On exact time-averages of a massive Poisson particle

In this work we study, under the Stratonovich definition, the problem of the damped oscillatory massive particle subject to a heterogeneous Poisson noise characterised by a rate of events, \lambda (t), and a magnitude, \Phi, following an exponential distribution. We tackle the problem by performing exact time-averages over the noise in a similar way to previous works analysing the problem of the Brownian particle. From this procedure we obtain the long-term equilibrium distributions of position and velocity as well as analytical asymptotic expressions for the injection and dissipation of energy terms. Considerations on the emergence of stochastic resonance in this type of system are also set forth.Comment: 21 pages, 5 figures. To be published in Journal of Statistical Mechanics: Theory and Experimen

Higgs Boson Sector of the Next-to-MSSM with CP Violation

We perform a comprehensive study of the Higgs sector in the framework of the next-to-minimal supersymmetric standard model with CP-violating parameters in the superpotential and in the soft-supersymmetry-breaking sector. Since the CP is no longer a good symmetry, the two CP-odd and the three CP-even Higgs bosons of the next-to-minimal supersymmetric standard model in the CP-conserving limit will mix. We show explicitly how the mass spectrum and couplings to gauge bosons of the various Higgs bosons change when the CP-violating phases take on nonzero values. We include full one-loop and the logarithmically enhanced two-loop effects employing the renormalization-group (RG) improved approach. In addition, the LEP limits, the global minimum condition, and the positivity of the square of the Higgs-boson mass have been imposed. We demonstrate the effects on the Higgs-mass spectrum and the couplings to gauge bosons with and without the RG-improved corrections. Substantial modifications to the allowed parameter space happen because of the changes to the Higgs-boson spectrum and their couplings with the RG-improved corrections. Finally, we calculate the mass spectrum and couplings of the few selected scenarios and compare to the previous results in literature where possible; in particular, we illustrate a scenario motivated by electroweak baryogenesis.Comment: 40 pages, 49 figures; v2: typos corrected and references added; v3: some clarification and new figures added, version published in PR

Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci

A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models. A multivariate form of the reduction principle is found: reduction results at individual loci combine topologically to produce a surface of mutation rate alterations that are neutral for a new modifier allele. New mutation rates survive if and only if they fall below this surface - a generalization of the hyperplane found by Zhivotovsky et al. (1994) for a multilocus recombination modifier. Increases in mutation rates at some loci may evolve if compensated for by decreases at other loci. The strength of selection on the modifier scales in proportion to the number of germline cell divisions, and increases with the number of loci affected. Loci that do not make a difference to marginal fitnesses at equilibrium are not subject to the reduction principle, and under fine tuning of mutation rates would be expected to have higher mutation rates than loci in mutation-selection balance. Other results include the nonexistence of 'viability analogous, Hardy-Weinberg' modifier polymorphisms under multiplicative mutation, and the sufficiency of average transmission rates to encapsulate the effect of modifier polymorphisms on the transmission of loci under selection. A conjecture is offered regarding situations, like recombination in the presence of mutation, that exhibit departures from the reduction principle. Constraints for tractability are: tight linkage of all loci, initial fixation at the modifier locus, and mutation distributions comprising transition probabilities of reversible Markov chains.Comment: v3: Final corrections. v2: Revised title, reworked and expanded introductory and discussion sections, added corollaries, new results on modifier polymorphisms, minor corrections. 49 pages, 64 reference

Infectious Default Model with Recovery and Continuous Limit

We introduce an infectious default and recovery model for N obligors. Obligors are assumed to be exchangeable and their states are described by N Bernoulli random variables S_{i} (i=1,...,N). They are expressed by multiplying independent Bernoulli variables X_{i},Y_{ij},Y'_{ij}, and default and recovery infections are described by Y_{ij} and Y'_{ij}. We obtain the default probability function P(k) for k defaults. Taking its continuous limit, we find two nontrivial probability distributions with the reflection symmetry of S_{i} \leftrightarrow 1-S_{i}. Their profiles are singular and oscillating and we understand it theoretically. We also compare P(k) with an implied default distribution function inferred from the quotes of iTraxx-CJ. In order to explain the behavior of the implied distribution, the recovery effect may be necessary.Comment: 13 pages, 7 figure

Gaussian queues in light and heavy traffic

In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. The setting considered is that of a centered Gaussian process $X\equiv\{X(t):t\in\mathbb R\}$ with stationary increments and variance function $\sigma^2_X(\cdot)$, equipped with a deterministic drift $c>0$, reflected at 0: $$Q_X^{(c)}(t)=\sup_{-\infty<s\le t}(X(t)-X(s)-c(t-s)).$$ We study the resulting stationary workload process $Q^{(c)}_X\equiv\{Q_X^{(c)}(t):t\ge0\}$ in the limiting regimes $c\to 0$ (heavy traffic) and $c\to\infty$ (light traffic). The primary contribution is that we show for both limiting regimes that, under mild regularity conditions on the variance function, there exists a normalizing function $\delta(c)$ such that $Q^{(c)}_X(\delta(c)\cdot)/\sigma_X(\delta(c))$ converges to a non-trivial limit in $C[0,\infty)$

On-the-fly Uniformization of Time-Inhomogeneous Infinite Markov Population Models

This paper presents an on-the-fly uniformization technique for the analysis of time-inhomogeneous Markov population models. This technique is applicable to models with infinite state spaces and unbounded rates, which are, for instance, encountered in the realm of biochemical reaction networks. To deal with the infinite state space, we dynamically maintain a finite subset of the states where most of the probability mass is located. This approach yields an underapproximation of the original, infinite system. We present experimental results to show the applicability of our technique

Hadronic production of light color-triplet Higgs bosons: an alternative signature for GUT

The conventional signature for grand unified theories (GUT) is the proton decay. Recently, some models in extra dimensions or with specific discrete symmetries, which aim at solving the doublet-triplet problem, allow the color-triplet in the TeV mass region by suppressing the Yukawa couplings of the triplets to matter fermions. We study the hadronic production and detection of these TeV colored Higgs bosons as an alternative signature for GUT, which would behave like massive stable charged particles in particle detectors producing a striking signature of a charged track in the central tracking system and being ionized in the outer muon chamber. We found that the LHC is sensitive to a colored Higgs boson up to about 1.5 TeV. If the color-triplets are stable in cosmological time scale, they may constitute an interesting fraction of the dark matter.Comment: We added the description of a model by Goldberger et al.-- a 5D SU(5) SUSY model in a slice of AdS space with special boundary conditions to suppress proton decay. The color-triplet also has a TeV mas

Does the Red Queen reign in the kingdom of digital organisms?

In competition experiments between two RNA viruses of equal or almost equal fitness, often both strains gain in fitness before one eventually excludes the other. This observation has been linked to the Red Queen effect, which describes a situation in which organisms have to constantly adapt just to keep their status quo. I carried out experiments with digital organisms (self-replicating computer programs) in order to clarify how the competing strains' location in fitness space influences the Red-Queen effect. I found that gains in fitness during competition were prevalent for organisms that were taken from the base of a fitness peak, but absent or rare for organisms that were taken from the top of a peak or from a considerable distance away from the nearest peak. In the latter two cases, either neutral drift and loss of the fittest mutants or the waiting time to the first beneficial mutation were more important factors. Moreover, I found that the Red-Queen dynamic in general led to faster exclusion than the other two mechanisms.Comment: 10 pages, 5 eps figure

Time-ordering and a generalized Magnus expansion

Both the classical time-ordering and the Magnus expansion are well-known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in statistical physics, we introduce a generalization of the Magnus expansion. Whereas the classical expansion computes the logarithm of the evolution operator of a linear differential equation, our generalization addresses the same problem, including however directly a non-trivial initial condition. As a by-product we recover a variant of the time ordering operation, known as T*-ordering. Eventually, placing our results in the general context of Rota-Baxter algebras permits us to present them in a more natural algebraic setting. It encompasses, for example, the case where one considers linear difference equations instead of linear differential equations