A general fractional porous medium equation

A general fractional porous medium equation

Inter-operator reliability of live football match statistics from OPTA Sportsdata

The aim of the study was to evaluate the inter-operator reliability of OPTA Client System which is used to collect live football match statistics by OPTA Sportsdata Company. Two groups of experienced operators were required to analyze a Spanish league match independently. Results showed that team events coded by independent operators reached a very good agreement (kappa values were 0.92 and 0.94) and average difference of event time was 0.06±0.04 s. The reliability of goalkeeper actions was also at high level, kappa values were 0.92 and 0.86. The high intra-class correlation coefficients (ranged from 0.88 to 1.00) and low standardized typical errors (varied from 0.00 to 0.37) of different match actions and indicators of individual outfield players showed a high level of inter-operator reliability as well. These results suggest that the OPTA Client System is reliable to be used to collect live football match statistics by well trained operators.

Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

Classical solutions for a logarithmic fractional diffusion equation

We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion ?tu + (?)1/2 log(1 + u) = 0, posed for x ? R, with nonnegative initial data in some function space of LlogL type. The solutions are shown to become bounded and C? smooth in (x, t) for all positive times. We also reformulate this equation as a transport equation with nonlocal velocity and critical viscosity, a topic of current relevance. Interesting functional inequalities are involved.

Multiple Robots, Single Operator: Considerations About Information And Commanding

Multiple robot, single operator scenarios suppose a challenge in terms of human factors. Two relevant issues are keeping the situational awareness and managing the workload of operators. In order to address these problems, this work analyses the management of information and commands in multi-robot missions. About the information, this paper proposes a selection based on mission and operator states. Regarding the commands, this work reflects about the levels of automation and the methods of commanding.

Orientation in operator algebras

A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics.

Contributions of distinct quaternary contacts to cooperative operator binding by Mnt repressor

Mnt, a tetrameric repressor encoded by bacteriophage P22, uses N-domain dimers to contact each half of its operator site. Experiments with a double mutant and structural homology with the P22 Arc repressor suggest that contacts made by Arg-28 and stabilized by Glu-33 are largely responsible for dimer–dimer cooperativity in Mnt. These dimer–dimer contacts are energetically more important for operator binding than solution tetramerization, which is mediated by an independent C-terminal coiled-coil domain. Indeed, once one dimer of the Mnt tetramer contacts an operator half site, binding of the second dimer occurs with an effective concentration much lower than that expected if both dimers were flexibly tethered. These results suggest that binding of the second dimer introduces some strain into the protein–DNA complex, a mechanism that could serve to limit the affinity of operator binding and to prevent strong binding of the Mnt tetramer to nonoperator sites.

The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

On the coefficients of the characteristic series of the U-operator

A conceptual proof is given of the fact that the coefficients of the characteristic series of the U-operator acting on families of overconvegent modular forms lie in the Iwasawa algebra.

Microsatellite instability in childhood rhabdomyosarcoma is locus specific and correlates with fractional allelic loss.

Replication errors (RERs) were initially identified in hereditary nonpolyposis colon cancer and other tumors of Lynch syndrome II. Mutations in genes involved in mismatch repair give rise to a mutator phenotype, resulting in RERs. The mutator phenotype is thought to predispose to malignant transformation. Here we show that in the embryonal form of childhood rhabdomyosarcoma, RERs also occur, but in contrast to hereditary nonpolyposis colon cancer, only a subset of the microsatellite loci analyzed show RERs. The occurrence of RERs is strongly correlated with increased fractional allelic loss (P < 0.001), suggesting that the occurrence of RERs is a secondary phenomenon in rhabdomyosarcoma. Coincidental loss of genes involved in mismatch repair, possibly due to their proximity to tumor suppressor genes involved in tumor progression of embryonal form of childhood rhabdomyosarcoma, could explain the observed phenomenon.

Operator binding by lambda repressor heterodimers with one or two N-terminal arms.

The first 6 amino acids (NH2-Ser1-Thr2-Lys3-Lys4-Lys5-Pro6) of bacteriophage lambda cI repressor form a flexible arm that wraps around the operator DNA. Homodimeric lambda repressor has two arms. To determine whether both arms are necessary or only one arm is sufficient for operator binding, we constructed heterodimeric repressors with two, one, or no arms by fusing the DNA binding domain of lambda repressor to leucine zippers from Fos and Jun. Although only one arm is visible in the cocrystal structure of the N-domain-operator complex, our results indicate that both arms are required for optimal operator binding and normal site discrimination.

Binding of purified multiple antibiotic-resistance repressor protein (MarR) to mar operator sequences.

Elevated expression of the marORAB multiple antibiotic-resistance operon enhances the resistance of Escherichia coli to various medically significant antibiotics. Transcription of the operon is repressed in vivo by the marR-encoded protein, MarR, and derepressed by salicylate and certain antibiotics. The possibility that repression results from MarR interacting with the marO operator-promoter region was studied in vitro using purified MarR and a DNA fragment containing marO. MarR formed at least two complexes with marO DNA, bound > 30-fold more tightly to it than to salmon sperm DNA, and protected two separate 21-bp sites within marO from digestion by DNase I. Site I abuts the downstream side of the putative -35 transcription-start signal and includes 4 bp of the -10 signal. Site II begins 13 bp downstream of site I, ending immediately before the first base pair of marR. Site II, approximately 80% homologous to site I, is not required for repression since a site II-deleted mutant (marO133) was repressed in trans by wild-type MarR. The absence of site II did not prevent MarR from complexing with the site I of marO133. Salicylate bound to MarR (Kd approximately 0.5 mM) and weakened the interaction of MarR with sites I and II. Thus, repression of the mar operon, which curbs the antibiotic resistance of E. coli, correlates with the formation of MarR-site I complexes. Salicylate appears to induce the mar operon by binding to MarR and inhibiting complex formation, whereas tetracycline and chloramphenicol, which neither bind MarR nor inhibit complex formation, must induce by an indirect mechanism.

Estimating and forecasting generalized fractional Long memory stochastic volatility models

In recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the statistical properties of the new model, suggest using the spectral likelihood estimation for long memory processes, and investigate the finite sample properties via Monte Carlo experiments. We apply the model to three exchange rate return series. Overall, the results of the out-of-sample forecasts show the adequacy of the new GLMSV model.

Absence of magnetically induced fractional quantization in atomic contacts

Using the mechanically controlled break junction technique at low temperatures and under cryogenic vacuum conditions we have studied atomic contacts of several magnetic (Fe, Co, and Ni) and nonmagnetic (Pt) metals, which recently were claimed to show fractional conductance quantization. In the case of pure metals we see no quantization of the conductance nor half quantization, even when high magnetic fields are applied. On the other hand, features in the conductance similar to (fractional) quantization are observed when the contact is exposed to gas molecules. Furthermore, the absence of fractional quantization when the contact is bridged by H2 indicates the current is never fully polarized for the metals studied here. Our results are in agreement with recent model calculations.

Local probe of fractional edge states of S=1 Heisenberg spin chains

Spin chains are among the simplest physical systems in which electron-electron interactions induce novel states of matter. Here we propose to combine atomic scale engineering and spectroscopic capabilities of state of the art scanning tunnel microscopy to probe the fractionalized edge states of individual atomic scale S=1 spin chains. These edge states arise from the topological order of the ground state in the Haldane phase. We also show that the Haldane gap and the spin-spin correlation length can be measured with the same technique.