Convergence and Convergence Rate of Stochastic Gradient Search in the Case of Multiple and Non-Isolated Extrema

The asymptotic behavior of stochastic gradient algorithms is studied. Relying on results from differential geometry (Lojasiewicz gradient inequality), the single limit-point convergence of the algorithm iterates is demonstrated and relatively tight bounds on the convergence rate are derived. In sharp contrast to the existing asymptotic results, the new results presented here allow the objective function to have multiple and non-isolated minima. The new results also offer new insights into the asymptotic properties of several classes of recursive algorithms which are routinely used in engineering, statistics, machine learning and operations research

Bias of Particle Approximations to Optimal Filter Derivative

In many applications, a state-space model depends on a parameter which needs to be inferred from a data set. Quite often, it is necessary to perform the parameter inference online. In the maximum likelihood approach, this can be done using stochastic gradient search and the optimal filter derivative. However, the optimal filter and its derivative are not analytically tractable for a non-linear state-space model and need to be approximated numerically. In [Poyiadjis, Doucet and Singh, Biometrika 2011], a particle approximation to the optimal filter derivative has been proposed, while the corresponding $L_{p}$ error bonds and the central limit theorem have been provided in [Del Moral, Doucet and Singh, SIAM Journal on Control and Optimization 2015]. Here, the bias of this particle approximation is analyzed. We derive (relatively) tight bonds on the bias in terms of the number of particles. Under (strong) mixing conditions, the bounds are uniform in time and inversely proportional to the number of particles. The obtained results apply to a (relatively) broad class of state-space models met in practice

Packet transport on scale free networks

We introduce a model of information packet transport on networks in which the packets are posted by a given rate and move in parallel according to a local search algorithm. By performing a number of simulations we investigate the major kinetic properties of the transport as a function of the network geometry, the packet input rate and the buffer size. We find long-range correlations in the power spectra of arriving packet density and the network's activity bursts. The packet transit time distribution shows a power-law dependence with average transit time increasing with network size. This implies dynamic queueing on the network, in which many interacting queues are mutually driven by temporally correlated packet stream

Fractal properties of relaxation clusters and phase transition in a stochastic sandpile automaton

We study numerically the spatial properties of relaxation clusters in a two dimensional sandpile automaton with dynamic rules depending stochastically on a parameter p, which models the effects of static friction. In the limiting cases p=1 and p=0 the model reduces to the critical height model and critical slope model, respectively. At p=p_c, a continuous phase transition occurs to the state characterized by a nonzero average slope. Our analysis reveals that the loss of finite average slope at the transition is accompanied by the loss of fractal properties of the relaxation clusters.Comment: 11 page

Preferential Behaviour and Scaling in Diffusive Dynamics on Networks

We study the fluctuation properties and return-time statistics on inhomogeneous scale-free networks using packets moving with two different dynamical rules; random diffusion and locally navigated diffusive motion with preferred edges. Scaling in the fluctuations occurs when the dispersion of a quantity at each node or edge increases like the its mean to the power $\mu$. We show that the occurrence of scaling in the fluctuations of both the number of packets passing nodes and the number flowing along edges is related to preferential behaviour in either the topology (in the case of nodes) or in the dynamics (in case the of edges). Within our model the absence of any preference leads to the absence of scaling, and when scaling occurs it is non-universal; for random diffusion the number of packets passing a node scales with an exponent $\mu$ which increases continuously with increased acquisition time window from $\mu =1/2$ at small windows, to $\mu =1$ at long time windows; In the preferentially navigated diffusive motion, busy nodes and edges have exponent $\mu =1$, in contrast to less busy parts of the network, where an exponent $\mu =1/2$ is found. Broad distributions of the return times at nodes and edges illustrate that the basis of the observed scaling is the cooperative behaviour between groups of nodes or edges. These conclusions are relevant for a large class of diffusive dynamics on networks, including packet transport with local navigation rules

Experimental Verification of Inertial Navigation with MEMS for Forensic Investigation of Vehicle Collision

This paper studies whether low-grade inertial sensors can be adequate source of data for the accident characterization and the estimation of vehicle trajectory near crash. Paper presents outcomes of an experiment carried out in accredited safety performance assessment facility in which full-size passenger car was crashed and the recordings of different types of motion sensors were compared to investigate practical level of accuracy of consumer grade sensors versus reference equipment and cameras. Inertial navigation system was developed by combining motion sensors of different dynamic ranges to acquire and process vehicle crash data. Vehicle position was reconstructed in three-dimensional space using strap-down inertial mechanization. Difference between the computed trajectory and the ground-truth position acquired by cameras was on decimeter level within short time window of 750 ms. Experiment findings suggest that inertial sensors of this grade, despite significant stochastic variations and imperfections, can be valuable for estimation of velocity vector change, crash severity, direction of impact force, and for estimation of vehicle trajectory in crash proximity

Right Heart Remodeling in Patients with End-Stage Alcoholic Liver Cirrhosis: Speckle Tracking Point of View

BACKGROUND: Data regarding cardiac remodeling in patients with alcoholic liver cirrhosis are scarce. We sought to investigate right atrial (RA) and right ventricular (RV) structure, function, and mechanics in patients with alcoholic liver cirrhosis. METHODS: This retrospective cross-sectional investigation included 67 end-stage cirrhotic patients, who were referred for evaluation for liver transplantation and 36 healthy controls. All participants underwent echocardiographic examination including strain analysis, which was performed offline. RESULTS: RV basal diameter and RV thickness were significantly higher in patients with cirrhosis. Conventional parameters of the RV systolic function were similar between the observed groups. Global, endocardial, and epicardial RV longitudinal strains were significantly lower in patients with cirrhosis. Active RA function was significantly higher in cirrhotic patients than in controls. The RA reservoir and conduit strains were significantly lower in cirrhotic patients, while there was no difference in the RA contractile strain. Early diastolic and systolic RA strain rates were significantly lower in cirrhotic patients than in controls, whereas there was no difference in the RA late diastolic strain rate between the two groups. Transaminases and bilirubin correlated negatively with RV global longitudinal strain and RV-free wall strain in patients with end-stage liver cirrhosis. The Model for End-stage Liver Disease (MELD) score, predictor of 3-month mortality, correlated with parameters of RV structure and systolic function, and RA active function in patients with end-stage liver cirrhosis. CONCLUSIONS: RA and RV remodeling is present in patients with end-stage liver cirrhosis even though RV systolic function is preserved. Liver enzymes, bilirubin, and the MELD score correlated with RV and RA remodeling

Dominantnost jezika dvojezicnih govornika talijanskog I hrvatskog jezika [Language dominance in bilingual speakers of Italian and Croatian language]

Because of the high variability in any bilingual population, it is of a great importance to control for language dominance in both research and language assessment. This control is crucial in research in order to form unified groups of participants according to language dominance. In the language assessment of bilingual children, determining language dominance should be a priority. Children exposed to two languages from an early age may acquire them at a slower rate when compared to their monolingual piers. While this lag is hardly noticeable in some children, for others it is significant. Without knowledge about the child\u2019s language skills in the other, non-assessed language, it is impossible to determine if the results of language assessment point to the dominance of one language over another or general language difficulties. In bilingual areas of Croatia, such as Rijeka and Istria, this can be quite a challenge. While language dominance has generally been measured using a large number of different methods, there is no universally accepted procedure. This research uses the results of the Italian and Croatian versions of the TROG test to determine language dominance. Participants were 56 preschool-aged children attending kindergartens with an Italian language programme in Rijeka and Istria. Participants were preselected by their kindergarten teachers as children that might be balanced bilinguals. Using the differences in results between both TROG tests, approximately 70% of children were placed in a balanced bilinguals group. No differences were shown between groups of participants from Rijeka and Istria