Time-Optimal Transfer of Coherence

We provide exact analytical solutions for the problem of time-optimal transfer of coherence from one spin polarization to a three-fold coherence in a trilinear Ising chain with a fixed energy available and subject to local controls with a non negligible time cost. The time of transfer is optimal and consistent with a previous numerical result obtained assuming instantaneous local controls.Comment: Published version (with typos in eqs. (25)-(27) corrected

Virtually optimized insoles for offloading the diabetic foot: a randomized crossover study

Integration of objective biomechanical measures of foot function into the design process for insoles has been shown to provide enhanced plantar tissue protection for individuals at-risk of plantar ulceration. The use of virtual simulations utilizing numerical modeling techniques offers a potential approach to further optimize these devices. In a patient population at-risk of foot ulceration, we aimed to compare the pressure offloading performance of insoles that were optimized via numerical simulation techniques against shape-based devices. Twenty participants with diabetes and at-risk feet were enrolled in this study. Three pairs of personalized insoles: one based on shape data and subsequently manufactured via direct milling; and two were based on a design derived from shape, pressure, and ultrasound data which underwent a finite element analysis-based virtual optimization procedure. For the latter set of insole designs, one pair was manufactured via direct milling, and a second pair was manufactured through 3D printing. The offloading performance of the insoles was analyzed for forefoot regions identified as having elevated plantar pressures. In 88% of the regions of interest, the use of virtually optimized insoles resulted in lower peak plantar pressures compared to the shape-based devices. Overall, the virtually optimized insoles significantly reduced peak pressures by a mean of 41.3 kPa (p < 0.001, 95% CI [31.1, 51.5]) for milled and 40.5 kPa (p < 0.001, 95% CI [26.4, 54.5]) for printed devices compared to shape-based insoles. The integration of virtual optimization into the insole design process resulted in improved offloading performance compared to standard, shape-based devices.Full Tex

Peripheral inflammation is associated with remote global gene expression changes in the brain

Background: Although the central nervous system (CNS) was once considered an immunologically privileged site, in recent years it has become increasingly evident that cross talk between the immune system and the CNS does occur. As a result, patients with chronic inflammatory diseases, such as rheumatoid arthritis, inflammatory bowel disease or psoriasis, are often further burdened with neuropsychiatric symptoms, such as depression, anxiety and fatigue. Despite the recent advances in our understanding of neuroimmune communication pathways, the precise effect of peripheral immune activation on neural circuitry remains unclear. Utilizing transcriptomics in a well-characterized murine model of systemic inflammation, we have started to investigate the molecular mechanisms by which inflammation originating in the periphery can induce transcriptional modulation in the brain.&lt;p&gt;&lt;/p&gt; Methods: Several different systemic and tissue-specific models of peripheral toll-like-receptor-(TLR)-driven (lipopolysaccharide (LPS), lipoteichoic acid and Imiquimod) and sterile (tumour necrosis factor (TNF) and 12-O-tetradecanoylphorbol-13-acetate (TPA)) inflammation were induced in C57BL/6 mice. Whole brain transcriptional profiles were assessed and compared 48 hours after intraperitoneal injection of lipopolysaccharide or vehicle, using Affymetrix GeneChip microarrays. Target gene induction, identified by microarray analysis, was validated independently using qPCR. Expression of the same panel of target genes was then investigated in a number of sterile and other TLR-dependent models of peripheral inflammation.&lt;p&gt;&lt;/p&gt; Results: Microarray analysis of whole brains collected 48 hr after LPS challenge revealed increased transcription of a range of interferon-stimulated genes (ISGs) in the brain. In addition to acute LPS challenge, ISGs were induced in the brain following both chronic LPS-induced systemic inflammation and Imiquimod-induced skin inflammation. Unique to the brain, this transcriptional response is indicative of peripherally triggered, interferon-mediated CNS inflammation. Similar models of sterile inflammation and lipoteichoic-acid-induced systemic inflammation did not share the capacity to trigger ISG induction in the brain.&lt;p&gt;&lt;/p&gt; Conclusions: These data highlight ISG induction in the brain as being a consequence of a TLR-induced type I interferon response. As considerable evidence links type I interferons to psychiatric disorders, we hypothesize that interferon production in the brain could represent an important mechanism, linking peripheral TLR-induced inflammation with behavioural changes.&lt;p&gt;&lt;/p&gt

Time-optimal Unitary Operations in Ising Chains II: Unequal Couplings and Fixed Fidelity

We analytically determine the minimal time and the optimal control laws required for the realization, up to an assigned fidelity and with a fixed energy available, of entangling quantum gates ($\mathrm{CNOT}$) between indirectly coupled qubits of a trilinear Ising chain. The control is coherent and open loop, and it is represented by a local and continuous magnetic field acting on the intermediate qubit. The time cost of this local quantum operation is not restricted to be zero. When the matching with the target gate is perfect (fidelity equal to one) we provide exact solutions for the case of equal Ising coupling. For the more general case when some error is tolerated (fidelity smaller than one) we give perturbative solutions for unequal couplings. Comparison with previous numerical solutions for the minimal time to generate the same gates with the same Ising Hamiltonian but with instantaneous local controls shows that the latter are not time-optimal.Comment: 11 pages, no figure

Predicting cortical bone adaptation to axial loading in the mouse tibia

The development of predictive mathematical models can contribute to a deeper understanding of the specific stages of bone mechanobiology and the process by which bone adapts to mechanical forces. The objective of this work was to predict, with spatial accuracy, cortical bone adaptation to mechanical load, in order to better understand the mechanical cues that might be driving adaptation. The axial tibial loading model was used to trigger cortical bone adaptation in C57BL/6 mice and provide relevant biological and biomechanical information. A method for mapping cortical thickness in the mouse tibia diaphysis was developed, allowing for a thorough spatial description of where bone adaptation occurs. Poroelastic finite-element (FE) models were used to determine the structural response of the tibia upon axial loading and interstitial fluid velocity as the mechanical stimulus. FE models were coupled with mechanobiological governing equations, which accounted for non-static loads and assumed that bone responds instantly to local mechanical cues in an on–off manner. The presented formulation was able to simulate the areas of adaptation and accurately reproduce the distributions of cortical thickening observed in the experimental data with a statistically significant positive correlation (Kendall's τ rank coefficient τ = 0.51, p < 0.001). This work demonstrates that computational models can spatially predict cortical bone mechanoadaptation to a time variant stimulus. Such models could be used in the design of more efficient loading protocols and drug therapies that target the relevant physiological mechanisms