On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30

Critical Exponents of Semilinear Equations via the Feynman-Kac Formula

2000 Mathematics Subject Classification: 60H30, 35K55, 35K57, 35B35.

Universal critical behavior of the two-dimensional Ising spin glass

We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy.

Nonequilibrium critical scaling from quantum thermodynamics

The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work produced in a quench exhibits finite-size scaling at quantum criticality. This scaling faithfully predicts the equilibrium critical exponents for the crossover length and the order parameter of the model, and, moreover, implies a new exponent for the rescaled irreversible work. By connecting the irreversible work to the two-impurity spin correlation function, our findings can be tested experimentally.

Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Critical behavior in the site-diluted three-dimensional three-state Potts model

We have studied numerically the effect of quenched site dilution on a weak first-order phase transition in three dimensions. We have simulated the site diluted three-states Potts model studying in detail the secondorder region of its phase diagram. We have found that the n exponent is compatible with the one of the three-dimensional diluted Ising model, whereas the h exponent is definitely different.

Molecular Variations In Aromatic Cosolutes: Critical Role In The Rheology Of Cationic Wormlike Micelles.

Wormlike micelles formed by the addition to cetyltrimethylammonium bromide (CTAB) of a range of aromatic cosolutes with small molecular variations in their structure were systematically studied. Phenol and derivatives of benzoate and cinnamate were used, and the resulting mixtures were studied by oscillatory, steady-shear rheology, and the microstructure was probed by small-angle neutron scattering. The lengthening of the micelles and their entanglement result in remarkable viscoelastic properties, making rheology a useful tool to assess the effect of structural variations of the cosolutes on wormlike micelle formation. For a fixed concentration of CTAB and cosolute (200 mmol L(-1)), the relaxation time decreases in the following order: phenol > cinnamate> o-hydroxycinnamate > salicylate > o-methoxycinnamate > benzoate > o-methoxybenzoate. The variations in viscoelastic response are rationalized by using Mulliken population analysis to map out the electronic density of the cosolutes and quantify the barrier to rotation of specific groups on the aromatics. We find that the ability of the group attached to the aromatic ring to rotate is crucial in determining the packing of the cosolute at the micellar interface and thus critically impacts the micellar growth and, in turn, the rheological response. These results enable us for the first time to propose design rules for the self-assembly of the surfactants and cosolutes resulting in the formation of wormlike micelles with the cationic surfactant CTAB.

[recommendations For Physical Exercise Practice During Pregnancy: A Critical Review].

Physical exercise is recommended for all healthy pregnant women. Regular practice of exercises during pregnancy can provide many physical and psychological benefits, with no evidence of adverse outcomes for the fetus or the newborn when exercise is performed at mild to moderate intensity. However, few pregnant women engage in this practice and many still have fears and doubts about the safety of exercise. The objective of the present study was to inform the professionals who provide care for Brazilian pregnant women about the current recommendations regarding physical exercise during pregnancy based on the best scientific evidence available. In view of the perception that few systematic models are available about this topic and after performing several studies in this specific area, we assembled practical information of interest to both the professionals and the pregnant women. We also provide recommendations about the indications, contraindications, modalities (aerobics, resistance training, stretching and pelvic floor training), frequency, intensity and duration indicated for each gestational trimester. The review addresses physical exercise recommendation both for low risk pregnant women and for special populations, such as athletes and obese, hypertensive and diabetic subjects. The advantages of an active and healthy lifestyle should be always reinforced during and after gestation since pregnancy is an appropriate period to introduce new habits because pregnant women are usually more motivated to adhere to recommendations. Thus, routine exams, frequent returns and supervision are recommended in order to provide new guidelines that will have long-term beneficial effects for both mother and child.

Chronicity Factors Of Temporomandibular Disorders: A Critical Review Of The Literature.

Facial pain often persists long after any identifiable organic pathology has healed. Moreover, in a subgroup of patients with temporomandibular disorder (TMD), no treatment is effective. Knowledge of factors associated with persistent pain in TMD could help identify personalized treatment approaches. Therefore, we conducted a critical review of the literature for the period from January 2000 to December 2013 to identify factors related to TMD development and persistence. The literature findings showed that chronic TMD is marked by psychological distress (somatization and depression, affective distress, fear of pain, fear of movement, and catastrophizing) and characteristics of pain amplification (hyperalgesia and allodynia). Furthermore, these factors seem to interact in TMD development. In addition, our review demonstrates that upregulation of the serotonergic pathway, sleep problems, and gene polymorphisms influence the chronicity of TMD. We conclude that psychological distress and pain amplification contribute to chronic TMD development, and that interactions among these factors complicate pain management. These findings emphasize the importance of multidisciplinary assistance in TMD treatment.

Repair of critical-size defects with autogenous periosteum-derived cells combined with bovine anorganic apatite/collagen: an experimental study in rat calvaria

The aim of this study was to evaluate the bone repair using autogenous periosteum-derived cells (PDC) and bovine anorganic apatite and collagen (HA-COL). PDC from Wistar rats (n=10) were seeded on HA-COL discs and subjected to osteoinduction during 6 days. Critical-size defects in rat calvarias were treated with blood clot (G1), autogenous bone (G2), HA-COL (G3) and HA-COL combined with PDC (G4) (n=40), and then analyzed 1 and 3 months after surgeries. Radiographic analysis exhibited no significant temporal change. G1 and G2 had discrete new marginal bone, but the radiopacity of graft materials in G2, G3 and G4 impaired the detection of osteogenesis. At 3 months, histopathological analysis showed the presence of ossification islets in G1, which was more evident in G2, homogeneous new bone around HA-COL in G3 and heterogeneous new bone around HA-COL in G4 in addition to moderate presence of foreign body cells in G3 and G4. Histomorphometric analysis showed no change in the volume density of xenograft (p>0.05) and bone volume density in G2 was twice greater than in G1 and G4 after 3 months (p<0.05), but similar to G3. The PDC did not increase bone formation in vivo, although the biomaterial alone showed biocompatibility and osteoconduction capacity.

Critical applications of SW 846 US EPA methods to evaluation of marine samples quality

Technical evaluation of analytical data is of extreme relevance considering it can be used for comparisons with environmental quality standards and decision-making as related to the management of disposal of dredged sediments and the evaluation of salt and brackish water quality in accordance with CONAMA 357/05 Resolution. It is, therefore, essential that the project manager discusses the environmental agency's technical requirements with the laboratory contracted for the follow-up of the analysis underway and even with a view to possible re-analysis when anomalous data are identified. The main technical requirements are: (1) method quantitation limits (QLs) should fall below environmental standards; (2) analyses should be carried out in laboratories whose analytical scope is accredited by the National Institute of Metrology (INMETRO) or qualified or accepted by a licensing agency; (3) chain of custody should be provided in order to ensure sample traceability; (4) control charts should be provided to prove method performance; (5) certified reference material analysis or, if that is not available, matrix spike analysis, should be undertaken and (6) chromatograms should be included in the analytical report. Within this context and with a view to helping environmental managers in analytical report evaluation, this work has as objectives the discussion of the limitations of the application of SW 846 US EPA methods to marine samples, the consequences of having data based on method detection limits (MDL) and not sample quantitation limits (SQL), and present possible modifications of the principal method applied by laboratories in order to comply with environmental quality standards.

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

Dependence of the crossover exponent with the diffusion rate in the generalized contact process model

We study how the crossover exponent, phi, between the directed percolation (DP) and compact directed percolation (CDP) behaves as a function of the diffusion rate in a model that generalizes the contact process. Our conclusions are based in results pointed by perturbative series expansions and numerical simulations, and are consistent with a value phi = 2 for finite diffusion rates and phi = 1 in the limit of infinite diffusion rate.

Microbiological indicators for the assessment of performance in the hazard analysis and critical control points (HACCP) system in meat lasagna production

The HACCP system is being increasingly used to ensure food safety. This study investigated the validation of the control measures technique in order to establish performance indicators of this HACCP system in the manufacturing process of Lasagna Bolognese (meat lasagna). Samples were collected along the manufacturing process as a whole, before and after the CCPs. The following microorganism s indicator (MIs) was assessed: total mesophile and faecal coliform counts. The same MIs were analyzed in the final product, as well as, the microbiological standards required by the current legislation. A significant reduction in the total mesophile count was observed after cooking (p < 0.001). After storage, there was a numerical, however non-significant change in the MI count. Faecal coliform counts were also significantly reduced (p < 0.001) after cooking. We were able to demonstrate that the HACCP system allowed us to meet the standards set by both, the company and the Brazilian regulations, proved by the reduction in the established indicators