On a total function which overtakes all total recursive functions

This paper discusses a function that is frequently presented as a simile or look-alike of the so-called ``counterexample function to P=NP,'' that is, the function that collects all first instances of a problem in NP where a poly machine incorrectly `guesses' about the instance. We state and give in full detail a crucial result on the computation of Goedel numbers for some families of poly machines.Comment: LaTe

A lemma on a total function defined over the Baker-Gill-Solovay set of polynomial Turing machines

If we establish that the counterexample function for P=NP, if total, overtakes all total recursive functions when extended over all Turing machines, then what happens to the same counterexample function when defined over the so-called Baker-Gill-Solovay (BGS) set of poly machines? We state and prove here a lemma that tries to answer this query.Comment: LaTe

On the existence of certain total recursive functions in nontrivial axiom systems, I

We investigate the existence of a class of ZFC-provably total recursive unary functions, given certain constraints, and apply some of those results to show that, for $\Sigma_1$-sound set theory, ZFC$\not\vdash P<NP$.Comment: LaTeX, 16 pages, no figures. This paper was submitted to a major journal in the field and rejected. The referee somehow misundesrtood Corollary 3.8 and wrongly concluded that the proof had either a gap or an error. Can you find whether that error exists

On the consistency of P=NPP=NP with fragments of ZFC whose own consistency strength can be measured by an ordinal assignment

We formulate the $P<NP$ hypothesis in the case of the satisfiability problem as a $\Pi ^0_2$ sentence, out of which we can construct a partial recursive function $f_{\neg A}$ so that $f_{\neg A}$ is total if and only if $P < NP$. We then show that if $f_{\neg A}$ is total, then it isn't ${\cal T}$--provably total (where ${\cal T}$ is a fragment of ZFC that adequately extends PA and whose consistency is of ordinal order). Follows that the negation of $P < NP$, that is, $P = NP$, is consistent with those ${\cal T}$.Comment: LaTeX, 19 pages, no figure

Effects of entanglement and instanton suppression at finite temperature in a SU(2) EPNJL model with anomaly

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 versio

Quantification of Einstein-Podolski-Rosen steering for two-qubit states

In the last few years, several criteria to identify Eistein-Podolski-Rosen steering have been proposed and experimentally implemented. On the operational side, however, the evaluation of the steerability degree of a given state has shown to be a difficult task and only a few results are known. In this work, we propose a measure of steering that is based on the maximal violation of well established steering inequalities. Applying this approach to two-qubit states, we managed to derive simple closed formulas for steering in the two- and three-measurement scenarios. Among the options investigated, a measure has been found that correctly satisfies the entanglement-steering-nonlocality hierarchy and reproduces results reported so far.Comment: 5 pages, published versio

Pseudoscalar Mesons in Asymmetric Matter

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 200

Restoration of axial symmetry and its possible relation with restoration of chiral symmetry and deconfinement at finite temperature

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 201

Thermodynamics and critical behavior in the Nambu-Jona-Lasinio model of QCD

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 versio

Migrations, vaccinations and epidemic control

We consider three regions with different public health conditions. In the absence of migration among these regions, the first two have good health conditions and the disease free state is stable; for the third region, on the other hand, the only stable state is the endemic one. When migration is included in the model, we assume that the second region has a disease risk that makes its inhabitants prone to accept to be vaccinated, while the population in the first region tends to reject the vaccination, considered riskier that the disease. Therefore, the second region is a "buffer zone" between the two extremal regions. We study the basic reproductive ratio as a function of the vaccination in all regions and migration among them. This problem is studied numerically, showing explicit situations in which migration will have an overall positive effect in the disease dynamics, with and without vaccinations. We also find explicit formula in the limit of small ("closed borders") and high migration ("open borders").Comment: 11 pages, 5 figure