Rabi oscillations of two-photon states in nonlinear optical resonators

We demonstrate that four-wave mixing processes in high-quality non-linear resonators can lead to Rabi-like oscillations in photon occupation numbers and second-order correlation functions, being a characteristic feature of the presence of entangled photon pairs in the optical signal. In the case of a system driven by a continuous coherent pump, the oscillations occur in the transient regime. We show that driving the system with pulsed coherent pumping would generate strongly anti-bunched photon states.Comment: 5 pages, 6 figure

Zappa-Sz\'ep product groupoids and C*-blends

We study the external and internal Zappa-Sz\'ep product of topological groupoids. We show that under natural continuity assumptions the Zappa-Sz\'ep product groupoid is \'etale if and only if the individual groupoids are \'etale. In our main result we show that the C*-algebra of a locally compact Hausdorff \'etale Zappa-Sz\'ep product groupoid is a C*-blend, in the sense of Exel, of the individual groupoid C*-algebras. We finish with some examples, including groupoids built from *-commuting endomorphisms, and skew product groupoids.Comment: Updated to agree with published versio

Topological spaces associated to higher-rank graphs

We investigate which topological spaces can be constructed as topological realisations of higher-rank graphs. We describe equivalence relations on higher-rank graphs for which the quotient is again a higher-rank graph, and show that identifying isomorphic co-hereditary subgraphs in a disjoint union of two rank-$k$ graphs gives rise to pullbacks of the associated $C^*$-algebras. We describe a combinatorial version of the connected-sum operation and apply it to the rank-2-graph realisations of the four basic surfaces to deduce that every compact 2-manifold is the topological realisation of a rank-2 graph. We also show how to construct $k$-spheres and wedges of $k$-spheres as topological realisations of rank-$k$ graphs.Comment: Updated to agree with published versio

Zappa-Sz\'ep products of semigroups and their C*-algebras

Zappa-Sz\'ep products of semigroups encompass both the self-similar group actions of Nekrashevych and the quasi-lattice-ordered groups of Nica. We use Li's construction of semigroup $C^*$-algebras to associate a $C^*$-algebra to Zappa-Sz\'ep products and give an explicit presentation of the algebra. We then define a quotient $C^*$-algebra that generalises the Cuntz-Pimsner algebras for self-similar actions. We indicate how known examples, previously viewed as distinct classes, fit into our unifying framework. We specifically discuss the Baumslag-Solitar groups, the binary adding machine, the semigroup $\mathbb{N}\rtimes\mathbb{N}^\times$, and the $ax+b$-semigroup $\mathbb{Z}\rtimes\mathbb{Z}^\times$

Time-Restricted Feeding Improves Circadian Dysfunction as well as Motor Symptoms in the Q175 Mouse Model of Huntington's Disease.

Huntington's disease (HD) patients suffer from a progressive neurodegeneration that results in cognitive, psychiatric, cardiovascular, and motor dysfunction. Disturbances in sleep/wake cycles are common among HD patients with reports of delayed sleep onset, frequent bedtime awakenings, and fatigue during the day. The heterozygous Q175 mouse model of HD has been shown to phenocopy many HD core symptoms including circadian dysfunctions. Because circadian dysfunction manifests early in the disease in both patients and mouse models, we sought to determine if early intervention that improve circadian rhythmicity can benefit HD and delay disease progression. We determined the effects of time-restricted feeding (TRF) on the Q175 mouse model. At six months of age, the animals were divided into two groups: ad libitum (ad lib) and TRF. The TRF-treated Q175 mice were exposed to a 6-h feeding/18-h fasting regimen that was designed to be aligned with the middle of the time when mice are normally active. After three months of treatment (when mice reached the early disease stage), the TRF-treated Q175 mice showed improvements in their locomotor activity rhythm and sleep awakening time. Furthermore, we found improved heart rate variability (HRV), suggesting that their autonomic nervous system dysfunction was improved. Importantly, treated Q175 mice exhibited improved motor performance compared to untreated Q175 controls, and the motor improvements were correlated with improved circadian output. Finally, we found that the expression of several HD-relevant markers was restored to WT levels in the striatum of the treated mice using NanoString gene expression assays

Accuracy of a video odometry system for trains

Reliable Data Systems is developing a video-based odometry system that enables trains to measure velocities and distances travelled without the need for trackside infrastructure. A camera is fixed in the cab, taking images of the track immediately ahead, at rates in the range 25–50 frames per second. The images in successive frames are ‘unwarped’ to provide a plan view of the track and then matched, to produce an ‘optical flow’ that measures the distance travelled. The Study Group was asked to investigate ways of putting bounds on the accuracy of such a system, and to suggest any improvements that might be made. The work performed in the week followed three strands: (a) an understanding of how deviations from the camera’s calibrated position lead to errors in the train’s calculated position and velocity; (b) development of models for the train suspension, designed to place bounds on these deviations; and (c) the performance of the associated image processing algorithms