Single shot parameter estimation via continuous quantum measurement

We present filtering equations for single shot parameter estimation using continuous quantum measurement. By embedding parameter estimation in the standard quantum filtering formalism, we derive the optimal Bayesian filter for cases when the parameter takes on a finite range of values. Leveraging recent convergence results [van Handel, arXiv:0709.2216 (2008)], we give a condition which determines the asymptotic convergence of the estimator. For cases when the parameter is continuous valued, we develop quantum particle filters as a practical computational method for quantum parameter estimation.Comment: 9 pages, 5 image

The Role of Chain Length in Cucurbit[8]uril Complexation of Methyl Alkyl Viologens

Viologens are among the most studied guests for cucurbit[8]uril (CB[8]) and their complexation is usually driven by bipyridyl core inclusion inside the cavity to maximize both hydrophobic and cation-dipole interactions. The presence of alkyl substituents on the guest alters this complexation mode, switching to aliphatic chain inclusion in U-folded conformation. Herein, we report a thorough study of the influence of the alkyl chain length on the binding mode of methyl alkyl viologens. The chain length of the studied guests was increased by two methylene groups starting from methyl dodecyl viologen (MVC12) to the octadecyl analogue (MVC18). Complexation in water, investigated by NMR spectroscopy and ITC, revealed a clear switch from 1 : 1 to 2 : 1 host/guest stoichiometry moving from 12 to 16 carbon atoms, as a consequence of the chain folding of the major portion of the longer alkyl chain in one CB[8] cavity and the inclusion of the full viologen unit by another host molecule. The CB[8]2.MVC18 complex crystal structure evidences the unprecedented 2 : 1 stoichiometry and quantified in 12 the number of carbon atoms necessary to fill the CB[8] cavity in U-shaped conformation

Survey of the Federal Circuit\u27s Patent Law Decisions in 2006: A New Chapter in the Ongoing Dialogue with the Supreme Court

In 2006, the Federal Circuit decided only one portion of one patent case en banc, and that was done mainly as a procedural matter (the entire case was not argued to an en banc court) in order to reconcile prior conflicting precedent on the issue of induced patent infringement with the recent Supreme Court decision in Metro-Goldwyn-Mayer Studios, Inc. v. Grokster, Ltd., involving induced copyright infringement. But in light of the Supreme Court’s much more muscular review of the Federal Circuit’s patent cases—which may not even reflect the full extent of the Court’s interest in the Federal Circuit’s patent decisions—the relative paucity of en banc decisions in 2006 is understandable, and in many ways irrelevant to gaining a better understanding of the Federal Circuit’s patent law jurisprudence. In the pages that follow, we will address these and many other developments reflected in the Federal Circuit’s patent jurisprudence of 2006. And, as we did in our article surveying the Federal Circuit’s year 2000 jurisprudence, we again conclude with an addendum that discusses the statistical output of the Federal Circuit and its judges

Survey of the Federal Circuit\u27s Patent Law Decisions in 2006: A New Chapter in the Ongoing Dialogue with the Supreme Court

In 2006, the Federal Circuit decided only one portion of one patent case en banc, and that was done mainly as a procedural matter (the entire case was not argued to an en banc court) in order to reconcile prior conflicting precedent on the issue of induced patent infringement with the recent Supreme Court decision in Metro-Goldwyn-Mayer Studios, Inc. v. Grokster, Ltd., involving induced copyright infringement. But in light of the Supreme Court’s much more muscular review of the Federal Circuit’s patent cases—which may not even reflect the full extent of the Court’s interest in the Federal Circuit’s patent decisions—the relative paucity of en banc decisions in 2006 is understandable, and in many ways irrelevant to gaining a better understanding of the Federal Circuit’s patent law jurisprudence. In the pages that follow, we will address these and many other developments reflected in the Federal Circuit’s patent jurisprudence of 2006. And, as we did in our article surveying the Federal Circuit’s year 2000 jurisprudence, we again conclude with an addendum that discusses the statistical output of the Federal Circuit and its judges

Methyl Hexadecyl Viologen Inclusion in Cucurbit[8]uril: Coexistence of Three Host-Guest Complexes with Different Stoichiometry in a Highly Hydrated Crystal

The host-guest inclusion complexes of cucurbiturils with alkyl viologen have interesting architectures, chemical properties, and potential applications in sensors and nanotechnology. A highly hydrated triclinic crystal of cucurbit[8]uril (CB[8]) complexed by methyl hexadecyl viologen (MVC16) is characterized by the unprecedented coexistence in the crystal of three host-guest complexes with 3:2, 2:2, and 1:1 stoichiometries. In all these complexes, the hook-shaped alkyl chain of the MVC16 is hosted in the CB[8] macrocycles, while the methyl viologen moieties have various environments. In the Z-shaped 3:2 complex, a central CB[8] unit hosts two viologen heads in the cavity, while the 2:2 complex is held together by \u3c0-stacking interactions between two viologen units. In the square 2D tiling crystal packing of CB[8] macrocycles, the same site which favors the dimerization observed in the 2:2 complex is also statistically occupied by a single methyl viologen moiety of the 1:1 complex. The rational interpretation of the crystal structure represented an intriguing challenge, due to the complicated statistical disorder in the alkyl chains hosted in CB[8] units and in the methyl viologen moieties of 2:2 and 1:1 complexes. In contrast with the solution behavior dominated by the 2:1 complex, the coexistence of three host-guest complexes with 3:2, 2:2, and 1:1 ratios highlights the fundamental importance of packing effects in the crystallized supramolecular complexes. Therefore, the crystallization process has permitted us to capture different host-guest systems in a single crystal, revealing a supramolecular landscape in a single photo

Tensor polarizability and dispersive quantum measurement of multilevel atoms

Optimally extracting information from measurements performed on a physical system requires an accurate model of the measurement interaction. Continuously probing the collective spin of an Alkali atom cloud via its interaction with an off-resonant optical probe is an important example of such a measurement where realistic modeling at the quantum level is possible using standard techniques from atomic physics. Typically, however, tutorial descriptions of this technique have neglected the multilevel structure of realistic atoms for the sake of simplification. In this paper we account for the full multilevel structure of Alkali atoms and derive the irreducible form of the polarizability Hamiltonian describing a typical dispersive quantum measurement. For a specific set of parameters, we then show that semiclassical predictions of the theory are consistent with our experimental observations of polarization scattering by a polarized cloud of laser-cooled Cesium atoms. We also derive the signal-to-noise ratio under a single measurement trial and use this to predict the rate of spin-squeezing with multilevel Alkali atoms for arbitrary detuning of the probe beam.Comment: Significant corrections to theory and data. Full quality figures and other information available from http://minty.caltech.edu/papers.ph

Magnetometry via a double-pass continuous quantum measurement of atomic spin

We argue that it is possible in principle to reduce the uncertainty of an atomic magnetometer by double-passing a far-detuned laser field through the atomic sample as it undergoes Larmor precession. Numerical simulations of the quantum Fisher information suggest that, despite the lack of explicit multi-body coupling terms in the system's magnetic Hamiltonian, the parameter estimation uncertainty in such a physical setup scales better than the conventional Heisenberg uncertainty limit over a specified but arbitrary range of particle number N. Using the methods of quantum stochastic calculus and filtering theory, we demonstrate numerically an explicit parameter estimator (called a quantum particle filter) whose observed scaling follows that of our calculated quantum Fisher information. Moreover, the quantum particle filter quantitatively surpasses the uncertainty limit calculated from the quantum Cramer-Rao inequality based on a magnetic coupling Hamiltonian with only single-body operators. We also show that a quantum Kalman filter is insufficient to obtain super-Heisenberg scaling, and present evidence that such scaling necessitates going beyond the manifold of Gaussian atomic states.Comment: 17 pages, updated to match print versio

Shallow vs deep learning architectures for white matter lesion segmentation in the early stages of multiple sclerosis

In this work, we present a comparison of a shallow and a deep learning architecture for the automated segmentation of white matter lesions in MR images of multiple sclerosis patients. In particular, we train and test both methods on early stage disease patients, to verify their performance in challenging conditions, more similar to a clinical setting than what is typically provided in multiple sclerosis segmentation challenges. Furthermore, we evaluate a prototype naive combination of the two methods, which refines the final segmentation. All methods were trained on 32 patients, and the evaluation was performed on a pure test set of 73 cases. Results show low lesion-wise false positives (30%) for the deep learning architecture, whereas the shallow architecture yields the best Dice coefficient (63%) and volume difference (19%). Combining both shallow and deep architectures further improves the lesion-wise metrics (69% and 26% lesion-wise true and false positive rate, respectively).Comment: Accepted to the MICCAI 2018 Brain Lesion (BrainLes) worksho

Transcriptome analysis of differentiating spermatogonia stimulated with kit ligand

Kit ligand (KL) is a survival factor and a mitogenic stimulus for differentiating spermatogonia. However, it is not known whether KL also plays a role in the differentiative events that lead to meiotic entry of these cells. We performed a wide genome analysis of difference in gene expression induced by treatment with KL of spermatogonia from 7-day-old mice, using gene chips spanning the whole mouse genome. The analysis revealed that the pattern of RNA expression induced by KL is compatible with the qualitative changes of the cell cycle that occur during the subsequent cell divisions in type A and B spermatogonia, i.e. the progressive lengthening of the S phase and the shortening of the G2/M transition. Moreover, KL up-regulates in differentiating spermatogonia the expression of early meiotic genes (for instance: Lhx8, Nek1, Rnf141, Xrcc3, Tpo1, Tbca, Xrcc2, Mesp1, Phf7, Rtel1), whereas it down-regulates typical spermatogonial markers (for instance: Pole, Ptgs2, Zfpm2, Egr2, Egr3, Gsk3b, Hnrpa1, Fst, Ptch2). Since KL modifies the expression of several genes known to be up-regulated or down-regulated in spermatogonia during the transition from the mitotic to the meiotic cell cycle, these results are consistent with a role of the KL/kit interaction in the induction of their meiotic differentiation

Angular Forces Around Transition Metals in Biomolecules

Quantum-mechanical analysis based on an exact sum rule is used to extract an semiclassical angle-dependent energy function for transition metal ions in biomolecules. The angular dependence is simple but different from existing classical potentials. Comparison of predicted energies with a computer-generated database shows that the semiclassical energy function is remarkably accurate, and that its angular dependence is optimal.Comment: Tex file plus 4 postscript figure