Continuous hidden Markov models (HMMs) assume that observations are generated from a mixture of Gaussian densities, limiting their ability to model more complex distributions. In this work, we address this shortcoming and propose novel continuous HMM models, dubbed FlowHMMs, that enable learning general continuous observation densities without constraining them to follow a Gaussian distribution or their mixtures. To that end, we leverage deep flow-based architectures that model complex, non-Gaussian functions and propose two variants of training a FlowHMM model. The first one, based on gradient-based technique, can be applied directly to continuous multidimensional data, yet its application to larger data sequences remains computationally expensive. Therefore, we also present a second approach to training our FlowHMM that relies on the co-occurrence matrix of discretized observations and considers the joint distribution of pairs of co-observed values, hence rendering the training time independent of the training sequence length. As a result, we obtain a model that can be flexibly adapted to the characteristics and dimensionality of the data. We perform a variety of experiments in which we compare both training strategies with a baseline of Gaussian mixture models. We show, that in terms of quality of the recovered probability distribution, accuracy of prediction of hidden states, and likelihood of unseen data, our approach outperforms the standard Gaussian methods.

This paper presents applicability of Strong Stationary Times (SST) techniques in the area of cryptography. The applicability is in three areas: (1) Propositions of a new class of cryptographic algorithms (pseudo-random permutation generators) which do not run for the predefined number of steps. Instead, these algorithms stop according to a stopping rule defined as SST, for which one can obtain provable properties: a) results are perfect samples from uniform distribution, b) immunity to timing attacks (no information about the resulting permutation leaks through the information about the number of steps SST algorithm performed). (2) We show how one can leverage properties of SST-based algorithms to construct an implementation (of a symmetric encryption scheme) which is immune to the timing-attack by reusing implementations which are not secure against timing-attacks. In symmetric key cryptography researchers mainly focus on constant time (re)implementations. Our approach goes in a different direction and explores ideas of input masking. (3) Analysis of idealized (mathematical) models of existing cryptographic schemes-i.e., we improve a result by Mironov [21].

We present herein a robust algorithm for cell tracking in a sequence of time-lapse 2-D fluorescent microscopy images. Tracking is performed automatically via a multiphase active contours algorithm adapted to the segmentation of clustered nuclei with obscure boundaries. An ellipse fitting method is applied to avoid problems typically associated with clustered, overlapping, or dying cells, and to obtain more accurate segmentation and tracking results. We provide quantitative validation of results obtained with this new algorithm by comparing them to the results obtained from the established CellProfiler, MTrack2 (plugin for Fiji), and LSetCellTracker software.