Recommendations and illustrations for the evaluation of photonic random number generators

The never-ending quest to improve the security of digital information combined with recent improvements in hardware technology has caused the field of random number generation to undergo a fundamental shift from relying solely on pseudo-random algorithms to employing optical entropy sources. Despite these significant advances on the hardware side, commonly used statistical measures and evaluation practices remain ill-suited to understand or quantify the optical entropy that underlies physical random number generation. We review the state of the art in the evaluation of optical random number generation and recommend a new paradigm: quantifying entropy generation and understanding the physical limits of the optical sources of randomness. In order to do this, we advocate for the separation of the physical entropy source from deterministic post-processing in the evaluation of random number generators and for the explicit consideration of the impact of the measurement and digitization process on the rate of entropy production. We present the Cohen-Procaccia estimate of the entropy rate $h(\epsilon,\tau)$ as one way to do this. In order to provide an illustration of our recommendations, we apply the Cohen-Procaccia estimate as well as the entropy estimates from the new NIST draft standards for physical random number generators to evaluate and compare three common optical entropy sources: single photon time-of-arrival detection, chaotic lasers, and amplified spontaneous emission

Granger causality analysis in neuroscience and neuroimaging

No description supplie

Linear and nonlinear optical excitations in spatially-inhomogeneous semiconductor systems

Gegenstand der vorliegenden Arbeit ist die Licht-Materie-Wechselwirkung in raeumlich inhomogenen Halbleiterstrukturen. In den Kapiteln 2, 3 und 4 werden grundlegende Eigenschaften herausgearbeitet, die dadurch entstehen, dass die untersuchten Systeme von dreidimensionaler raeumlicher Homogenitaet abweichen. Darunter ist zu verstehen, dass sowohl das (anregende) Lichtfeld inhomogen verteilt (Kap 2 und 3) als auch die intrinsischen Materialeigenschaften des Halbleiters raeumlich strukturiert sein koennen (Kap. 2 und 4). In Kapitel 2 wird eine Theorie entwickelt, die es ermoeglicht, Halbleiterstrukturen zu beschreiben, die sich in der Naehe eines photonischen Kristalls befinden. Lineare und nichtlineare optische Eigenschaften von verschiedenen Silizium-Halbleiteroberflaechen werden in Kapitel 4 behandelt

Linear and nonlinear optical excitations in spatially-inhomogeneous semiconductor systems

Gegenstand der vorliegenden Arbeit ist die Licht-Materie-Wechselwirkung in raeumlich inhomogenen Halbleiterstrukturen. In den Kapiteln 2, 3 und 4 werden grundlegende Eigenschaften herausgearbeitet, die dadurch entstehen, dass die untersuchten Systeme von dreidimensionaler raeumlicher Homogenitaet abweichen. Darunter ist zu verstehen, dass sowohl das (anregende) Lichtfeld inhomogen verteilt (Kap 2 und 3) als auch die intrinsischen Materialeigenschaften des Halbleiters raeumlich strukturiert sein koennen (Kap. 2 und 4). In Kapitel 2 wird eine Theorie entwickelt, die es ermoeglicht, Halbleiterstrukturen zu beschreiben, die sich in der Naehe eines photonischen Kristalls befinden. Lineare und nichtlineare optische Eigenschaften von verschiedenen Silizium-Halbleiteroberflaechen werden in Kapitel 4 behandelt

Multifractality of Posture Modulates Multisensory Perception of Stand-On-Ability

By definition, perception is a multisensory process that unfolds in time as a complex sequence of exploratory activities of the organism. In such a system perception and action are integrated, and multiple energy arrays are available simultaneously. Perception of affordances interweaves sensory and motor activities into meaningful behavior given task constraints. The present contribution offers insight into the manner in which perception and action usher the organism through competent functional apprehension of its surroundings. We propose that the tensegrity structure of the body, manifested via multifractality of exploratory bodily movements informs perception of affordances. The affordance of stand-on-ability of ground surfaces served as the experimental paradigm. Observers viewed a surface set to a discrete angle and attempted to match it haptically with a continuously adjustable surface occluded by a curtain, or felt an occluded surface set to a discrete angle then matched it visually with a continuously adjustable visible surface. The complex intertwining of perception and action was demonstrated by the interactions of multifractality of postural sway with multiple energy arrays, responses, and changing geometric task demands

Environmental effects with Frozen Density Embedding in Real-Time Time-Dependent Density Functional Theory using localized basis functions

Frozen Density Embedding (FDE) represents a versatile embedding scheme to describe the environmental effect on the electron dynamics in molecular systems. The extension of the general theory of FDE to the real-time time-dependent Kohn-Sham method has previously been presented and implemented in plane-waves and periodic boundary conditions (Pavanello et al. J. Chem. Phys. 142, 154116, 2015). In the current paper, we extend our recent formulation of real-time time-dependent Kohn-Sham method based on localized basis set functions and developed within the Psi4NumPy framework (De Santis et al. J. Chem. Theory Comput. 2020, 16, 2410) to the FDE scheme. The latter has been implemented in its "uncoupled" flavor (in which the time evolution is only carried out for the active subsystem, while the environment subsystems remain at their ground state), using and adapting the FDE implementation already available in the PyEmbed module of the scripting framework PyADF. The implementation was facilitated by the fact that both Psi4NumPy and PyADF, being native Python API, provided an ideal framework of development using the Python advantages in terms of code readability and reusability. We demonstrate that the inclusion of the FDE potential does not introduce any numerical instability in time propagation of the density matrix of the active subsystem and in the limit of weak external field, the numerical results for low-lying transition energies are consistent with those obtained using the reference FDE calculations based on the linear response TDDFT. The method is found to give stable numerical results also in the presence of strong external field inducing non-linear effects