proton spin puzzle and understand the hadronizaton processes in vacuum or in the QCD medium. Due to the asymmetric collisions at the EIC, most of the final state hadrons are produced in the nucleon/nuclei beam going (forward) direction. A silicon vertex/tracking is critical to precisely measure these forward hadrons at the EIC. Details of different conceptual designs of the proposed Forward Silicon Tracker (FST) and the relevant detector performance are presented in this technical note. The associated heavy flavor and jet studies with the evaluated FST performance are discussed as well., Comment: 47 pages, 64 figures, technical note for a proposed forward silicon tracker detector and associated detector/physics simulation studies for the future Electron-Ion Collider by the Los Alamos National Laboratory team. This work is supported by the Los Alamos National Laboratory LDRD office 20200022DR project

Using Mickens nonstandard method, we obtain a discrete family of nonautonomous eco-epidemiological models that include general functions corresponding to the predation of the infected and uninfected preys. We obtain results on the persistence and extinction of the infected preys assuming that the bi-dimensional predator-prey subsystem that describes the dynamics in the absence of the infection satisfies some assumptions. Some examples and simulations are undertaken to illustrate our results.

We consider random perturbations of a general eco-epidemiological model. We prove the existence of a global random attractor, the persistence of susceptibles preys and provide conditions for the simultaneous extinction of infectives and predators. We also discuss the dynamics of the corresponding random epidemiological $SI$ and predator-prey models. We obtain for this cases a global random attractor, prove the prevalence of susceptibles/preys and provide conditions for the extinctions of infectives/predators.

The proposed high-energy and high-luminosity Electron-Ion Collider (EIC) will provide one of the cleanest environments to precisely determine the nuclear parton distribution functions (nPDFs) in a wide $x$-$Q^{2}$ range. Heavy flavor production at the EIC provides access to nPDFs in the poorly constrained high Bjorken-$x$ region, allows us to study the quark and gluon fragmentation processes, and constrains parton energy loss in cold nuclear matter. Scientists at the Los Alamos National Laboratory are developing a new physics program to study heavy flavor production, flavor tagged jets, and heavy flavor hadron-jet correlations in the nucleon/nucleus going direction at the future EIC. The proposed measurements will provide a unique way to explore the flavor dependent fragmentation functions and energy loss in a heavy nucleus. They will constrain the initial-state effects that are critical for the interpretation of previous and ongoing heavy ion measurements at the Relativistic Heavy Ion Collider and the Large Hadron Collider. We show an initial conceptual design of the proposed Forward Silicon Tracking (FST) detector at the EIC, which is essential to carry out the heavy flavor measurements. We further present initial feasibility studies/simulations of heavy flavor hadron reconstruction using the proposed FST., Comment: 6 pages, 5 figures, proceedings for the XLIX International Symposium on Multiparticle Dynamics (ISMD2019) (9-13 September 2019) conference

We consider a nonautonomous eco-epidemiological model with general functions for predation on infected and uninfected preys as well as general functions associated to the vital dynamics of the susceptible prey and predator populations. We obtain persistence and extinction results for the infected prey based on assumptions on systems related to the dynamics in the absence of infected preys. We apply our results to eco-epidemiological models constructed from predator-prey models existent in the literature. Some illustrative simulation is undertaken., Comment: 26 pages, 30 figures

In this paper we give explicit characterizations, based on the cutting and spacer parameters, of (a) which rank-one transformations factor onto a given finite cyclic permutation, (b) which rank-one transformations factor onto a given odometer, and (c) which rank-one transformations are isomorphic to a given odometer. These naturally yield characterizations of (d) which rank-one transformations factor onto some (unspecified) finite cyclic permutation, (d') which rank-one transformations are totally ergodic, (e) which rank-one transformations factor onto some (unspecified) odometer, and (f) which rank-one transformations are isomorphic to some (unspecified) odometer.

For a class of irrational numbers, depending on their Diophantine properties, we construct explicit rank-one transformations that are totally ergodic and not weakly mixing. We classify when the measure is finite or infinite. In the finite case they are isomorphic to irrational rotations. We also obtain rank-one nonrigid infinite invariant measures for irrational rotations, and, for each Krieger type, nonsingular measures on irrational rotations. In the third version, in the infinite case we use the constructions to provide examples of non-weakly mixing infinite measure-preserving ergodic transformations which do not have any nontrivial probability preserving factors with discrete spectrum, thereby answering a questions of Aaronson and Nakada and of Glasner and Weiss., Comment: Added new section 9 (answering a questions of Aaronson and Nakada and of Glasner and Weiss). (Sections 10 and 11 were previously numbered 9 and 10.)

We give a short proof, that can be used in an introductory real analysis course, that if a function that is defined on the set of real numbers is continuous on a countable dense set, then it is continuous on an uncountable set. This is done for functions defined on complete metric spaces without isolated points, and the argument only uses that Cauchy sequences converge, and we prove the version related to Volterra's theorem. We discuss how this theorem is a direct consequence of the Baire category theorem, and also discuss Volterra's theorem and the history of this problem. We conclude with a simple example, for each complete metric space without isolated points and each set that is a countable union of closed subsets, of a real-valued function that is discontinuous only on that set., Comment: Clarified the title a bit, added a reference, small corrections