Exact solution of the zero-range process: fundamental diagram of the corresponding exclusion process

In this paper, we propose a general way of computing expectation values in the zero-range process, using an exact form of the partition function. As an example, we provide the fundamental diagram (the flux-density plot) of the asymmetric exclusion process corresponding to the zero-range process.We express the partition function for the steady state by the Lauricella hypergeometric function, and thereby have two exact fundamental diagrams each for the parallel and random sequential update rules. Meanwhile, from the viewpoint of equilibrium statistical mechanics, we work within the canonical ensemble but the result obtained is certainly in agreement with previous works done in the grand canonical ensemble.Comment: 12 pages, 2 figure

Visualization of Minute Mechanical-Excitation/Relaxation Wave-front Propagation in Myocardial Tissue

Unlike the case of skeletal muscle, the direction of myocardial contraction does not coincide with the direction of work necessary to eject the intraventricular blood, contributing to great complexity of the wall deformation sequence of cardiac contraction. The advent of advanced techniques (CT^1^, MRI^2,3^, SPECT^4^, echocardiology^5-9^, electrocardiography^10^, and magnetocardiography^11,12^) has enabled to the evaluation of cardiac function and disorders by the measurement of blood flow, pressure, electrical reaction process, and other factors. However, complexity of the contraction sequence is still not fully understood because the dynamic mechanical excitation process, which directly correlates with contraction, cannot be accurately measured based on these electro-magnetic phenomena. Here, developing and using a noninvasive novel imaging modality with high temporal and spatial resolutions^13-17^, we show that the propagation of the mechanical wave-front occurs at the beginning of each cardiac contraction and relaxation sequence for the first time. The former occurs about 60 ms prior to the ordinarily accepted onset time of the contraction (R-wave of the electrocardiogram). From the apical side of the interventricular septum, close to the terminal of the Purkinje fibers (specialized to carry contraction impulses), a minute velocity component with an amplitude of several tenth micrometers is generated and propagates sequentially to the entire left ventricle, that is, it propagates from the apex to the base of the posterior wall, and then from the base to the apex of the septum, with a propagation speed of 3-9 m/s. The latter occurs at the end of the first heart sound at the apical side and propagates to the base side with a speed of 0.6 m/s. These physiological findings, unlike the widely accepted myocardial excitation process, have potential for accurate assessment of myocardial tissue damage in coronary disease and cardiomyopathy. This dynamic measurement modality is also applicable to various tissues in biology

Time-locked perceptual fading induced by visual transients

After prolonged fixation, a stationary object placed in the peripheral visual field fades and disappears from our visual awareness, especially at low luminance contrast (the Troxler effect). Here, we report that similar fading can be triggered by visual transients, such as additional visual stimuli flashed near the object, apparent motion, or a brief removal of the object itself (blinking). The fading occurs even without prolonged adaptation and is time-locked to the presentation of the visual transients. Experiments show that the effect of a flashed object decreased monotonically as a function of the distance from the target object. Consistent with this result, when apparent motion, consisting of a sequence of flashes was presented between stationary disks, these target disks perceptually disappeared as if erased by the moving object. Blinking the target disk, instead of flashing an additional visual object, turned out to be sufficient to induce the fading. The effect of blinking peaked around a blink duration of 80 msec. Our findings reveal a unique mechanism that controls the visibility of visual objects in a spatially selective and time-locked manner in response to transient visual inputs. Possible mechanisms underlying this phenomenon will be discussed

Efficient Algorithms for Searching the Minimum Information Partition in Integrated Information Theory

The ability to integrate information in the brain is considered to be an essential property for cognition and consciousness. Integrated Information Theory (IIT) hypothesizes that the amount of integrated information ($\Phi$) in the brain is related to the level of consciousness. IIT proposes that to quantify information integration in a system as a whole, integrated information should be measured across the partition of the system at which information loss caused by partitioning is minimized, called the Minimum Information Partition (MIP). The computational cost for exhaustively searching for the MIP grows exponentially with system size, making it difficult to apply IIT to real neural data. It has been previously shown that if a measure of $\Phi$ satisfies a mathematical property, submodularity, the MIP can be found in a polynomial order by an optimization algorithm. However, although the first version of $\Phi$ is submodular, the later versions are not. In this study, we empirically explore to what extent the algorithm can be applied to the non-submodular measures of $\Phi$ by evaluating the accuracy of the algorithm in simulated data and real neural data. We find that the algorithm identifies the MIP in a nearly perfect manner even for the non-submodular measures. Our results show that the algorithm allows us to measure $\Phi$ in large systems within a practical amount of time