261 research outputs found
AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs
Stochastic differential equations are an important modeling class in many
disciplines. Consequently, there exist many methods relying on various
discretization and numerical integration schemes. In this paper, we propose a
novel, probabilistic model for estimating the drift and diffusion given noisy
observations of the underlying stochastic system. Using state-of-the-art
adversarial and moment matching inference techniques, we avoid the
discretization schemes of classical approaches. This leads to significant
improvements in parameter accuracy and robustness given random initial guesses.
On four established benchmark systems, we compare the performance of our
algorithms to state-of-the-art solutions based on extended Kalman filtering and
Gaussian processes.Comment: Published at the Thirty-sixth International Conference on Machine
Learning (ICML 2019
Metatags, Keywords, and Links: Recent Developments Addressing Trademark Threats in Cyberspace
This Article addresses the trademark issues that stem from current developments in technology and capabilities specific to the Internet, and discusses how trademark law has evolved in order to provide remedies to trademark holders for unauthorized uses of their trademarks in ways that are likely to cause consumer confusion or allow for unfair competition. The authors begin by examining the current state of technology with respect to metatags, keywords, and links, the current trademark issues that stem from their use, and the recent judicial developments with respect to each type of technology. Based on this examination, the authors argue that the courts are willing to alter trademark law and unfair competition principles to protect against unauthorized uses that do not fit the traditional concepts of trademark infringement. The authors conclude that trademarks, as a form of intellectual property, should be protected when used on the Internet
Many-spin effects in inelastic neutron scattering and electron paramagnetic resonance of molecular nanomagnets
Many molecular magnetic clusters, such as single-molecule magnets, are
characterized by spin ground states with defined total spin S exhibiting
zero-field-splittings. In this work, the spectroscopic intensities of the
transitions within the ground-state multiplet are analyzed. In particular, the
effects of a mixing with higher-lying spin multiplets, which is produced by
anisotropic interactions and is neglected in the standard single-spin
description, are investigated systematically for the two experimental
techniques of inelastic neutron scattering (INS) and electron paramagnetic
resonance (EPR), with emphasis on the former technique. The spectroscopic
transition intensities are calculated analytically by constructing
corresponding effective spin operators perturbationally up to second order and
consequently using irreducible tensor operator techniques. Three main effects
of spin mixing are observed. Firstly, a pronounced dependence of the INS
intensities on the momentum transfer Q, with a typical oscillatory behavior,
emerges in first order, signaling the many-spin nature of the wave functions in
exchange-coupled clusters. Secondly, as compared to the results of a
first-order calculation, the intensities of the transitions within the spin
multiplet are affected differently by spin mixing. This allows one, thirdly, to
differentiate the higher-order contributions to the cluster magnetic anisotropy
which come from the single-ion ligand-field terms and spin mixing,
respectively. The analytical results are illustrated by means of the three
examples of an antiferromagnetic heteronuclear dimer, the Mn-[3 x 3] grid
molecule, and the single-molecule magnet Mn12.Comment: 18 pages, 3 figures, REVTEX4, to appear in PR
The Pure State Space of Quantum Mechanics as Hermitian Symmetric Space
The pure state space of Quantum Mechanics is investigated as Hermitian
Symmetric Kaehler manifold. The classical principles of Quantum Mechanics
(Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum
Probability Principle) and Spectral Theory of observables are discussed in this
non linear geometrical context.Comment: 18 pages, no figure
Spin dynamics in molecular ring nanomagnets: Significant effect of acoustic phonons and magnetic anisotropies
The nuclear spin-lattice relaxation rate 1/T_1_ is calculated for magnetic
ring clusters by fully diagonalizing their microscopic spin Hamiltonians.
Whether the nearest-neighbor exchange interaction J is ferromagnetic or
antiferromagnetic, 1/T_1_ versus temperature T in ring nanomagnets may be
peaked at around k_B_T=|J| provided the lifetime broadening of discrete energy
levels is in proportion to T^3^. Experimental findings for ferromagnetic and
antiferromagnetic Cu^II^ rings are reproduced with crucial contributions of
magnetic anisotropies as well as acoustic phonons.Comment: 5 pages with 5 figures embedded, to be published in J. Phys. Soc.
Jpn. 75, No. 10 (2006
On Differential Structure for Projective Limits of Manifolds
We investigate the differential calculus defined by Ashtekar and Lewandowski
on projective limits of manifolds by means of cylindrical smooth functions and
compare it with the C^infty calculus proposed by Froehlicher and Kriegl in more
general context. For products of connected manifolds, a Boman theorem is
proved, showing the equivalence of the two calculi in this particular case.
Several examples of projective limits of manifolds are discussed, arising in
String Theory and in loop quantization of Gauge Theories.Comment: 38 pages, Latex 2e, to be published on J. Geom. Phys minor misprints
corrected, reference adde
Rotational modes in molecular magnets with antiferromagnetic Heisenberg exchange
In an effort to understand the low temperature behavior of recently
synthesized molecular magnets we present numerical evidence for the existence
of a rotational band in systems of quantum spins interacting with
nearest-neighbor antiferromagnetic Heisenberg exchange. While this result has
previously been noted for ring arrays with an even number of spin sites, we
find that it also applies for rings with an odd number of sites as well as for
all of the polytope configurations we have investigated (tetrahedron, cube,
octahedron, icosahedron, triangular prism, and axially truncated icosahedron).
It is demonstrated how the rotational band levels can in many cases be
accurately predicted using the underlying sublattice structure of the spin
array. We illustrate how the characteristics of the rotational band can provide
valuable estimates for the low temperature magnetic susceptibility.Comment: 14 pages, 7 figures, to be published in Phys. Rev.
Thermal Transient Measurements of an Ultra-Low-Power MOX Sensor
This paper describes a system for the simultaneous dynamic control and thermal characterization of the heating of an Ultra Low Power (ULP) micromachined sensor. A Pulse Width Modulated (PWM) powering system has been realized using a microcontroller to characterize the thermal behavior of a device. Objectives of the research were to analyze the relation between the time period and duty cycle of the PWM signal and the operating temperature of such ULP micromachined systems, to observe the thermal time constants of the device during the heating phase and to measure the total thermal conductance. Constant target heater resistance experiments highlighted that an approximately constant heater temperature at regime can only be obtained if the time period of the heating signal is smaller than 50 s. Constant power experiments show quantitatively a thermal time constant that decreases during heating in a range from 2.3 ms to 2 ms as a function of an increasing temperature rise between the ambient and the operating temperature. Moreover, we calculated the total thermal conductance. Finally, repeatability of experimental results was assessed by guaranteeing the standard deviation of the controlled temperature which was within C in worst case conditions
CEA and CYFRA 21-1 as prognostic biomarker and as a tool for treatment monitoring in advanced NSCLC treated with immune checkpoint inhibitors
Aims: To assess prognostic value of pre-therapy carcinoembryonic antigen (CEA) and cytokeratin-19 fragments (CYFRA 21-1) blood levels in non-small cell lung cancer (NSCLC) patients treated with immune-checkpoint inhibitors (ICIs) and their early change as predictor of benefit. Materials and methods: This is a retrospective cohort study including patients with stage IIIB–IV NSCLC who received anti PD-1/PD-L1 in first or advanced lines of therapy in two institutions. A control cohort of patients treated only with chemotherapy has been enrolled as well. Results: A total of 133 patients treated with nivolumab or atezolizumab were included in the test set, 74 treated with pembrolizumab first line in the validation set and 89 in the chemotherapy only cohort. CYFRA 21-1 >8 ng/mL was correlated with overall survival (OS) in the test set, validation set and in univariate and multivariate analysis (pooled cohort hazard ratio (HR) 1.90, 95% confidence interval (CI) 1.24–2.93, p 0.003). Early 20% reduction after the third cycle was correlated with OS for CEA (HR 0.12; 95% CI 0.04–0.33; p < 0.001), and for CYFRA 21-1 (HR 0.19; 95% CI 0.07–0.55; p 0.002) Conclusions: CYFRA 21-1 pre-therapy assessment provides clinicians with relevant prognostic information about patients treated with ICI. CEA and CYFRA 21-1 repeated measures could be useful as an early marker of benefit
The Geometric Phase and Ray Space Isometries
We study the behaviour of the geometric phase under isometries of the ray
space. This leads to a better understanding of a theorem first proved by
Wigner: isometries of the ray space can always be realised as projections of
unitary or anti-unitary transformations on the Hilbert space. We suggest that
the construction involved in Wigner's proof is best viewed as an use of the
Pancharatnam connection to ``lift'' a ray space isometry to the Hilbert space.Comment: 17 pages, Latex file, no figures, To appear in Pramana J. Phy
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