Distributive Laws and Decidable Properties of SOS Specifications

Some formats of well-behaved operational specifications, correspond to natural transformations of certain types (for example, GSOS and coGSOS laws). These transformations have a common generalization: distributive laws of monads over comonads. We prove that this elegant theoretical generalization has limited practical benefits: it does not translate to any concrete rule format that would be complete for specifications that contain both GSOS and coGSOS rules. This is shown for the case of labeled transition systems and deterministic stream systems.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127

A New Phase Transition for Local Delays in MANETs

We consider Mobile Ad-hoc Network (MANET) with transmitters located according to a Poisson point in the Euclidean plane, slotted Aloha Medium Access (MAC) protocol and the so-called outage scenario, where a successful transmission requires a Signal-to-Interference-and-Noise (SINR) larger than some threshold. We analyze the local delays in such a network, namely the number of times slots required for nodes to transmit a packet to their prescribed next-hop receivers. The analysis depends very much on the receiver scenario and on the variability of the fading. In most cases, each node has finite-mean geometric random delay and thus a positive next hop throughput. However, the spatial (or large population) averaging of these individual finite mean-delays leads to infinite values in several practical cases, including the Rayleigh fading and positive thermal noise case. In some cases it exhibits an interesting phase transition phenomenon where the spatial average is finite when certain model parameters are below a threshold and infinite above. We call this phenomenon, contention phase transition. We argue that the spatial average of the mean local delays is infinite primarily because of the outage logic, where one transmits full packets at time slots when the receiver is covered at the required SINR and where one wastes all the other time slots. This results in the "RESTART" mechanism, which in turn explains why we have infinite spatial average. Adaptive coding offers a nice way of breaking the outage/RESTART logic. We show examples where the average delays are finite in the adaptive coding case, whereas they are infinite in the outage case.Comment: accepted for IEEE Infocom 201

SMT Solving for Functional Programming over Infinite Structures

We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets are represented by logical formulas that define them, and an external satisfiability modulo theories (SMT) solver is regularly run by the interpreter to check their basic properties. The language is implemented as a Haskell module.Comment: In Proceedings MSFP 2016, arXiv:1604.0038

Symmetric image registration with directly calculated inverse deformation field

This paper presents a novel technique for a symmetric deformable image registration based on a new method for fast and accurate direct inversion of a large motion model deformation field. The proposed image registration algorithm maintain a one-to-one mapping between registered images by symmetrically warping them to each other, and by ensuring the inverse consistency criterion at each iteration. This makes the final estimation of forward and backward deformation fields anatomically plausible. The quantitative validation of the method has been performed on magnetic resonance data obtained for a pelvis area demonstrating applicability of the method to adaptive prostate radiotherapy. The experiments demonstrate the improved robustness in terms of inverse consistency error when compared to previously proposed methods for symmetric image registration

Stochastic Analysis of Non-slotted Aloha in Wireless Ad-Hoc Networks

In this paper we propose two analytically tractable stochastic models of non-slotted Aloha for Mobile Ad-hoc NETworks (MANETs): one model assumes a static pattern of nodes while the other assumes that the pattern of nodes varies over time. Both models feature transmitters randomly located in the Euclidean plane, according to a Poisson point process with the receivers randomly located at a fixed distance from the emitters. We concentrate on the so-called outage scenario, where a successful transmission requires a Signal-to-Interference-and-Noise Ratio (SINR) larger than a given threshold. With Rayleigh fading and the SINR averaged over the duration of the packet transmission, both models lead to closed form expressions for the probability of successful transmission. We show an excellent matching of these results with simulations. Using our models we compare the performances of non-slotted Aloha to previously studied slotted Aloha. We observe that when the path loss is not very strong both models, when appropriately optimized, exhibit similar performance. For stronger path loss non-slotted Aloha performs worse than slotted Aloha, however when the path loss exponent is equal to 4 its density of successfully received packets is still 75% of that in the slotted scheme. This is still much more than the 50% predicted by the well-known analysis where simultaneous transmissions are never successful. Moreover, in any path loss scenario, both schemes exhibit the same energy efficiency.Comment: accepted for IEEE Infocom 201

Direct inverse deformation field approach to pelvic-area symmetric image registration

This paper presents a novel technique for a consistent symmetric deformable image registration based on an accurate method for a direct inversion of a large motion model deformation field. The proposed image registration algorithm maintains one-to-one mapping between registered images by symmetrically warping them to another image. This makes the final estimation of forward and backward deformation fields anatomically plausible and applicable to adaptive prostate radiotherapy. The quantitative validation of the method is performed on magnetic resonance data obtained for pelvis area. The experiments demonstrate the improved robustness in terms of inverse consistency error and estimation accuracy of prostate position in comparison to the previously proposed methods

A general approach to posterior contraction in nonparametric inverse problems

In this paper we propose a general method to derive an upper bound for the contraction rate of the posterior distribution for nonparametric inverse problems. We present a general theorem that allows us to derive con- traction rates for the parameter of interest from contraction rates of the related direct problem of estimating transformed parameter of interest. An interesting aspect of this approach is that it allows us to derive con- traction rates for priors that are not related to the singular value decomposition of the operator. We apply our result to several examples of linear inverse problems, both in the white noise sequence model and the nonparametric regression model, using priors based on the singular value decomposition of the operator, location-mixture priors and splines prior, and recover minimax adaptive contraction rates