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We present a sequential cellular automaton of radius 2 1 as a solution to the density classification task that makes use of an intermediate alphabet, and converges to a clean fixed point with no remaining auxiliary or intermediate information. We extend this solution to arbitrary finite alphabets and to configurations in higher dimensions.

We rigorously establish the existence of many free boundary minimal annuli with boundary in a geodesic sphere of $\mathbb{S}^3$. These arise as compact subdomains of a one-parameter family of complete minimal immersions of $\mathbb{R} \times \mathbb{S}^1$ into $\mathbb{S}^3$ described by do Carmo and Dajczer [1]. While the free boundary minimal annuli we exhibit may have self-intersections and may not be contained in a geodesic ball, we show that there is at least a one-parameter family of embedded examples that are contained in geodesic balls whose radius may be less than, equal to or greater than $\pi$/2. After explaining the connection to Otsuki tori [13], we establish lower bounds on the number of free boundary minimal annuli contained in each Otsuki torus in terms of the corresponding rational number. Finally, we show that some of the recent work of Lee and Seo [7] on isoperimetric inequalities and of Lima and Menezes [10] on index bounds extends to geodesic balls equal to or larger than a hemisphere., Comment: 17 pages, 6 figures

We present R-matrix calculations of photoionization of molecular monomers and dimers, focusing on ammonia (NH3) and formic acid (HCOOH), utilizing configuration-interaction models including the Occupation-Restricted Multiple Active Space (ORMAS) approach. We show that ORMAS is a highly efficient choice for calculating photoionization observables, yielding results that are in excellent agreement with those obtained using the much more demanding configuration-interaction method, Complete Active Space (CAS). We demonstrate that models incorporating single and double (SD) excitations with respect to the Hartree-Fock configuration provide good agreement with experimental data. The approach developed here can be readily applied to study photoionization in complex molecular systems.

We present a family of automata networks that solve the k-parity problem when run in parallel. These solutions are constructed by connecting cliques in a non-cyclical fashion. The size of the local neighbourhood is linear in the size of the alphabet, and the convergence time is proven to always be the diameter of the interaction graph. We show that this family of solutions can be slightly altered to obtain an equivalent family of solutions to the k-synchronisation problem, which means that these solutions converge from any initial configuration to the cycle which contains all the uniform configurations over the alphabet, in order.

We investigate the behaviour of split extensions in the category OrdGrp of (pre)\-ordered groups. Namely we show that the lexicographic order plays a key role on the existence of compatible orders for semidirect products, establishing necessary and sufficient conditions for such existence; we prove that the Split Short Five Lemma holds for stably strong split extensions, and identify classes of split extensions which admit a classifier.

This document describes a deep learning-based point cloud geometry codec and a deep learning-based point cloud joint geometry and colour codec, submitted to the Call for Proposals on JPEG Pleno Point Cloud Coding issued in January 2022. The proposed codecs are based on recent developments in deep learning-based PC geometry coding and offer some of the key functionalities targeted by the Call for Proposals. The proposed geometry codec offers a compression efficiency that outperforms the MPEG G-PCC standard and outperforms or is competitive with the V-PCC Intra standard for the JPEG Call for Proposals test set; however, the same does not happen for the joint geometry and colour codec due to a quality saturation effect that needs to be overcome., Comment: 52 pages, 8 figures. Document submitted to the 96th ISO/IEC JTC 1/SC 29/WG 1 (JPEG) meeting

Motor imagery (MI)-based brain-computer interface (BCI) systems are being increasingly employed to provide alternative means of communication and control for people suffering from neuro-motor impairments, with a special effort to bring these systems out of the controlled lab environments. Hence, accurately classifying MI from brain signals, e.g., from electroencephalography (EEG), is essential to obtain reliable BCI systems. However, MI classification is still a challenging task, because the signals are characterized by poor SNR, high intra-subject and cross-subject variability. Deep learning approaches have started to emerge as valid alternatives to standard machine learning techniques, e.g., filter bank common spatial pattern (FBCSP), to extract subject-independent features and to increase the cross-subject classification performance of MI BCI systems. In this paper, we first present a review of the most recent studies using deep learning for MI classification, with particular attention to their cross-subject performance. Second, we propose DynamicNet, a Python-based tool for quick and flexible implementations of deep learning models based on convolutional neural networks. We show-case the potentiality of DynamicNet by implementing EEGNet, a well-established architecture for effective EEG classification. Finally, we compare its performance with FBCSP in a 4-class MI classification over public datasets. To explore its cross-subject classification ability, we applied three different cross-validation schemes. From our results, we demonstrate that DynamicNet-implemented EEGNet outperforms FBCSP by about 25%, with a statistically significant difference when cross-subject validation schemes are applied.

In [11] and [13] the authors showed that elementary cellular automata rules 0, 3, 8, 12, 15, 28, 32, 34, 44, 51, 60, 128, 136, 140, 160, 162, 170, 200 and 204 (and their conjugation, reflection, reflected-conjugation) are not maximum sensitive to synchronism, i.e. they do not have a different dynamics for each (non-equivalent) block-sequential update schedule (defined as ordered partitions of cell positions). In this work we present exact measurements of the sensitivity to synchronism for these rules, as functions of the size. These exhibit a surprising variety of values and associated proof methods, such as the special pairs of rule 128, and the connection to the bissection of Lucas numbers of rule 8.

The phase transitions characterized by deconfinement and restoration of chiral symmetry as well as the restoration of axial symmetry, at finite temperature, are investigated in the framework of SU(2) Polyakov-Nambu-Jona-Lasinio (PNJL) models with the U$_A$(1) anomaly. The thermodynamics of the phase transitions, the topological susceptibility, the meson spectrum, and, in particular, the convergence of axial and chiral partners are analyzed, in the framework of the ordinary PNJL model and in its extension, the entangled Polyakov-Nambu-Jona-Lasinio (EPNJL) model. The latter incorporates entanglement between restoration of chiral symmetry and deconfinement., Comment: Contribution to the International Meeting "Excited QCD", Bjelasnica Mountain, Sarajevo, 3-9 February 2013

We investigate the phase transitions characterized by deconfinement and restoration of chiral and axial symmetries,at finite temperature, in the framework of QCD inspired models. We compare the results obtained in the SU(2) Polyakov-Nambu-Jona-Lasinio model with anomaly and in its extended version, the Entangled Polyakov-Nambu-Jona-Lasinio model. In the last version, four-quark vertices with entanglement between the chiral condensate and the Polyakov loop are considered. The thermodynamics of the phase transitions, the meson spectrum, and in particular the convergence of axial and chiral partners, will be analyzed, as well as the topological susceptibility. We find that an explicit temperature dependence of the coupling vertices is necessary in both models in order to have effective restoration of the U$_A$(1) symmetry., Comment: 19 pages, 4 figures; PRD version

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio (PNJL) model at finite temperature and nonzero chemical potential. The calculations are performed in the light and strange quark sectors ($u$, $d$, $s$), which includes the 't Hooft instanton induced interaction term that breaks the axial symmetry, and the quarks are coupled to the (spatially constant) temporal background gauge field. On one hand, a special attention is payed to the critical end point (CEP). The strength of the flavor-mixing interaction alters the CEP location, since when it becomes weaker the CEP moves to low temperatures and can even disappear. On the other hand, we also explore the connection between QCD, a nonlocal Nambu--Jona-Lasinio type model and the Landau gauge gluon propagator. Possible links between the quenched gluon propagator and low energy hadronic phenomenology are investigated., Comment: Contribution to the International Meeting "Excited QCD", Peniche, Portugal, 06 - 12 May 2012

We consider a two flavor Polyakov--Nambu--Jona-Lasinio (PNJL) model where the Lagrangian includes an interaction term that explicitly breaks the U$_A(1)$ anomaly. At finite temperature, the restoration of chiral and axial symmetries, signaled by the behavior of several observables, is investigated. We compare the effects of two regularizations at finite temperature, one of them, that allows high momentum quarks states, leading to the full recovery of chiral symmetry. From the analysis of the behavior of the topological susceptibility and of the mesonic masses of the axial partners, it is found in the SU(2) model that, unlike the SU(3) results, the recovery of the axial symmetry is not a consequence of the full recovery of the chiral symmetry. Thus, one needs to use an additional idea, by means of a temperature dependence of the anomaly coefficient, that simulates instanton suppression effects., Comment: 21 pages, 5 figures; PRD version

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio model at finite temperature and nonzero chemical potential with three quark flavors. Chiral and deconfinement phase transitions are discussed, and the relevant order-like parameters are analyzed. A special attention is payed to the critical end point (CEP): the influence of the strangeness on the location of the CEP is studied; also the strength of the flavor-mixing interaction alters the CEP location, once when it becomes weaker the CEP moves to low temperatures and can even disappear., Comment: Prepared for Strangeness in Quark Matter 2011, Sept. 18--24, Cracow, Poland

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio model at finite temperature and nonzero chemical potential with three quark flavours. Chiral and deconfinement phase transitions are discussed, and the relevant order-like parameters are analyzed. The results are compared with simple thermodynamic expectations and lattice data. A special attention is payed to the critical end point: as the strength of the flavour-mixing interaction becomes weaker, the critical end point moves to low temperatures and can even disappear., Comment: Talk given at the 9th International Conference on Quark Confinement and the Hadron Spectrum - QCHS IX, Madrid, Spain, 30 August - September 2010

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio model at finite temperature and non-zero chemical potential with three quark flavors. Chiral and deconfinement phase transitions are discussed and the relevant order-like parameters are analyzed. The results are compared with simple thermodynamic expectations and lattice data. We present the phase diagram in the ($T,\,\mu_B)$ plane, paying special attention to the critical end point: as the strength of the flavor-mixing interaction becomes weaker, the critical end point moves to low temperatures and can even disappear., Comment: 46 pages, 11 figures, 3 tables

The equation of state and the critical behavior around the critical end point are studied in the context of the Polyakov--Nambu--Jona--Lasinio model. We prove that a convenient choice of the model parameters is crucial to get the correct description of isentropic trajectories. The physical relevance of the effects of the regularization procedure is insured by the agreement with general thermodynamic requirements. The results are compared with simple thermodynamic expectations and lattice data., Comment: Talk given at XIII International Conference on Hadron Spectroscopy (Hadron 2009), Tallahassee, Florida, USA, 29 Nov - 4 Dec, 2009

The effects of the Polyakov loop and of a regularization procedure that allows the presence of high momentum quark states at finite temperature is investigated within the Polyakov-loop extended Nambu--Jona-Lasinio model. The characteristic temperatures, as well as the behavior of observables that signal deconfinement and restoration of chiral and axial symmetries, are analyzed, paying special attention to the behavior of strangeness degrees of freedom. We observe that the cumulative effects of the Polyakov loop and of the regularization procedure contribute to a better description of the thermodynamics, as compared with lattice estimations. We find a faster partial restoration of chiral symmetry and the restoration of the axial symmetry appears as a natural consequence of the full recovering of the chiral symmetry that was dynamically broken. These results show the relevance of the effects of the interplay among the Polyakov loop dynamics, the high momentum quark sates and the restoration of the chiral and axial symmetries at finite temperature., Comment: Talk given at XIII International Conference on Hadron Spectroscopy (Hadron 2009), Tallahassee, Florida, USA, 29 Nov - 4 Dec, 2009

We explore the phase diagram and the critical behavior of QCD thermodynamic quantities in the context of the so-called Polyakov--Nambu--Jona-Lasinio model. We show that this improved field theoretical model is a successful candidate for studying the equation of state and the critical behavior around the critical end point. We argue that a convenient choice of the model parameters is crucial to get the correct description of isentropic trajectories. The effects of the regularization procedure in several thermodynamic quantities is also analyzed. The results are compared with simple thermodynamic expectations and lattice data., Comment: 27 pages, 7 figures, 4 tables; PRD version

We investigate the modifications of mesonic properties in a hot medium having in mind to use the mesonic modes as a tool to analyze the restoration of chiral and axial symmetries in the context of the SU(3) Polyakov--Nambu--Jona-Lasinio (PNJL) model. The results lead to the conclusion that the effects of the Polyakov loop are fundamental for reproducing lattice findings. It is found that the restoration of chiral symmetry in the PNJL model occurs in a small range of temperature (smaller that in the Nambu--Jona-Lasinio (NJL)), and the topological susceptibility reproduces well the lattice results around $T/T_c^\chi\approx 1.0$., Comment: Talk given at the 8th International Conference on Quark Confinement and the Hadron Spectrum, Mainz, Germany, September 1-6, 2008

The modification of mesonic observables in a hot medium is analyzed as a tool to investigate the restoration of chiral and axial symmetries in the context of the Polyakov-loop extended Nambu--Jona-Lasinio model. The results of the extended model lead to the conclusion that the effects of the Polyakov loop are fundamental for reproducing lattice findings. In particular, the partial restoration of the chiral symmetry is faster in the PNJL model than in the NJL one, and it is responsible for several effects: the meson-quark coupling constants show a remarkable difference in both models, there is a faster tendency to recover the Okubo-Zweig-Iizuka rule, and finally the topological susceptibility nicely reproduces the lattice results around $T/T_c\approx 1.0$., Comment: 23 pages, 5 figures, PRD version

We investigate the role played by the Polyakov loop in the dynamics of the chiral phase transition in the framework of the so-called PNJL model in the SU(2)sector. We present the phase diagram where the inclusion of the Polyakov loop moves the critical points to higher temperatures, compared with the NJL model results. The critical properties of physical observables, such as the baryon number susceptibility and the specific heat, are analyzed in the vicinity of the critical end point, with special focus on their critical exponents. The results with the PNJL model are closer to lattice results and we also recover the universal behavior of the critical exponents of both the baryon susceptibility and the specific heat., Comment: 12 pages, 3 figures, EPL version

We investigate the chiral phase transition at finite temperature and chemical potential within SU(2) and SU(3) Nambu-Jona-Lasinio type models. The behavior of the baryon number susceptibility and the specific heat, in the vicinity of the critical end point, is studied. The class of the critical points is analyzed by calculating critical exponents., Comment: Talk given at 12th International Conference on Hadron Spectroscopy (Hadron 07), Frascati, Italy, 8-13 Oct 2007

We investigate the phase diagram of strongly interacting matter as a function of temperature and baryonic density/chemical potential, within Nambu--Jona-Lasinio type models. We perform a systematic study concerning the existence, location, and properties of a critical end point/tricritical point, both in SU(2) and SU(3) versions of the model. We verify that, for $m_u=m_d=0$ and up to a critical strange quark mass, there is a tricritical point, which becomes a critical end point in a world with realistic values of the current quark masses. The properties of physical observables, such as the baryon number susceptibility and the specific heat, are analyzed in the vicinity of the critical end point, with special focus on their critical exponents. The behavior of mesons in the $T-\mu_B(\rho_B)$ plane is analyzed in connection with possible signatures of partial and effective restoration of chiral symmetry., Comment: 29 pages, 8 figures; PRD version

The effects of a type of regularization for finite temperatures on the estoration of chiral and axial symmetries are investigated within the SU(3) Nambu-Jona-Lasinio model. The regularization consists in using an infinite cutoff in the integrals that are convergent at finite temperature, a procedure that allows one to take into account the effects of high momentum quarks at high temperatures. It is found that the critical temperature for the phase transition is closer to lattice results than the one obtained with the conventional regularization, and the restoration of chiral and axial symmetries, signaled by the behavior of several observables, occurs simultaneously and at a higher temperature. The restoration of the axial symmetry appears as a natural consequence of the full recovering of the chiral symmetry that was dynamically broken. By using an additional ansatz that simulates instanton suppression effects, by means of a convenient temperature dependence of the anomaly coefficient, we found that the restoration of U(2) symmetry is shifted to lower values, but the dominant effect at high temperatures comes from the new regularization that enhances the decrease of quark condensates, especially in the strange sector., Comment: 15 pages, 5 figures; PRD version

We study the chiral phase transition at finite $T$ and $\mu_B$ within the framework of the SU(3) Nambu-Jona-Lasinio (NJL) model. The QCD critical end point (CEP) and the critical line at finite temperature and baryonic chemical potential are investigated: the study of physical quantities, such as the baryon number susceptibility near the CEP, will provide complementary information concerning the order of the phase transition. We also analyze the information provided by the study of the critical exponents around the CEP., Comment: Talk given at the IVth International Conference on Quarks and Nuclear Physics (QNP06), Madrid, 5-10 June 2006

We study the chiral phase transition at finite temperature $T$ and baryonic chemical potential $\mu_B$ within the framework of the SU(3) Nambu-Jona-Lasinio (NJL) model. The QCD critical end point (CEP) and the critical line at finite $T$ and $\mu_B$ are investigated: the study of physical quantities, such as the baryon number susceptibility and the specific heat in the vicinity the CEP, will provide relevant information concerning the order of the phase transition. The class of the CEP is determined by calculating the critical exponents of those quantities., Comment: 10 pages, 4 figures; PLB version

We investigate the possible restoration of chiral and axial symmetries across the phase transition at finite temperature and chemical potential, by analyzing the behavior of several physics quantities, such as the quark condensates and the topological susceptibility, the respective derivatives in order to chemical potential, and the masses of meson chiral partners. We discuss whether only chiral symmetry or both chiral and axial symmetries are restored and what is the role of the strange quark. The results are compared with recent lattice results., Comment: Talk given at the IVth International Conference on Quarks and Nuclear Physics (QNP06), Madrid, 5-10 June 2006

We investigate the restoration of chiral SU$(3)\otimes$SU$(3)$ and axial U$_A$(1) symmetries, at finite temperature and density, in the framework of the three flavor Nambu-Jona-Lasinio model with anomaly. We implement a temperature (density) dependence of the anomaly coefficient motivated by lattice results for the topological susceptibility and we discuss the restoration of symmetries by analyzing the behavior of the mesonic chiral partners and of the mixing angles. The results indicate that the axial part of the symmetry is restored before the possible restoration of the full U(3)$\otimes$U(3) chiral symmetry can occur., Comment: 4 pages, 1 figure. Contribution to Proc. Int. Europhysics Conf. on High Energy Physics (HEP2005), 21-27.7.2005, Lisboa, Portugal

We explore patterns of effective restoration of the chiral U$_A$(1) symmetry using an extended three-flavor Nambu-Jona-Lasinio model that incorporates explicitly the axial anomaly through the 't Hooft interaction, and assuming that the coefficient of the anomaly term is temperature and density dependent. The special case of explicit breaking of chiral symmetry without U$_A$(1) anomaly is also considered, since this scenario can provide additional information allowing to understand the interplay between the U$_A$(1) anomaly and (spontaneous) chiral symmetry breaking effects. The pseudoscalar and scalar sectors are analyzed in detail bearing in mind the identification of chiral partners and the study of its convergence. We also concentrate on the behavior of the mixing angles that give us relevant information on the issue under discussion. In the region of temperatures (densities) studied, we do not observe signs indicating a full restoration of U(3)$\otimes$U(3) symmetry as, for instance, the degeneracy of both $a_0$ and $f_0$ mesons with the pion. As we work in a real world scenario ($m_u=m_d<

We explore the effects of breaking and restoration of chiral and axial symmetries using an extended three-flavor Nambu-Jona-Lasinio model that incorporates explicitly the axial anomaly through the 't Hooft interaction. We implement a temperature (density) dependence of the anomaly coefficient motivated by lattice results for the topological susceptibility. The spectrum of scalar and pseudoscalar mesons is analyzed bearing in mind the identification of chiral partners and the study of its convergence. We also concentrate on the behavior of the mixing angles that give us relevant information on the issue under discussion. The results suggest that the axial part of the symmetry is restored before the possible restoration of the full U(3)$\otimes$U(3) chiral symmetry might occur., Comment: 9 pages, 5 figures. Talk given at Joint Meeting Heidelberg-Liege-Paris-Rostock (HLPR 2004), Spa, Belgium, 16-18 Dec 2004

We investigate the full U(3)$\otimes$U(3) chiral symmetry restoration, at finite temperature and density, on the basis of the three flavor Nambu-Jona-Lasinio model with the anomaly term given by the 't Hooft interaction. We implement a temperature (density) dependence of the anomaly coefficient motivated by lattice results for the topological susceptibility. The results suggest that the axial part of the symmetry is restored before the possible restoration of the full U(3)$\otimes$U(3) chiral symmetry can occur., Comment: 3 pages, 1 figure. Talk given at 6th Conference on Quark Confinement and the Hadron Spectrum, Villasimius, Sardinia, Italy, 21-25 Sep 2004

We study phase transitions and the behavior of kaons in hot and dense matter, giving special attention to the role of strange quarks. At T=0, it is found that the fraction of the strange valence quarks affects the energy per particle of the system, without changing the nature of the phase transition, and, on the other side, it has meaningful effects on the behavior of kaons and antikaons masses. The phase behavior of kaons in the $T-\rho$ plane is analyzed in connection with the chiral phase transition., Comment: 3 pages, 1 figure. Talk given at 6th Conference on Quark Confinement and the Hadron Spectrum, Villasimius, Sardinia, Italy, 21-25 Sep 2004

The effective restoration of chiral and axial symmetries is investigated within the framework of the SU(3) Nambu-Jona-Lasinio model. The topological susceptibility, modeled from lattice data at finite temperature, is used to extract the temperature dependence of the coupling strength of the anomaly. The study of the scalar and pseudoscalar mixing angles is performed in order to discuss the evolution of the flavor combinations of $q \bar q$ pairs and its consequences for the degeneracy of chiral partners. A similar study at zero temperature and finite density is also realized., Comment: 5 pages, 1 figure. Talk given at Strange Quark Matter 2004, Cape Town, South Africa, 15-20 September, 2004

A comparative study of the anomalous decays $\pi^0, \eta \to\gamma\gamma$, at finite temperature and at finite density, is performed in the framework of the three--flavor Nambu--Jona-Lasinio. The similarities and differences between both scenarios are discussed. In both cases the lifetimes of these mesons decrease significantly at the critical point, although this might not be sufficient to observe enhancement of these decays in heavy-ion collisions., Comment: 5 pages, 1 figure. Talk given at Strange Quark Matter 2004, Cape Town, South Africa, 15-20 September, 2004

We investigate the full U(3)$\otimes$U(3) chiral symmetry restoration, at finite temperature and density, on the basis of a quark model which incorporates the most relevant properties of QCD in this context: explicit and spontaneous breaking of chiral symmetry and axial U$_A$(1) symmetry breaking. A specific lattice-inspired behavior of the topological susceptibility, combined with the convergence of chiral partners, signals the onset of an effective chiral symmetry restoration. The results suggest that the axial part of the symmetry is restored before the possible restoration of the full U(3)$\otimes$U(3) chiral symmetry can occur. This conclusion is valid in the context of both finite temperature and density., Comment: 5 pages, 2 figures; PRD version

We study the anomalous decays $\pi^0, \eta \to\gamma\gamma$ in the framework of the three--flavor Nambu--Jona-Lasinio [NJL] model at finite temperature. The similarities and differences between these results and those obtained at zero temperature and finite density are discussed. In both cases the lifetimes of these mesons decrease significantly at the critical point, although this might not be sufficient to observe enhancement of these decays in heavy-ion collisions., Comment: 4 pages, 4 figures, PRC version

The weak leptonic decays $\pi^\pm\to\mu^\pm\nu_{\mu}(\bar{\nu}_{\mu}), \pi^\pm\to e^\pm\nu_e(\bar{\nu}_{e}), K^\pm\to\mu^\pm\nu_{\mu}(\bar{\nu}_{\mu})$ and $K^\pm\to e^\pm \nu_e(\bar{\nu}_{e})$ are investigated within the framework of the SU(3) Nambu-Jona-Lasinio model, in the vacuum and in quark matter in $\beta$ equilibrium. It is found that, at low densities, the decay rates of the charge multiplets, that are decoupled in this kind of flavor asymmetric matter, are affected differently. As the density increases, these decay rates become closer and show a tendency to vanish. This shows that weak interactions are strongly influenced by the medium as a consequence of restoration of chiral symmetry., Comment: 10 pages, 3 figures, 1 table; submitted for publication

We study the anomalous decays $\pi^0, \eta \to\gamma\gamma$ in the framework of the three--flavor Nambu--Jona-Lasinio [NJL] model, in the vacuum and in quark matter in $\beta$ --equilibrium. It is found that the behavior of the relevant observables essentially reflects a manifestation of the partial restoration of chiral symmetry, in non strange and strange sectors. The probability of such decays decreases with density, showing that anomalous mesonic interactions are significantly affected by the medium., Comment: 12 pages, 4 figures included; revised version, to be published in Phys. Lett. B

The behavior of $\eta$ and $\eta'$ in hot strange quark matter in weak equilibrium with temperature, is investigated within the SU(3) Nambu-Jona-Lasinio [NJL] model. Possible manifestations of restoration of symmetries, by temperature or density, in the behavior of $\eta$ and $\eta'$ are discussed. The role played by the combined effect of temperature and density in the nature of the phase transition and meson behavior is also analyzed., Comment: 15 pages, 5 figures. Contribution to the Second International Workshop on Hadron Physics, Effective Theories of Low Energy QCD, 25-29 September, 2002 (Coimbra, Portugal)

Phase transitions in hot and dense matter and the in--medium behavior of pseudoscalar mesons ($\pi^{\pm}, \pi^0, K^{\pm}, K^0 ,\bar K^0,\eta {and} \eta' $) are investigated, in the framework of the three flavor Nambu--Jona-Lasinio model, including the 't Hooft interaction, which breaks the $U_A(1)$ symmetry. Three different scenarios are considered: zero density and finite temperature, zero temperature and finite density in quark matter with different degrees of strangeness, and finite temperature and density. At T=0, the role of strange valence quarks in the medium is discussed, in connection with the phase transition and the mesonic behavior. It is found that the appearance of strange quarks, above certain densities, leads to meaningful changes in different observables, especially in matter with \beta$ --equilibrium. The behavior of mesons in the $T-\rho$ plane is analyzed in connection with possible signatures of restoration of symmetries., Comment: 33 pages, 12 figures, PRC version

The behavior of neutral pseudoscalar mesons $\pi^0, \eta$ and $\eta'$ in hot and dense matter is investigated, in the framework of the three flavor Nambu-Jona-Lasinio model. Three different scenarios are considered: zero density and finite temperature, zero temperature and finite density in a flavor asymmetric medium with and without strange valence quarks, and finite temperature and density. The behavior of mesons is analyzed in connection with possible signatures of restoration of symmetries. In the high density region and at zero temperature it is found that the mass of the $\eta'$ increases, the deviation from the mass of the $\eta$ being more pronounced in matter without strange valence quarks., Comment: 10 pages, 4 figures included; revised version with one additional figure, some changes in the discussion, to be published in Phys. Lett. B

The behavior of kaons and pions in strange quark matter in weak equilibrium, is investigated within the SU(3) Nambu-Jona-Lasinio [NJL] model. This work focuses a region of high densities where the behavior of mesons has not been explored in the framework of this model. It is found that above the density where strange valence quarks appear in the medium, $\rho = 3.8 \rho_0$, a change of behavior of different observables is observed indicating a tendency to the restoration of flavor symmetry. In particular, the splitting between charge multiplets, $K^+, K^-; K^0, {\bar K^0} {and} \pi^+, \pi^-$ decrease and the low energy modes with quantum numbers of $K^-, \bar K^0 {and} \pi^+$, which are excitations of the Fermi sea, are less relevant than for lower densities., Comment: 10 pages, 3 figures included; revised version, some changes in the discussion

The behavior of kaons and pions in hot non strange quark matter, simulating neutron matter, is investigated within the SU(3) Nambu-Jona-Lasinio [NJL] and in the Enlarged Nambu-Jona-Lasinio [ENJL] (including vector pseudo-vector interaction) models. At zero temperature, it is found that in the NJL model, where the phase transition is first order, low energy modes with K-, Pi+ quantum numbers, which are particle-hole excitations of the Fermi sea, appear. Such modes are not found in the ENJL model and in NJL at finite temperatures. The increasing temperature has also the effect of reducing the splitting between the charge multiplets., Comment: 10 pages, 4 figures. Published in the Proc. of the workshop 'Quark Matter in Astro- and Particle Physics', Rostock, November 2000

We investigate strong and radiative meson decays in a generalized Nambu--Jona-Lasinio model. The one loop order calculation provides a satisfactory agreement with the data for the mesonic spectrum and for radiative decays. Higher order effects for strong decays of $\rho$ and $K^*$ are estimated to be large. We also discuss the role of the flavour mixing determinantal interaction., Comment: 7 pages, LaTeX, 2 figs available upon request, CRN 92-49