HOM4PS-2.0 is a software package in FORTRAN 90 which implements the polyhedral homotopy continuation method for solving polynomial systems. It updates its original version HOM4PS in three key aspects: (1) New method for finding mixed cells, (2) Combining the polyhedral and linear homotopies in one step, (3) New way of dealing with the curve jumping. Numerical results show that this revision leads to a spectacular speed-up, ranging up to the 50's, over its original version on all bench mark systems, especially for large ones. It surpasses established packages in this category, such as PHCpack [25] and PHoM [8], in speed by huge margins.

Red blood cells (RBC) circulate the human body several hundred thousand times in their life span. Therefore, their deformability is really important, especially when they pass through a local capillary whose diameter can be as narrow as 3 μm. While there have been a number of works discussing the deformability in a simulated capillary such as a microchannel, as far as we examined in the literature, no work focusing on the change of shape after reciprocated mechanical stress has been reported so far. One of the reasons is that there have been no appropriate experimental systems to achieve such a test. This paper presents a new concept of RBC fatigue evaluation. The fatigue state is defined by the time of reciprocated mechanical stress when the extensibility and the recoverability characteristics meet each other. Our challenge is how to construct a system capable of achieving stable and accurate control of RBCs in a microchannel. For this purpose, we newly introduced two fundamental components. One is a robotic pump capable of manipulating a cell in the accuracy of ±0.24 μm in an equilibrium state with a maximum response time of 15 ms. The other is an online high speed camera capable of chasing the position of RBCs with a sampling rate of 1 kHz. By utilizing these components, we could achieve continuous observation of the length of a RBC over a 1000 times reciprocated mechanical stress. Through these experiments, we found that the repeat number that results in the fatigue state has a close correlation with extensibility.

High entropy oxide (HEO) is a new class of lithium-ion battery anode with high specific capacity and excellent cyclability. The beauty of HEO lies in the unique tailorable properties with respect to tunable chemical composition, which enables the use of infinite element combinations to develop new electrode materials. This study synthesizes a series of Co-free spinel-type HEOs via a facile hydrothermal method. Based on quaternary medium-entropy (CrNiMnFe) 3 O 4 , the fifth elements of V, Mg, and Cu are added, and their ability to form single-phase HEOs is investigated. It is demonstrated that the chemical composition of HEOs is critical to the phase purity and corresponding charge-discharge performance. The oxygen vacancy concentration seems to be decisive for the rate capability and reversibility of the HEO electrodes. An inactive spectator element is not necessary for achieving high cyclability, given that the phase purity of the HEO is wisely controlled. The single-phase (CrNiMnFeCu) 3 O 4 shows a great high-rate capacity of 480 mAh g −1 at 2000 mA g −1 and almost no capacity decay after 400 cycles. Its phase transition behavior during the lithiation/delithiation process is characterized with operando X-ray diffraction. A (CrNiMnFeCu) 3 O 4 ||LiNi 0.8 Co 0.1 Mn 0.1 O 2 cell is constructed with 590 Wh kg −1 (based on electrode materials) gravimetric energy density.

This paper proposes a new index for evaluating the stiffness-based deformability of a cell using a microchannel. In conventional approaches, the transit time of a cell through a microchannel is often utilized for the evaluation of cell deformability. However, such time includes both the information of cell stiffness and viscosity. In this paper, we eliminate the effect from cell viscosity, and focus on the cell stiffness only. We find that the velocity of a cell varies when it enters a channel, and eventually reaches to equilibrium where the velocity becomes constant. The constant velocity is defined as the equilibrium velocity of the cell, and it is utilized to define the observability of stiffness-based deformability. The necessary and sufficient numbers of sensing points for evaluating stiffness-based deformability are discussed. Through the dimensional analysis on the microchannel system, three dimensionless parameters determining stiffness-based deformability are derived, and a new index is introduced based on these parameters. The experimental study is conducted on the red blood cells from a healthy subject and a diabetes patient. With the proposed index, we showed that the experimental data can be nicely arranged.

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An on-chip deformability checker is proposed to improve the velocity–deformation correlation for red blood cell (RBC) evaluation. RBC deformability has been found related to human diseases, and can be evaluated based on RBC velocity through a microfluidic constriction as in conventional approaches. The correlation between transit velocity and amount of deformation provides statistical information of RBC deformability. However, such correlations are usually only moderate, or even weak, in practical evaluations due to limited range of RBC deformation. To solve this issue, we implemented three constrictions of different width in the proposed checker, so that three different deformation regions can be applied to RBCs. By considering cell responses from the three regions as a whole, we practically extend the range of cell deformation in the evaluation, and could resolve the issue about the limited range of RBC deformation. RBCs from five volunteer subjects were tested using the proposed checker. The results show that the correlation between cell deformation and transit velocity is significantly improved by the proposed deformability checker. The absolute values of the correlation coefficients are increased from an average of 0.54 to 0.92. The effects of cell size, shape and orientation to the evaluation are discussed according to the experimental results. The proposed checker is expected to be useful for RBC evaluation in medical practices.

Large deformability of erythrocytes in microvasculature is a prerequisite to realize smooth circulation. We develop a novel tool for the three-step “Catch-Load-Launch” manipulation of a human erythrocyte based on an ultra-high speed position control by a microfluidic “robotic pump”. Quantification of the erythrocyte shape recovery as a function of loading time uncovered the critical time window for the transition between fast and slow recoveries. The comparison with erythrocytes under depletion of adenosine triphosphate revealed that the cytoskeletal remodeling over a whole cell occurs in 3 orders of magnitude longer timescale than the local dissociation-reassociation of a single spectrin node. Finally, we modeled septic conditions by incubating erythrocytes with endotoxin, and found that the exposure to endotoxin results in a significant delay in the characteristic transition time for cytoskeletal remodeling. The high speed manipulation of erythrocytes with a robotic pump technique allows for high throughput mechanical diagnosis of blood-related diseases.

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