We unveil a mechanism for generating oscillations with arbitrary multiplets of the period of a given external drive, in long-range interacting quantum many-particle spin systems. These oscillations break discrete time translation symmetry as in time crystals, but they are understood via two intertwined stroboscopic effects similar to the aliasing resulting from video taping a single fast rotating helicopter blade. The first effect is similar to a single blade appearing as multiple blades due to a frame rate that is in resonance with the frequency of the helicopter blades’ rotation; the second is akin to the optical appearance of the helicopter blades moving in reverse direction. Analogously to other dynamically stabilized states in interacting quantum many-body systems, this stroboscopic aliasing is robust to detuning and excursions from a chosen set of driving parameters, and it offers a novel route for engineering dynamical n-tuplets in long-range quantum simulators, with potential applications to spin squeezing generation and entangled state preparation.

Quantum gravity is expected to gauge all global symmetries of effective theories, in the ultraviolet. Inspired by this expectation, we explore the consequences of gauging CPT as a quantum boundary condition in phase space. We find that it provides for a natural semiclassical regularisation and discretisation of the continuous spectrum of a quantum Hamiltonian related to the Dilation operator. We observe that the said spectrum is in correspondence with the zeros of the Riemann zeta and Dirichlet beta functions. Following ideas of Berry and Keating, this may help the pursuit of the Riemann hypothesis. It strengthens the proposal that this quantum Hamiltonian captures the near horizon dynamics of the scattering matrix of the Schwarzschild black hole, given the rich chaotic spectrum upon discretisation. It also explains why the spectrum appears to be erratic despite the unitarity of the scattering matrix.

Both percutaneous endoscopic lumbar discectomy (PELD) and minimally invasive transforaminal lumbar interbody fusion (MIS-TLIF) have been demonstrated as two common and effective choices for lumbar disc herniation (LDH) minimally invasive surgery. In order to get a better understanding of these two procedures, we made this contrastive review. By looking up recent literature and combining it with our clinical practice, the indications/contraindications, advantages/disadvantages as well as complications/recurrences of PELD and MIS-TLIF were summarized in this review. It was concluded that PELD and MIS-TLIF are safe and effective minimally invasive operative techniques for symptomatic LDH treatment. A better understanding of these two procedures will help to improve clinical outcomes by selecting proper indications, and also benefit the further development of minimally invasive spine surgery.

An experiment was conducted in Haramaya University Dairy Technology Laboratory to evaluate the effect of starter cultures on physicochemical, textures and consumer preference of soft cheese made from cow milk. Cow milk inoculated with cultures XPL-2 and CHN-22 resulted in slower acidification time than cow milk inoculated using cultures STI-12, RST-743 and R-707. Soft Cheese (SC) made using culture R-707 gave lower pH (4.52) and higher titratable acidity (1.04%). Higher cheese yield (18.08%), fat (18.48%), protein (16.18%), total solids (40.53%) and ash (2.73%) were obtained from cow milk SC made using culture STI-12. Instrumental analysis showed that SC of higher firmness (5.50 N) and brittleness (4.56) were obtained from cheese made using culture R-707, whereas higher (-0.18 N) adhesiveness was recorded from using culture XPL-2. Except color and appearance, consumer preference of taste, aroma and over all acceptance were significantly (P<0.05) affected by inoculation of cultures. In a conclusion, inoculations of commercial starter cultures influence the physicochemical, texture and consumer preference test of cow milk SC.