Imprecise continuous-time Markov chains : efficient computational methods with guaranteed error bounds

Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential equation. As there is no general analytical expression for this solution, efficient numerical approximation methods are essential to the applicability of this model. We here improve the uniform approximation method of Krak et al. (2016) in two ways and propose a novel and more efficient adaptive approximation method. For ergodic chains, we also provide a method that allows us to approximate stationary distributions up to any desired maximal error

Sum-rate Maximizing in Downlink Massive MIMO Systems with Circuit Power Consumption

The downlink of a single cell base station (BS) equipped with large-scale multiple-input multiple-output (MIMO) system is investigated in this paper. As the number of antennas at the base station becomes large, the power consumed at the RF chains cannot be anymore neglected. So, a circuit power consumption model is introduced in this work. It involves that the maximal sum-rate is not obtained when activating all the available RF chains. Hence, the aim of this work is to find the optimal number of activated RF chains that maximizes the sum-rate. Computing the optimal number of activated RF chains must be accompanied by an adequate antenna selection strategy. First, we derive analytically the optimal number of RF chains to be activated so that the average sum-rate is maximized under received equal power. Then, we propose an efficient greedy algorithm to select the sub-optimal set of RF chains to be activated with regards to the system sum-rate. It allows finding the balance between the power consumed at the RF chains and the transmitted power. The performance of the proposed algorithm is compared with the optimal performance given by brute force search (BFS) antenna selection. Simulations allow to compare the performance given by greedy, optimal and random antenna selection algorithms.Comment: IEEE International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob 2015

A survey on maximal green sequences

Maximal green sequences appear in the study of Fomin-Zelevinsky's cluster algebras. They are useful for computing refined Donaldson-Thomas invariants, constructing twist automorphisms and proving the existence of theta bases and generic bases. We survey recent progress on their existence and properties and give a representation-theoretic proof of Greg Muller's theorem stating that full subquivers inherit maximal green sequences. In the appendix, Laurent Demonet describes maximal chains of torsion classes in terms of bricks generalizing a theorem by Igusa.Comment: 15 pages, submitted to the proceedings of the ICRA 18, Prague, comments welcome; v2: misquotation in section 6 corrected; v3: minor changes, final version; v4: reference to Jiarui Fei's work added, post-final version; v4: formulation of Remark 4.3 corrected; v5: misquotation of Hermes-Igusa's 2019 paper corrected; v5: reference to Kim-Yamazaki's paper adde

Probabilistic Opacity in Refinement-Based Modeling

Given a probabilistic transition system (PTS) $\cal A$ partially observed by an attacker, and an $\omega$-regular predicate $\varphi$over the traces of $\cal A$, measuring the disclosure of the secret $\varphi$ in $\cal A$ means computing the probability that an attacker who observes a run of $\cal A$ can ascertain that its trace belongs to $\varphi$. In the context of refinement, we consider specifications given as Interval-valued Discrete Time Markov Chains (IDTMCs), which are underspecified Markov chains where probabilities on edges are only required to belong to intervals. Scheduling an IDTMC $\cal S$ produces a concrete implementation as a PTS and we define the worst case disclosure of secret $\varphi$ in ${\cal S}$ as the maximal disclosure of $\varphi$ over all PTSs thus produced. We compute this value for a subclass of IDTMCs and we prove that refinement can only improve the opacity of implementations

On semiring complexity of Schur polynomials

Semiring complexity is the version of arithmetic circuit complexity that allows only two operations: addition and multiplication. We show that semiring complexity of a Schur polynomial {s_\lambda(x_1,\dots,x_k)} labeled by a partition {\lambda=(\lambda_1\ge\lambda_2\ge\cdots)} is bounded by {O(\log(\lambda_1))} provided the number of variables $k$ is fixed