Online tool for the discrimination of equi-distributions

For many applications one wishes to decide whether a certain set of numbers originates from an equiprobability distribution or whether they are unequally distributed. Distributions of relative frequencies may deviate significantly from the corresponding probability distributions due to finite sample effects. Hence, it is not trivial to discriminate between an equiprobability distribution and non-equally distributed probabilities when knowing only frequencies. Based on analytical results we provide a software tool which allows to decide whether data correspond to an equiprobability distribution. The tool is available at http://bioinf.charite.de/equifreq/. Its application is demonstrated for the distribution of point mutations in coding genes.Comment: 12 pages, 8 figure

Correction algorithm for finite sample statistics

Assume in a sample of size M one finds M_i representatives of species i with i=1...N^*. The normalized frequency p^*_i=M_i/M, based on the finite sample, may deviate considerably from the true probabilities p_i. We propose a method to infer rank-ordered true probabilities r_i from measured frequencies M_i. We show that the rank-ordered probabilities provide important informations on the system, e.g., the true number of species, the Shannon- and the Renyi-entropies.Comment: 11 pages, 9 figure

The new technique for accurate estimation of the spinal cord circuitry:recording reflex responses of large motor unit populations

We propose and validate a non-invasive method that enables accurate detection of the discharge times of a relatively large number of motor units during excitatory and inhibitory reflex stimulations. HDsEMG and intramuscular EMG (iEMG) were recorded from the tibialis anterior muscle during ankle dorsiflexions performed at 5%, 10%, and 20% of the maximum voluntary contraction (MVC) force, in 9 healthy subjects. The tibial nerve (inhibitory reflex) and the peroneal nerve (excitatory reflex) were stimulated with constant current stimuli. In total, 416 motor units were identified from the automatic decomposition of the HDsEMG. The iEMG was decomposed using a state-of-the-art decomposition tool and provided 84 motor units (average of two recording sites). The reflex responses of the detected motor units were analyzed using the peri-stimulus time histogram (PSTH) and the peri-stimulus frequencygram (PSF). The reflex responses of the common motor units identified concurrently from the HDsEMG and the iEMG signals showed an average disagreement (the difference between number of observed spikes in each bin relative to the mean) of 8.2±2.2% (5% MVC), 6.8±1.0% (10% MVC), and 7.5±2.2% (20% MVC), for reflex inhibition, and 6.5±4.1%, 12.0±1.8%, 13.9±2.4%, for reflex excitation. There was no significant difference between the characteristics of the reflex responses, such as latency, amplitude and duration, for the motor units identified by both techniques. Finally, reflex responses could be identified at higher force (four of the nine subjects performed contraction up to 50% MVC) using HDsEMG but not iEMG, because of the difficulty in decomposing the iEMG at high forces. In conclusion, single motor unit reflex responses can be estimated accurately and non-invasively in relatively large populations of motor units using HDsEMG. This non-invasive approach may enable a more thorough investigation of the synaptic input distribution on active motor units at various force levels