On the shape of spectra for non-self-adjoint periodic Schr\"odinger operators

The spectra of the Schr\"odinger operators with periodic potentials are studied. When the potential is real and periodic, the spectrum consists of at most countably many line segments (energy bands) on the real line, while when the potential is complex and periodic, the spectrum consists of at most countably many analytic arcs in the complex plane. In some recent papers, such operators with complex $\mathcal{PT}$-symmetric periodic potentials are studied. In particular, the authors argued that some energy bands would appear and disappear under perturbations. Here, we show that appearance and disappearance of such energy bands imply existence of nonreal spectra. This is a consequence of a more general result, describing the local shape of the spectrum.Comment: 5 pages, 2 figure

Anomalous frequency and intensity scaling of collective and local modes in a coupled spin tetrahedron system

We report on the magnetic excitation spectrum of the coupled spin tetrahedral system Cu$_{2}$Te$_{2}$O$_{5}$Cl$_{2}$ using Raman scattering on single crystals. The transition to an ordered state at T$_{N}^{Cl}$=18.2 K evidenced from thermodynamic data leads to the evolution of distinct low-energy magnetic excitations superimposed by a broad maximum. These modes are ascribed to magnons with different degree of localization and a two-magnon continuum. Two of the modes develop a substantial energy shift with decreasing temperature similar to the order parameter of other Neel ordered systems. The other two modes show only a negligible temperature dependence and dissolve above the ordering temperature in a continuum of excitations at finite energies. These observations point to a delicate interplay of magnetic inter- and intra-tetrahedra degrees of freedom and an importance of singlet fluctuations in describing a spin dynamics.Comment: 7pages, 6figures, 1tabl

Gain Modulation by Corticostriatal and Thalamostriatal Input Signals during Reward-Conditioned Behavior.

The cortex and thalamus send excitatory projections to the striatum, but little is known about how these inputs, either individually or collectively, regulate striatal dynamics during behavior. The lateral striatum receives overlapping input from the secondary motor cortex (M2), an area involved in licking, and the parafascicular thalamic nucleus (PF). Using neural recordings, together with optogenetic terminal inhibition, we examine the contribution of M2 and PF projections on medium spiny projection neuron (MSN) activity as mice performed an anticipatory licking task. Each input has a similar contribution to striatal activity. By comparing how suppressing single or multiple projections altered striatal activity, we find that cortical and thalamic input signals modulate MSN gain and that this effect is more pronounced in a temporally specific period of the task following the cue presentation. These results demonstrate that cortical and thalamic inputs synergistically regulate striatal output during reward-conditioned behavior

Cost effectiveness of school-located influenza vaccination programs for elementary and secondary school children.

BackgroundStudies have noted variations in the cost-effectiveness of school-located influenza vaccination (SLIV), but little is known about how SLIV's cost-effectiveness may vary by targeted age group (e.g., elementary or secondary school students), or vaccine consent process (paper-based or web-based). Further, SLIV's cost-effectiveness may be impacted by its spillover effect on practice-based vaccination; prior studies have not addressed this issue.MethodsWe performed a cost-effectiveness analysis on two SLIV programs in upstate New York in 2015-2016: (a) elementary school SLIV using a stepped wedge design with schools as clusters (24 suburban and 18 urban schools) and (b) secondary school SLIV using a cluster randomized trial (16 suburban and 4 urban schools). The cost-per-additionally-vaccinated child (i.e., incremental cost-effectiveness ratio (ICER)) was estimated by dividing the incremental SLIV intervention cost by the incremental effectiveness (i.e., the additional number of vaccinated students in intervention schools compared to control schools). We performed deterministic analyses, one-way sensitivity analyses, and probabilistic analyses.ResultsThe overall effectiveness measure (proportion of children vaccinated) was 5.7 and 5.5 percentage points higher, respectively, in intervention elementary (52.8%) and secondary schools (48.2%) than grade-matched control schools. SLIV programs vaccinated a small proportion of children in intervention elementary (5.2%) and secondary schools (2.5%). In elementary and secondary schools, the ICER excluding vaccine purchase was $85.71 and$86.51 per-additionally-vaccinated-child, respectively. When additionally accounting for observed spillover impact on practice-based vaccination, the ICER decreased to $80.53 in elementary schools -- decreasing substantially in secondary schools. (to$53.40). These estimates were higher than the published practice-based vaccination cost (median = $25.50, mean =$45.48). Also, these estimates were higher than our 2009-2011 urban SLIV program mean costs ($65) due to additional costs for use of a new web-based consent system ($12.97 per-additionally-vaccinated-child) and higher project coordination costs in 2015-2016. One-way sensitivity analyses showed that ICER estimates were most sensitive to the SLIV effectiveness.ConclusionsSLIV raises vaccination rates and may increase practice-based vaccination in primary care practices. While these SLIV programs are effective, to be as cost-effective as practice-based vaccination our SLIV programs would need to vaccinate more students and/or lower the costs for consent systems and project coordination.Trial registrationClinicalTrials.gov NCT02227186 (August 25, 2014), updated NCT03137667 (May 2, 2017)

Interaction of Na+ Ion With the Solvated Gramicidin A Transmembrane Channel

A 6-12-1 atom-atom pair potential for the interaction of a Na+ion with gramicidin A (GA) has been derived from ab initio SCF calculations on the intermolecular interaction energies between one Na+ion and GA molecular fragments. This potential has been used to obtain iso-energy maps, which in turn provide an energy profile of the Na+ion in the GA channel. We have applied this potential in Monte Carlo simulations in order to obtain i) the number of water molecules which can be placed inside the GA channel and ii) the hydration structures of the GA channel in the presence of one Na+ion

Interaction of Na+ Ion With the Solvated Gramicidin A Transmembrane Channel

A 6-12-1 atom-atom pair potential for the interaction of a Na+ion with gramicidin A (GA) has been derived from ab initio SCF calculations on the intermolecular interaction energies between one Na+ion and GA molecular fragments. This potential has been used to obtain iso-energy maps, which in turn provide an energy profile of the Na+ion in the GA channel. We have applied this potential in Monte Carlo simulations in order to obtain i) the number of water molecules which can be placed inside the GA channel and ii) the hydration structures of the GA channel in the presence of one Na+ion

Metrological power of incompatible measurements

We show that measurement incompatibility is a necessary resource to enhance the precision of quantum metrology. To utilize incompatible measurements, we propose a probabilistic method of operational quasiprobability (OQ) consisting of the measuring averages. OQ becomes positive semidefinite for some quantum states. We prove that Fisher information (FI), based on positive OQ, can be larger than the conventional quantum FI. Applying the proof, we show that FI of OQ can be extremely larger than quantum FI, when estimating a parameter encoded onto a qubit state with two mutually unbiased measurements. By adopting maximum likelihood estimator and linear error propagation methods, we illustrate that they achieve the high precision that our model predicts. This approach is expected to be applicable to improve quantum sensors

Contextual quantum metrology

Quantum metrology promises higher precision measurements than classical methods. Entanglement has been identified as one of quantum resources to enhance metrological precision. However, generating entangled states with high fidelity presents considerable challenges, and thus attaining metrological enhancement through entanglement is generally difficult. Here, we show that contextuality of measurement selection can enhance metrological precision, and this enhancement is attainable with a simple linear optical experiment. We call our methodology "contextual quantum metrology" (coQM). Contextuality is a nonclassical property known as a resource for various quantum information processing tasks. Until now, it has remained an open question whether contextuality can be a resource for quantum metrology. We answer this question in the affirmative by showing that the coQM can elevate precision of an optical polarimetry by a factor of 1.4 to 6.0, much higher than the one by quantum Fisher information, known as the limit of conventional quantum metrology. We achieve the contextuality-enabled enhancement with two polarization measurements which are mutually complementary, whereas, in the conventional method, some optimal measurements to achieve the precision limit are either theoretically difficult to find or experimentally infeasible. These results highlight that the contextuality of measurement selection is applicable in practice for quantum metrology.Comment: 18 pages, 6 figures, companion paper: arXiv:2311.1178