Explicit solutions for effective four- and five-loop QCD running coupling

We start with the explicit solution, in terms of the Lambert W function, of the renormalization group equation (RGE) for the gauge coupling in the supersymmetric Yang-Mills theory described by the well-known beta function of Novikov et al.(NSVZ). We then construct a class of beta functions for which the RGE can be solved in terms of the Lambert W function. These beta functions are expressed in terms of a function which is a truncated Laurent series in the inverse of the gauge coupling. The parameters in the Laurent series can be adjusted so that the first coefficients of the Taylor expansion of the beta function in the gauge coupling reproduce the four-loop or five-loop QCD (or SQCD) beta function.Comment: 21 pages, 13 figures; in v2, minor changes in the text, two figures added, ref.[3] (2nd entry) is new; version to appear in JHE

Quasi-normal frequencies: Key analytic results

The study of exact quasi-normal modes [QNMs], and their associated quasi-normal frequencies [QNFs], has had a long and convoluted history - replete with many rediscoveries of previously known results. In this article we shall collect and survey a number of known analytic results, and develop several new analytic results - specifically we shall provide several new QNF results and estimates, in a form amenable for comparison with the extant literature. Apart from their intrinsic interest, these exact and approximate results serve as a backdrop and a consistency check on ongoing efforts to find general model-independent estimates for QNFs, and general model-independent bounds on transmission probabilities. Our calculations also provide yet another physics application of the Lambert W function. These ideas have relevance to fields as diverse as black hole physics, (where they are related to the damped oscillations of astrophysical black holes, to greybody factors for the Hawking radiation, and to more speculative state-counting models for the Bekenstein entropy), to quantum field theory (where they are related to Casimir energies in unbounded systems), through to condensed matter physics, (where one may literally be interested in an electron tunelling through a physical barrier).Comment: V1: 29 pages; V2: Reformatted, 31 pages. Title changed to reflect major additions and revisions. Now describes exact QNFs for the double-delta potential in terms of the Lambert W function. V3: Minor edits for clarity. Four references added. No physics changes. Still 31 page

Is the outer Solar System chaotic?

The existence of chaos in the system of Jovian planets has been in question for the past 15 years. Various investigators have found Lyapunov times ranging from about 5 millions years upwards to infinity, with no clear reason for the discrepancy. In this paper, we resolve the issue. The position of the outer planets is known to only a few parts in 10 million. We show that, within that observational uncertainty, there exist Lyapunov timescales in the full range listed above. Thus, the ``true'' Lyapunov timescale of the outer Solar System cannot be resolved using current observations.Comment: 8 pages, 2 figure

Power allocation strategies for distributed precoded multicell based systems

Multicell cooperation is a promising solution for cellular wireless systems to mitigate intercell interference, improve system fairness, and increase capacity. In this article, we propose power allocation techniques for the downlink of distributed, precoded, multicell cellular-based systems. The precoder is designed in two phases: first the intercell interference is removed by applying a set of distributed precoding vectors; then the system is further optimized through power allocation. Three centralized power allocation algorithms with per-BS power constraint and diferente complexity trade-offs are proposed: one optimal in terms of minimization of the instantaneous average bit error rate (BER), and two suboptimal. In this latter approach, the powers are computed in two phases. First, the powers are derived under total power constraint (TPC) and two criterions are considered, namely, minimization of the instantaneous average BER and minimization of the sum of inverse of signal-to-noise ratio. Then, the final powers are computed to satisfy the individual per-BS power constraint. The performance of the proposed schemes is evaluated, considering typical pedestrian scenarios based on LTE specifications. The numerical results show that the proposed suboptimal schemes achieve a performance very close to the optimal but with lower computational complexity. Moreover, the performance of the proposed per-BS precoding schemes is close to the one obtained considering TPC over a supercell.Portuguese CADWIN - PTDC/ EEA TEL/099241/200

On the stability of the exact solutions of the dual-phase lagging model of heat conduction

The dual-phase lagging (DPL) model has been considered as one of the most promising theoretical approaches to generalize the classical Fourier law for heat conduction involving short time and space scales. Its applicability, potential, equivalences, and possible drawbacks have been discussed in the current literature. In this study, the implications of solving the exact DPL model of heat conduction in a three-dimensional bounded domain solution are explored. Based on the principle of causality, it is shown that the temperature gradient must be always the cause and the heat flux must be the effect in the process of heat transfer under the dual-phase model. This fact establishes explicitly that the single- and DPL models with different physical origins are mathematically equivalent. In addition, taking into account the properties of the Lambert W function and by requiring that the temperature remains stable, in such a way that it does not go to infinity when the time increases, it is shown that the DPL model in its exact form cannot provide a general description of the heat conduction phenomena

Counting the number of τ-exceptional sequences over Nakayama algebras

The notion of a τ-exceptional sequence was introduced by Buan and Marsh in (2018) as a generalisation of an exceptional sequence for finite dimensional algebras. We calculate the number of complete τ-exceptional sequences over certain classes of Nakayama algebras. In some cases, we obtain closed formulas which also count other well known combinatorial objects, and exceptional sequences of path algebras of Dynkin quivers

Positional Information Generated by Spatially Distributed Signaling Cascades

The temporal and stationary behavior of protein modification cascades has been extensively studied, yet little is known about the spatial aspects of signal propagation. We have previously shown that the spatial separation of opposing enzymes, such as a kinase and a phosphatase, creates signaling activity gradients. Here we show under what conditions signals stall in the space or robustly propagate through spatially distributed signaling cascades. Robust signal propagation results in activity gradients with long plateaus, which abruptly decay at successive spatial locations. We derive an approximate analytical solution that relates the maximal amplitude and propagation length of each activation profile with the cascade level, protein diffusivity, and the ratio of the opposing enzyme activities. The control of the spatial signal propagation appears to be very different from the control of transient temporal responses for spatially homogenous cascades. For spatially distributed cascades where activating and deactivating enzymes operate far from saturation, the ratio of the opposing enzyme activities is shown to be a key parameter controlling signal propagation. The signaling gradients characteristic for robust signal propagation exemplify a pattern formation mechanism that generates precise spatial guidance for multiple cellular processes and conveys information about the cell size to the nucleus

An Efficient Strategy for Broad-Range Detection of Low Abundance Bacteria without DNA Decontamination of PCR Reagents

BACKGROUND: Bacterial DNA contamination in PCR reagents has been a long standing problem that hampers the adoption of broad-range PCR in clinical and applied microbiology, particularly in detection of low abundance bacteria. Although several DNA decontamination protocols have been reported, they all suffer from compromised PCR efficiency or detection limits. To date, no satisfactory solution has been found. METHODOLOGY/PRINCIPAL FINDINGS: We herein describe a method that solves this long standing problem by employing a broad-range primer extension-PCR (PE-PCR) strategy that obviates the need for DNA decontamination. In this method, we first devise a fusion probe having a 3'-end complementary to the template bacterial sequence and a 5'-end non-bacterial tag sequence. We then hybridize the probes to template DNA, carry out primer extension and remove the excess probes using an optimized enzyme mix of Klenow DNA polymerase and exonuclease I. This strategy allows the templates to be distinguished from the PCR reagent contaminants and selectively amplified by PCR. To prove the concept, we spiked the PCR reagents with Staphylococcus aureus genomic DNA and applied PE-PCR to amplify template bacterial DNA. The spiking DNA neither interfered with template DNA amplification nor caused false positive of the reaction. Broad-range PE-PCR amplification of the 16S rRNA gene was also validated and minute quantities of template DNA (10-100 fg) were detectable without false positives. When adapting to real-time and high-resolution melting (HRM) analytical platforms, the unique melting profiles for the PE-PCR product can be used as the molecular fingerprints to further identify individual bacterial species. CONCLUSIONS/SIGNIFICANCE: Broad-range PE-PCR is simple, efficient, and completely obviates the need to decontaminate PCR reagents. When coupling with real-time and HRM analyses, it offers a new avenue for bacterial species identification with a limited source of bacterial DNA, making it suitable for use in clinical and applied microbiology laboratories