MLEFlow: Learning from History to Improve Load Balancing in Tor

Tor has millions of daily users seeking privacy while browsing the Internet. It has thousands of relays to route users’ packets while anonymizing their sources and destinations. Users choose relays to forward their traffic according to probability distributions published by the Tor authorities. The authorities generate these probability distributions based on estimates of the capacities of the relays. They compute these estimates based on the bandwidths of probes sent to the relays. These estimates are necessary for better load balancing. Unfortunately, current methods fall short of providing accurate estimates leaving the network underutilized and its capacities unfairly distributed between the users’ paths. We present MLEFlow, a maximum likelihood approach for estimating relay capacities for optimal load balancing in Tor. We show that MLEFlow generalizes a version of Tor capacity estimation, TorFlow-P, by making better use of measurement history. We prove that the mean of our estimate converges to a small interval around the actual capacities, while the variance converges to zero. We present two versions of MLEFlow: MLEFlow-CF, a closed-form approximation of the MLE and MLEFlow-Q, a discretization and iterative approximation of the MLE which can account for noisy observations. We demonstrate the practical benefits of MLEFlow by simulating it using a flow-based Python simulator of a full Tor network and packet-based Shadow simulation of a scaled down version. In our simulations MLEFlow provides significantly more accurate estimates, which result in improved user performance, with median download speeds increasing by 30%.

Establishment of local adaptation in partly self-fertilizing populations

Populations often inhabit multiple ecological patches and thus experience divergent selection, which can lead to local adaptation if migration is not strong enough to swamp locally adapted alleles. Conditions for the establishment of a locally advantageous allele have been studied in randomly mating populations. However, many species reproduce, at least partially, through self-fertilization, and how selfing affects local adaptation remains unclear and debated. Using a two-patch branching process formalism, we obtained a closed-form approximation under weak selection for the probability of establishment of a locally advantageous allele (P) for arbitrary selfing rate and dominance level, where selection is allowed to act on viability or fecundity, and migration can occur via seed or pollen dispersal. This solution is compared to diffusion approximation and used to investigate the consequences of a shift in a mating system on P, and the establishment of protected polymorphism. We find that selfing can either increase or decrease P, depending on the patterns of dominance in the two patches, and has conflicting effects on local adaptation. Globally, selfing favors local adaptation when locally advantageous alleles are (partially) recessive, when selection between patches is asymmetrical and when migration occurs through pollen rather than seed dispersal. These results establish a rigorous theoretical background to study heterogeneous selection and local adaptation in partially selfing species.

Pricing Basket Options by Polynomial Approximations

We propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model. The method is based on Taylor and Chebyshev expansions and involves mixed exponential-power moments of a Gaussian distribution. Our numerical results show that both approaches are comparable in accuracy to a standard Monte Carlo method, with a lesser computational effort

Pricing Basket Options by Polynomial Approximations

We propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model. The method is based on Taylor and Chebyshev expansions and involves mixed exponential-power moments of a Gaussian distribution. Our numerical results show that both approaches are comparable in accuracy to a standard Monte Carlo method, with a lesser computational effort

Pricing the exotic: Path-dependent American options with stochastic barriers

We develop a novel pricing strategy that approximates the value of an American option with exotic features through a portfolio of European options with different maturities. Among our findings, we show that: (i) our model is numerically robust in pricing plain vanilla American options; (ii) the model matches observed bids and premiums of multidimensional options that integrate Ratchet, Asian, and Barrier characteristics; and (iii) our closed-form approximation allows for an analytical solution of the option’s greeks, which characterize the sensitivity to various risk factors. Finally, we highlight that our estimation requires less than 1% of the computational time compared to other standard methods, such as Monte Carlo simulations.

A Closed-Form Approximation to the Distribution for the Sum of Independent Non-identically Generalized Gamma Variates and Applications

Evaluating the sum of independent and not necessarily identically distributed (i.n.i.d) random variables (RVs) is essential to study different variables linked to various scientific fields, particularly, in wireless communication channels. However, it is difficult to evaluate the distribution of this sum when the number of RVs increases. Consequently, the complex contour integral will be difficult to determine. Considering this issue, a more accurate approximation of the distribution function is required. By assuming the probability density function (PDF) of a generalized gamma (GG) RV evaluated in terms of a proper subset H1,0 1,1 class of Fox’s H-function (FHF) and the moment-based approximation to estimate the FHF parameters, a closed-form tight approximate expression for the distribution of the sum of i.n.i.d GG RVs and a sufficient condition for the convergence are investigated. The proposed approximate may be an analytical useful tool for analyzing the performance of certain numbers branch maximal-ratio combining receivers subject to GG fading channels. Hence, various closed-form performance metrics are derived and examined in terms of FHF. Numerical simulations are carried out to illustrate the theoretical results.