Twisted analytic torsion

We review the Reidemeister, Ray-Singer’s analytic torsion and the Cheeger-Mller theorem. We describe the analytic torsion of the de Rham complex twisted by a flux form introduced by the current authors and recall its properties. We define a new twisted analytic torsion for the complex of invariant differential forms on the total space of a principal circle bundle twisted by an invariant flux form. We show that when the dimension is even, such a torsion is invariant under certain deformation of the metric and the flux form. Under T-duality which exchanges the topology of the bundle and the flux form and the radius of the circular fiber with its inverse, the twisted torsion of invariant forms are inverse to each other for any dimension.     

Camouflaging Structural Diversity: Co‐crystallization of Two Different Nanoparticles Having Different Cores But the Same Shell

Two ligand‐protected nanoscale silver moieties, [Ag₄₆(SPhMe₂)₂₄(PPh₃)₈](NO₃)₂ and [Ag₄₀(SPhMe₂)₂₄(PPh₃)₈](NO₃)₂ (abbreviated as Ag₄₆ and Ag₄₀, respectively) with almost the same shell but different cores were synthesized simultaneously. As their external structures are identical, the clusters were not distinguishable and become co‐crystallized. The occupancy of each cluster was 50 %. The outer shell of both is composed of Ag₃₂S₂₄P₈, which is reminiscent of fullerenes, and it encapsulates a well‐studied core, Ag₁₄ and a completely new core, Ag₈, which correspond to a face‐centered cube and a simple cube, respectively, resulting in the Ag₄₆ and Ag₄₀ clusters. The presence of two entities (Ag₄₀ and Ag₄₆ clusters) in a single crystal and their molecular formulae were confirmed by detailed electrospray ionization mass spectrometry. The optical spectrum of the mixture showed unique features which were in good agreement with the results from time‐dependent density functional theory (TD‐DFT).     

An Unexpected Role of Hyaluronic Acid in Trafficking siRNA Across the Cellular Barrier: The First Biomimetic,Anionic, Non‐Viral Transfection Method

Circulating nucleic acids, such as short interfering RNA (siRNA), regulate many biological processes; however, the mechanism by which these molecules enter the cell is poorly understood. The role of extracellular‐matrix‐derived polymers in binding siRNAs and trafficking them across the plasma membrane is reported. Thermal melting, dynamic light scattering, scanning electron microscopy, and computational analysis indicate that hyaluronic acid can stabilize siRNA via hydrogen bonding and Van der Waals interactions. This stabilization facilitated HA size‐ and concentration‐dependent gene silencing in a CD44‐positive human osteosarcoma cell line (MG‐63) and in human mesenchymal stromal cells (hMSCs). This native HA‐based siRNA transfection represents the first report on an anionic, non‐viral delivery method that resulted in approximately 60 % gene knockdown in both cell types tested, which correlated with a reduction in translation levels.     

Stimuli‐Responsive Supramolecular Hydrogels and Their Applications in Regenerative Medicine

Supramolecular hydrogels are a class of self‐assembled network structures formed via non‐covalent interactions of the hydrogelators. These hydrogels capable of responding to external stimuli are considered to be smart materials due to their ability to undergo sol–gel and/or gel–sol transition upon subtle changes in their surroundings. Such stimuli‐responsive hydrogels are intriguing biomaterials with applications in tissue engineering, delivery of cells and drugs, modulating tissue environment to promote innate tissue repair, and imaging for medical diagnostics among others. This review summarizes the recent developments in stimuli‐responsive supramolecular hydrogels and their potential applications in regenerative medicine. Specifically, various structural aspects of supramolecular hydrogelators involved in self‐assembly, the role of external stimuli in tuning/controlling their phase transitions, and how these functions could be harnessed to advance applications in regenerative medicine are focused on. Finally, the key challenges and future prospects for these versatile materials are briefly described.     

High angle phase modulated low coherence interferometry for path length resolved Doppler measurements of multiply scattered light

We describe an improved method for coherence domain path length resolved measurements of multiply scattered photons in turbid media. An electro-optic phase modulator sinusoidally modulates the phase in the reference arm of a low coherence fiber optic Mach-Zehnder interferometer, at a high phase modulation angle. For dynamic turbid media this results in Doppler broadened phase modulation interference peaks at the modulation frequency and its multiples. The signal to noise ratio is increased by almost one order or magnitude for large modulation angles and the shape of the spectral peaks resulting from the interference of Doppler shifted sample waves and reference light is not changed. The path length dependent Doppler broadening is compared with the theoretical predictions in the single scattered and diffusive regimes. The experimentally measured optical path lengths are validated with the Monte Carlo technique.     

Ultrasound simulation of real-time temperature estimation during radiofrequency ablation using finite element models

Radiofrequency ablation is the most common minimally invasive therapy used in the United States to treat hepatocellular carcinoma and liver metastases. The ability to perform real-time temperature imaging while a patient is undergoing ablation therapy may help reduce the high recurrence rates following ablation therapy. Ultrasound echo signals undergo time shifts with increasing temperature due to sound speed and thermal expansion, which are tracked using both 1D cross correlation and 2D block matching based speckle tracking methods. In this paper, we present a quantitative evaluation of the accuracy and precision of temperature estimation using the above algorithms on both simulated and experimental data.A finite element analysis simulation of radiofrequency ablation of hepatic tissue was developed. Finite element analysis provides a method to obtain the exact temperature distribution along with a mapping of the tissue displacement due to thermal expansion. These local displacement maps were combined with the displacement due to speed of sound changes and utilized to generate ultrasound radiofrequency frames at specified time increments over the entire ablation procedure. These echo signals provide an ideal test-bed to evaluate the performance of both speckle tracking methods, since the estimated temperature results can be compared directly to the exact finite element solution. Our results indicate that the 1D cross-correlation (CC) method underestimates the cumulative displacement by 0.20 mm, while the underestimation with 2D block matching (BM) is about 0.14 mm after 360 s of ablation. The 1D method also overestimates the size of the ablated region by 5.4% when compared to 2.4% with the 2D method after 720 s of ablation. Hence 2D block matching provides better tracking of temperature variations when compared to the 1D cross-correlation method over the entire duration of the ablation procedure. In addition, results obtained using 1D cross-correlation diverge from the ideal finite element results after 7 min of ablation and for temperatures greater than 65 °C.In a similar manner, experimental results presented using a tissue-mimicking phantom also demonstrate that the maximum percent difference with 2D block matching was 5%, when compared to 31% with the 1D method over the 700 s heating duration on the phantom.     

Cobalt oxide thin films for high capacity and stable Li-ion battery anode

Journal of Solid State Electrochemistry - Here, we report reactive DC-sputter deposited Co3O4 thin films as a promising and stable Li-ion battery anode. Thin films were deposited on stainless steel...     

Slippage of a Porphyrin Macrocycle over Threads of Varying Bulkiness: Implications for the Mechanism of Threading Polymers through a Macrocyclic Ring

Threading of a polymer through a macrocyclic ring may occur directly, that is, by finding the end of the polymer chain, or by a process in which the polymer chain first folds and then threads through the macrocyclic ring in a hairpin‐like conformation. We present kinetic and thermodynamic studies on the threading of a macrocyclic porphyrin receptor ( H₂1 ) onto molecular threads that are blocked on one side and are open on the other side. The open side is modified by groups that vary in ease of folding and in bulkiness. Additionally, the threads contain a viologen binding site for the macrocyclic receptor, which is located close to the blocking group. The rates of threading of H₂1 were measured under various conditions, by recording as a function of time the quenching of the fluorescence of the porphyrin, which occurs when receptor H₂1 reaches the viologen binding site. The kinetic data suggest that threading is impossible if the receptor encounters an open side that is sterically encumbered in a similar way as a folded polymer chain. This indicates that threading of polymers through macrocyclic compounds through a folded chain mechanism is unlikely.