Developments in the Khintchine-Meinardus probabilistic method for asymptotic enumeration

A theorem of Meinardus provides asymptotics of the number of weighted partitions under certain assumptions on associated ordinary and Dirichlet generating functions. The ordinary generating functions are closely related to Euler's generating function $\prod_{k=1}^\infty S(z^k)$ for partitions, where $S(z)=(1-z)^{-1}$. By applying a method due to Khintchine, we extend Meinardus' theorem to find the asymptotics of the coefficients of generating functions of the form $\prod_{k=1}^\infty S(a_kz^k)^{b_k}$ for sequences $a_k$, $b_k$ and general $S(z)$. We also reformulate the hypotheses of the theorem in terms of generating functions. This allows us to prove rigorously the asymptotics of Gentile statistics and to study the asymptotics of combinatorial objects with distinct components.Comment: 28 pages, This is the final version that incorporated referee's remarks.The paper will be published in Electronic Journal of Combinatoric

New Uses for Sensitivity Analysis: How Different Movement Tasks Effect Limb Model Parameter Sensitivity

Original results for a newly developed eight-order nonlinear limb antagonistic muscle model of elbow flexion and extension are presented. A wider variety of sensitivity analysis techniques are used and a systematic protocol is established that shows how the different methods can be used efficiently to complement one another for maximum insight into model sensitivity. It is explicitly shown how the sensitivity of output behaviors to model parameters is a function of the controller input sequence, i.e., of the movement task. When the task is changed (for instance, from an input sequence that results in the usual fast movement task to a slower movement that may also involve external loading, etc.) the set of parameters with high sensitivity will in general also change. Such task-specific use of sensitivity analysis techniques identifies the set of parameters most important for a given task, and even suggests task-specific model reduction possibilities

Neural substrates of mnemonic discrimination: A whole-brain fMRI investigation.

IntroductionA fundamental component of episodic memory is the ability to differentiate new and highly similar events from previously encountered events. Numerous functional magnetic resonance imaging (fMRI) studies have identified hippocampal involvement in this type of mnemonic discrimination (MD), but few studies have assessed MD-related activity in regions beyond the hippocampus. Therefore, the current fMRI study examined whole-brain activity in healthy young adults during successful discrimination of the test phase of the Mnemonic Similarity Task.MethodIn the study phase, participants made "indoor"/"outdoor" judgments to a series of objects. In the test phase, they made "old"/"new" judgments to a series of probe objects that were either repetitions from the memory set (targets), similar to objects in the memory set (lures), or novel. We assessed hippocampal and whole-brain activity consistent with MD using a step function to identify where activity to targets differed from activity to lures with varying degrees of similarity to targets (high, low), responding to them as if they were novel.ResultsResults revealed that the hippocampus and occipital cortex exhibited differential activity to repeated stimuli relative to even highly similar stimuli, but only hippocampal activity predicted discrimination performance.ConclusionsThese findings are consistent with the notion that successful MD is supported by the hippocampus, with auxiliary processes supported by cortex (e.g., perceptual discrimination)

Visual and control aspects of saccadic eye movements

Physiological, behavioral, and control investigation of rapid saccadic jump eye movement in human

Meinardus' theorem on weighted partitions: extensions and a probabilistic proof

We give a probalistic proof of the famous Meinardus' asymptotic formula for the number of weighted partitions with weakened one of the three Meinardus' conditions, and extend the resulting version of the theorem to other two classis types of decomposable combinatorial structures, which are called assemblies and selections. The results obtained are based on combining Meinardus' analytical approach with probabilistic method of Khitchine.Comment: The version contains a few minor corrections.It will be published in Advances in Applied Mathematic

Physiology of the visual control system

Neurophysiological aspects of eye movement in visual control system with differentiation of version and vergenc

Vision during manned booster operation Final report

Retinal images and accomodation control mechanism under conditions of space flight stres