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

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

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