We summarize the recently-developed framework of linearly-solvable stochastic optimal control. Using an exponential transformation, the (Hamilton-Jacobi) Bellman equation for such problems can bemade linear, giving rise to efficient numericalmethods. Extensions to game theory are also possible and lead to linear Isaacs equations. The key restriction that makes a stochastic optimal control probl...

In this article, a time dependent partial differential equation is used to model the nonlinear boundary value problem describing heat transfer through a radial porous moving fin with rectangular profile. The study is performed by applying a numerical solver in MATLAB (pdepe), which is a centered finite difference scheme. The thermal conductivity and fin surface emissivity are linearly ...

Session types capture precise protocol structure in concurrent programming, but do not specify properties of the exchanged values beyond their basic type. Refinement types are a form of dependent types that can address this limitation, combining types with logical formulae that may refer to program values and can constrain types using arbitrary predicates. We present a pi calculus with assume a...

An important procedure in the mathematics of phylogenetic analysis is to associate, to any collection of weighted splits, the metric given by the corresponding linear combination of split metrics. In this note, we study necessary and sufficient conditions for a collection of splits of a given finite set X to give rise to a linearly independent collection of split metrics. In addition, we study ...

The theorem of Hochster and Roberts says that for any module V of a linearly reductive group G over a eld K the invariant ring KV ] G is Cohen-Macaulay. We prove the following converse: if G is a reductive group and KV ] G is Cohen-Macaulay for any module V , then G is linearly reductive.

The process of electron-positron pair production by linearly polarized photons is used as a polarimeter to perform mobile measurement of linear photon polarization. In the limit of high photon energies, ω, the distributions of the recoil-electron momentum and azimuthal angle do not depend on the photon energy in the laboratory frame. We calculate the power corrections of order m/ω to the above ...

We consider bandit problems involving a large (possibly infinite) collection of arms, in which the expected reward of each arm is a linear function of an r-dimensional random vector Z ∈ Rr, where r ≥ 2. The objective is to minimize the cumulative regret and Bayes risk. When the set of arms corresponds to the unit sphere, we prove that the regret and Bayes risk is of order Θ(r √ T ), by establis...

Network-coded multiple access (NCMA) is a communication scheme for wireless multiple-access networks where physical-layer network coding (PNC) is employed. In NCMA, a user encodes and spreads its message into multiple packets. Time is slotted and multiple users transmit packets (one packet each) simultaneously in each timeslot. A sink node aims to decode the messages of all the users from the s...