Sensitivity analysis beyond linearity

A wide array of graphical models can be parametrized to have atomic probabilities represented by monomial functions. Such a monomial structure has proven very useful when studying robustness under the assumption of a multilinear model where all monomials have either zero or one exponents. Robustness in probabilistic graphical models is usually investigated by varying some of the input probabilities and observing the effects of these on output probabilities of interest. Here the assumption of multilinearity is relaxed and a general approach for one-way sensitivity analysis in non-multilinear models is presented. It is shown that in non-multilinear models sensitivity functions have a polynomial form, conversely to multilinear models where these are simply linear. The form of various divergences and distances under different covariation schemes is also formally derived. Proportional covariation is proven to be optimal in non-multilinear models under some specific choices of varied parameters. The methodology is illustrated throughout by an educational application

Interaction-based quantum metrology showing scaling beyond the Heisenberg limit

Quantum metrology studies the use of entanglement and other quantum resources to improve precision measurement. An interferometer using N independent particles to measure a parameter X can achieve at best the "standard quantum limit" (SQL) of sensitivity {\delta}X \propto N^{-1/2}. The same interferometer using N entangled particles can achieve in principle the "Heisenberg limit" {\delta}X \propto N^{-1}, using exotic states. Recent theoretical work argues that interactions among particles may be a valuable resource for quantum metrology, allowing scaling beyond the Heisenberg limit. Specifically, a k-particle interaction will produce sensitivity {\delta}X \propto N^{-k} with appropriate entangled states and {\delta}X \propto N^{-(k-1/2)} even without entanglement. Here we demonstrate this "super-Heisenberg" scaling in a nonlinear, non-destructive measurement of the magnetisation of an atomic ensemble. We use fast optical nonlinearities to generate a pairwise photon-photon interaction (k = 2) while preserving quantum-noise-limited performance, to produce {\delta}X \propto N^{-3/2}. We observe super-Heisenberg scaling over two orders of magnitude in N, limited at large N by higher-order nonlinear effects, in good agreement with theory. For a measurement of limited duration, super-Heisenberg scaling allows the nonlinear measurement to overtake in sensitivity a comparable linear measurement with the same number of photons. In other scenarios, however, higher-order nonlinearities prevent this crossover from occurring, reflecting the subtle relationship of scaling to sensitivity in nonlinear systems. This work shows that inter-particle interactions can improve sensitivity in a quantum-limited measurement, and introduces a fundamentally new resource for quantum metrology

Where Does the Density Localize? Convergent Behavior for Global Hybrids, Range Separation, and DFT+U

Approximate density functional theory (DFT) suffers from many-electron self- interaction error, otherwise known as delocalization error, that may be diagnosed and then corrected through elimination of the deviation from exact piecewise linear behavior between integer electron numbers. Although paths to correction of energetic delocalization error are well- established, the impact of these corrections on the electron density is less well-studied. Here, we compare the effect on density delocalization of DFT+U, global hybrid tuning, and range- separated hybrid tuning on a diverse test set of 32 transition metal complexes and observe the three methods to have qualitatively equivalent effects on the ground state density. Regardless of valence orbital diffuseness (i.e., from 2p to 5p), ligand electronegativity (i.e., from Al to O), basis set (i.e., plane wave versus localized basis set), metal (i.e., Ti, Fe, Ni) and spin state, or tuning method, we consistently observe substantial charge loss at the metal and gain at ligand atoms (ca. 0.3-0.5 e or more). This charge loss at the metal is preferentially from the minority spin, leading to increasing magnetic moment as well. Using accurate wavefunction theory references, we observe that a minimum error in partial charges and magnetic moments occur at higher tuning parameters than typically employed to eliminate energetic delocalization error. These observations motivate the need to develop multi-faceted approximate-DFT error correction approaches that separately treat density delocalization and energetic errors in order to recover both correct density and magnetization properties.Comment: 34 pages, 11 figure

The iso-response method

Throughout the nervous system, neurons integrate high-dimensional input streams and transform them into an output of their own. This integration of incoming signals involves filtering processes and complex non-linear operations. The shapes of these filters and non-linearities determine the computational features of single neurons and their functional roles within larger networks. A detailed characterization of signal integration is thus a central ingredient to understanding information processing in neural circuits. Conventional methods for measuring single-neuron response properties, such as reverse correlation, however, are often limited by the implicit assumption that stimulus integration occurs in a linear fashion. Here, we review a conceptual and experimental alternative that is based on exploring the space of those sensory stimuli that result in the same neural output. As demonstrated by recent results in the auditory and visual system, such iso-response stimuli can be used to identify the non-linearities relevant for stimulus integration, disentangle consecutive neural processing steps, and determine their characteristics with unprecedented precision. Automated closed-loop experiments are crucial for this advance, allowing rapid search strategies for identifying iso-response stimuli during experiments. Prime targets for the method are feed-forward neural signaling chains in sensory systems, but the method has also been successfully applied to feedback systems. Depending on the specific question, “iso-response” may refer to a predefined firing rate, single-spike probability, first-spike latency, or other output measures. Examples from different studies show that substantial progress in understanding neural dynamics and coding can be achieved once rapid online data analysis and stimulus generation, adaptive sampling, and computational modeling are tightly integrated into experiments

Beyond the Waterbed Effect: Development of Fractional Order CRONE Control with Non-Linear Reset

In this paper a novel reset control synthesis method is proposed: CRONE reset control, combining a robust fractional CRONE controller with non-linear reset control to overcome waterbed effect. In CRONE control, robustness is achieved by creation of constant phase behaviour around bandwidth with the use of fractional operators, also allowing more freedom in shaping the open-loop frequency response. However, being a linear controller it suffers from the inevitable trade-off between robustness and performance as a result of the waterbed effect. Here reset control is introduced in the CRONE design to overcome the fundamental limitations. In the new controller design, reset phase advantage is approximated using describing function analysis and used to achieve better open-loop shape. Sufficient quadratic stability conditions are shown for the designed CRONE reset controllers and the control design is validated on a Lorentz-actuated nanometre precision stage. It is shown that for similar phase margin, better performance in terms of reference-tracking and noise attenuation can be achieved.Comment: American Control Conference 201

Examination of silver-graphite lithographically printed resistive strain sensors

This paper reports the design and manufacture of three differing types of resistive strain sensitive structures fabricated using the Conductive Lithographic Film (CLF) printing process. The structures, utilising two inks prepared with silver and graphite particulates as the conductive phase, have been analysed to determine electrical and mechanical properties with respect to strain, temperature and humidity when deposited on four alternative substrate materials (GlossArt, PolyArt, Teslin and Melinex)

Results from the First Science Run of the ZEPLIN-III Dark Matter Search Experiment

The ZEPLIN-III experiment in the Palmer Underground Laboratory at Boulby uses a 12kg two-phase xenon time projection chamber to search for the weakly interacting massive particles (WIMPs) that may account for the dark matter of our Galaxy. The detector measures both scintillation and ionisation produced by radiation interacting in the liquid to differentiate between the nuclear recoils expected from WIMPs and the electron recoil background signals down to ~10keV nuclear recoil energy. An analysis of 847kg.days of data acquired between February 27th 2008 and May 20th 2008 has excluded a WIMP-nucleon elastic scattering spin-independent cross-section above 8.1x10(-8)pb at 55GeV/c2 with a 90% confidence limit. It has also demonstrated that the two-phase xenon technique is capable of better discrimination between electron and nuclear recoils at low-energy than previously achieved by other xenon-based experiments.Comment: 12 pages, 17 figure