Non-zero Probability Research Articles

Fault-Tolerant Cooperative Signal Detection for Petahertz Short-Range Communication With Continuous Waveform Wideband Detectors

Motivated by unique scattering properties at petahertz frequencies, we present a novel statistical model of fault-tolerant cooperative signal detection for short-range optical petahertz wireless communications, where a single-scattering assumption holds valid. We characterize the received non-line-of-sight (NLOS) signal by a fault-tolerant continuous waveform wideband detector with a non-zero failure probability. To better reflect the physical properties of the petahertz communication, both signal-independent and signal-dependent noise sources are considered in characterizing the received signal. The distribution of the received signal is quantified with each scattered path following the Málaga distribution. We leverage the location flexibility of randomly distributed collaborative users, considering each user experiences an independent channel condition. Utilizing the Neyman-Pearson criterion, we develop the binary hypothesis testing problem and subsequently derive the likelihood ratio for the test statistics. Moreover, to quantify the performance, a framework is developed for the average area under the receiver operating characteristic (ROC) curve for both single user and cooperative scenarios. An optimal decision fusion with a majority rule for fault-tolerant signal detection is applied to exploit the maximum spectrum opportunity. It is found that with the optimal voting rule and for a given target error rate, the network requires fewer collaborative secondary users than the total number of users available in an optical network. However, in the limiting case, it is shown that, as the cost function approaches its minimum or maximum value within its allowable range, the optimal number of collaborative users becomes independent of the failure probabilities. With the realistic assumption of fault-tolerant users, it is found that the false alarm probability increases faster than the detection probability.

Quantum mechanical aspects of cardiac arrhythmias: A mathematical model and pathophysiological implications

<abstract> <p>Cardiac arrhythmias are serious myocardial electrical disturbances that affect the rate and rhythm of heartbeats. Despite the rapidly accumulating data about the pathophysiology and the treatment, new insights are required to improve the overall clinical outcome of patients with cardiac arrhythmias. Three major arrhythmogenic processes can contribute to the pathogenesis of cardiac arrhythmias; 1) enhanced automaticity, 2) afterdepolarization-triggered activity and 3) reentry circuits. The mathematical model of the quantum tunneling of ions is used to investigate these mechanisms from a quantum mechanical perspective. The mathematical model focuses on applying the principle of quantum tunneling to sodium and potassium ions. This implies that these ions have a non-zero probability of passing through the gate, which has an energy that is higher than the kinetic energy of ions. Our mathematical findings indicate that, under pathological conditions, which affect ion channels, the quantum tunneling of sodium and potassium ions is augmented. This augmentation creates a state of hyperexcitability that can explain the enhanced automaticity, after depolarizations that are associated with triggered activity and a reentry circuit. Our mathematical findings stipulate that the augmented and thermally assisted quantum tunneling of sodium and potassium ions can depolarize the membrane potential and trigger spontaneous action potentials, which may explain the automaticity and afterdepolarization. Furthermore, the quantum tunneling of potassium ions during an action potential can provide a new insight regarding the formation of a reentry circuit. Introducing these quantum mechanical aspects may improve our understanding of the pathophysiological mechanisms of cardiac arrhythmias and, thus, contribute to finding more effective anti-arrhythmic drugs.</p> </abstract>

Adiabaticity in nonreciprocal Landau-Zener tunneling

We investigate the Landau-Zener tunneling (LZT) of a self-interacting two-level system in which the coupling between the levels is nonreciprocal. In such a non-Hermitian system, when the energy bias between two levels is adjusted very slowly, i.e., in the adiabatic limit, we find that a quantum state can still closely follow the eigenstate solution until it encounters the exceptional points (EPs) at which two eigenvalues and their corresponding eigenvectors coalesce. In the absence of the nonlinear self-interaction, we can obtain explicit expressions for the eigenvectors and eigenvalues and analytically derive the adiabatic LZT probability from invariants at EPs. In the presence of the nonlinear interaction, the dynamics of the adiabatic evolutions are explicitly demonstrated with the help of classical trajectories in the plane of the two canonical variables of the corresponding classical Josephson Hamiltonian. We show that the adiabatic tunneling probabilities can be precisely predicted by the classical action at EPs in the weak nonreciprocal regime. In a certain region of strong nonreciprocity, we find that interestingly, the nonlinear interaction effects can be completely suppressed so that the adiabatic tunneling probabilities are identical to their linear counterparts. We also obtain a phase diagram for large ranges of nonreciprocity and nonlinear interaction parameters to explicitly demonstrate where the adiabaticity can break down, i.e., the emergence of the nonzero tunneling probabilities even in adiabatic limit.

Joint Offloading and Trajectory Optimization for Complex Status Updates in UAV-Assisted Internet of Things

Unmanned aerial vehicles (UAVs) can utilize multiaccess edge computing (MEC) to help Internet of Things (IoT) devices complete the complex status update by efficient offloading and proper trajectory design. However, considering that IoT devices usually communicate with UAVs in the finite blocklength regime, the uplink transmission cannot be error free. Due to the nonzero packet error probability (PEP), it is difficult to evaluate the instantaneous system performance as in the case with small blocklength. Moreover, the PEP is simultaneously coupled with the offloading parameters and trajectories of UAVs, which makes the performance optimization even more challenging. To this end, we first derive the analytical expressions of the average peak Age of Information (AoI), the average energy consumption of IoT devices and the average energy consumption of UAVs. Then, we formulate a joint optimization problem aiming to minimize the weighted sum of the three performance metrics by jointly optimizing the offloading parameters and the UAV trajectories. By dividing the original problem into multiple subproblems, an alternating optimization-based algorithm is proposed to solve it suboptimally. Simulation results validate the effectiveness of our proposed algorithm and reveal that by properly setting the transmit power and computing capacity of IoT devices, the desired tradeoff among the three performance metrics can be achieved and thus the system performance can be improved effectively.

Cooperative dynamics in two-component out-of-equilibrium systems: molecular ‘spinning tops’

We study the two-dimensional Langevin dynamics of a mixture of two types of particles that live respectively at two different temperatures. Dynamics is constrained by an optical trap and the dissimilar species interact via a quadratic potential. We realize that the system evolves toward a peculiar non-equilibrium steady-state with a non-zero probability current possessing a non-zero curl. This implies that if the particles were to have a finite-size and therefore a rotational degree of freedom, they would experience a torque generated by the non-zero local curl and spin around their geometric centers, like ‘spinning top’ toys. Our analysis shows that the spinning motion is correlated and also reveals an emerging cooperative behavior of the spatial components of the probability currents of dissimilar species.

Spherically symmetric stationary flows of a rarefied two-phase fluid

The spherically symmetric stationary flows of isothermal rarefied two-phase fluid are studied. The results of the research give a qualitative description such flows for arbitrary positive initial data. Namely, for arbitrary positive initial velocities and densities of the first and the second phase, which are set at the initial sphere of arbitrary radius, the obtained phase portrait gives a qualitative description of the distribution of characteristics at the spheres of other radii. A classification of all possible types of spherically symmetric stationary flows of isothermal two-phase fluid in a case of the spread of a substance has been carried out. In the work it is also described a bifurcation of a dynamical system. As a result of this bifurcation, some attracting set appears at the curve of singular points. The emergence of this set greatly changes a quantity of the types of two-phase flows. Another result of the study is a description of all types of continuous transonic spherically symmetric stationary flows at the investigating model of two-phase fluid. The study showed that if the ratio of the flows of the first and second phases through an initial sphere is bigger than 8, then there is a non-zero probability of a realization in two-phase fluid dynamics a continuous transition from supersonic mode to subsonic mode. There have been carried out different numerical experiments, which are illustrated the obtained results.

Piecewise-Tunneled Captive Processes and Corridored Random Particle Systems

We introduce a family of processes that generalises captive diffusions, whereby the stochastic evolution that remains within a pair of time-dependent boundaries can further be piecewise-tunneled internally. The tunneling effect on the dynamics can be random such that the process has non-zero probability to find itself within any possible tunnel at any given time. We study some properties of these processes and apply them in modelling corridored random particles that can be observed in fluid dynamics and channeled systems. We construct and simulate mean-reverting piecewise-tunneled captive models for demonstration. We also propose a doubly-stochastic system in which the tunnels themselves are generated randomly by another stochastic process that jumps at random times.

Investigation of the shocked Viñales ordinary chondrite (L6) meteorite fall – Implications for shock classification, fragmentation, and collision dynamics

The effects of collisions on the evolution of asteroids, ranging from local fracturing to brecciation or even to catastrophic disruption, depend primarily on the encounter velocities. Here we present a refined view of the mineralogy and texture of the recent fall Viñales, an L6 ordinary chondrite meteorite. It preserves features that require at least one energetic impact, including numerous shock melt veins of variable thickness. We report the identification of two high-pressure phases, majorite and albitic jadeite, limited to just one of these shock melt veins. Viñales is a moderately shocked sample, shock stage S4, that experienced a complex and spatially variable pressure-temperature-time history with a low (but non-zero) probability of preservation of high-pressure phases.

On a Class of Harko-Kovacs-Lobo Wormholes

The Harko, Kovács, and Lobo wormhole (HKLWH) metric contains two free parameters: one is the wormhole throat r0, and the other is a dimensionless deviation parameter γ with values 0<γ<1, the latter ensuring the needed violation of the null energy condition at the throat. In this paper, we study the energetics of the HKLWH and the influence of γ on the tidal forces in the Lorentz-boosted frame. Finally, we apply a new concept, namely, the probabilistic identity of the object observed by different external observers in terms of the Fresnel coefficients derived by Tangherlini. The intriguing result is that observations can differ depending on the location of the observer, i.e., there is a nonzero probability that the HKLWH will be identified as a black hole even when γ≠0.

Stranger than we can imagine: the possibility and potential significance of non-human forms of consciousness and wellbeing

ABSTRACT Recent decades have seen a flourishing of scholarship on wellbeing. Looking ahead, the next frontier may be engaging with the possibility of non-human forms of wellbeing. This paper reviews various candidates for what these forms may be, focusing on entities that are living and potentially capable of conscious experience. However, what makes this topic so complex and fascinating is that what exactly constitutes life or conscious experience is not self-evident. Thus, this paper considers various potential life forms – which vary in the extent to which they challenge standard conceptions of life – including organic life forms on earth, matter, AI, and extra-terrestrial beings. Some possibilities are unlikelier and more speculative than others, but all have arguably a non-zero probability, so merit at least some consideration and attention. Moreover, these possibilities have considerable relevance for human wellbeing, and so warrant the attention of wellbeing scholars.

Robotic observation pipeline for small bodies in the solar system based on open-source software and commercially available telescope hardware

The observation of small bodies in the Space Environment is an ongoing important task in astronomy. While nowadays new objects are mostly detected in larger sky surveys, several follow-up observations are usually needed for each object to improve the accuracy of orbit determination. In particular objects orbiting close to Earth, so called Near-Earth Objects (NEOs) are of special concern as a small but not negligible fraction of them can have a non-zero impact probability with Earth. Additionally, the observation of manmade space debris and tracking of satellites falls in the same class measurements. Telescopes for these follow-up observations are mainly in a aperture class between 1 m down to approximately 25 cm. These telescopes are often hosted by amateur observatories or dedicated companies like 6ROADS specialized on this type of observation. With upcoming new NEO search campaigns by very wide field of view telescopes, like the Vera C. Rubin Observatory, NASA’s NEO surveyor space mission and ESA’s Flyeye telescopes, the number of NEO discoveries will increase dramatically. This will require an increasing number of useful telescopes for follow-up observations at different geographical locations. While well-equipped amateur astronomers often host instruments which might be capable of creating useful measurements, both observation planning and scheduling, and also analysis are still a major challenge for many observers. In this work we present a fully robotic planning, scheduling and observation pipeline that extends the widely used open-source cross-platform software KStars/Ekos for Instrument Neutral Distributed Interface (INDI) devices. The method consists of algorithms which automatically select NEO candidates with priority according to ESA’s Near-Earth Object Coordination Centre (NEOCC). It then analyses detectable objects (based on limiting magnitudes, geographical position, and time) with preliminary ephemeris from the Minor Planet Center (MPC). Optimal observing slots during the night are calculated and scheduled. Immediately before the measurement the accurate position of the minor body is recalculated and finally the images are taken. Besides the detailed description of all components, we will show a complete robotic hard- and software solution based on our methods.

Rational Origins of Revisionist War

Abstract The rise of China has returned attention to the links between power transitions and war. In this literature, three different causal mechanisms can be confused. This essay disentangles them. Power transitions can lead to three kinds of war: preventive, accidental, and revisionist. Formal models tend to study the first, in which a declining state tries to delay or prevent a rival’s ascent. However, major wars during great power transitions are usually initiated by the rising state, not the declining one. To describe these historical cases, less formal theories, especially neorealism and neoclassical realism, focus on accidental and revisionist wars, but these theories tend to fall back on nonrational mechanisms to connect changing power to the risk of conflict. This leaves a theoretical gap: Why would a rising, rational actor deliberately choose conflict, i.e., start a revisionist war? To suggest an answer, this essay demonstrates how a simple change in standard bargaining models—incorporating a nonzero probability of indecisive war—can ground realist intuitions on rationalist foundations. It further shows how this change leads immediately to an intuitive, formal definition of stability that aligns naturally with existing informal work. Then, contrary to existing realist theory, it shows why the rigorous analysis of realist assumptions leads to a nonmonotonic relationship between the offense/defense balance and war. It thus uses realism to inform and potentially redirect formal scholarship; it also uses formal scholarship to sharpen the logical foundations of realism and, in so doing, derive novel empirical predictions. The essay concludes by applying this synthesis to the rise of China today and indicating directions for deepening the formal/realist synthesis.

On Wendel’s equality for intersections of balls

We study the analogue of Wendel’s equality in random polytope models in which the hull of the random points is formed by intersections of congruent balls, called the spindle (or hyper-) convex hull. According to the classical identity of Wendel the probability that the origin is contained in the (linear) convex hull of n i.i.d. random points distributed according to an origin symmetric probability distribution in the d-dimensional Euclidean space mathbb {R}^{d} that assigns measure zero to hyperplanes is a constant depending only on n and d. While in the classical convex case one gets nonzero probabilities only for nge d+1 points in mathbb {R}^{d}, for the spindle convex hull this happens for all nge 2. We study this question for the uniform and normally distributed random models.

Entanglement harvesting between two inertial Unruh-DeWitt detectors from nonvacuum quantum fluctuations

Entanglement harvesting from the quantum field is a well-known fact that, in recent times, is being rigorously investigated further in flat and different curved backgrounds. The usually understood formulation studies the possibility of two uncorrelated Unruh-DeWitt detectors getting entangled over time due to the effects of quantum vacuum fluctuations. Our current work presents a thorough formulation to realize the entanglement harvesting from non-vacuum background fluctuations. In particular, we further consider single excitation field states and a pair of inertial detectors, respectively, in $(1+1)$ and $(1+3)$ dimensions for this investigation. Our main observation asserts that entanglement harvesting is suppressed compared to the vacuum fluctuations in this situation. Our other observations confirm a non-zero individual detector transition probability in this background and vanishing entanglement harvesting for parallel co-moving detectors. We look into the characteristics of the harvested entanglement and discuss its dependence on different system parameters.

Mobile Collaborative Secrecy Performance Prediction for Artificial IoT Networks

The integration of artificial intelligence and Internet of Things (IoT) has promoted the rapid development of artificial IoT (AIoT) networks. A wide range of AIoT applications have generated a great deal of data. The fifth-generation (5G) mobile communication has powerful data processing capabilities, and it is a key technology to enable AIoT big data processing. The explosive growth of the 5G users has made information security in AIoT networks a significant issue. Real-time security evaluation in AIoT networks is difficult due to user mobility and dynamic wireless environments. Thus, the evaluation and prediction of secrecy performance is a very critical research. In this article, new expressions for the nonzero secrecy capacity probability (NSCP) are derived to evaluate the mobile collaborative secrecy performance. An improved convolutional neural network (CNN) model, named as SI-CNN in this article, is proposed to predict the NSCP performance. The SI-CNN model combines the SqueezeNet and InceptionNet, and it has four convolution layers, which all adopt the same convolution model. For the first two layers, they employ a 2 × 1 convolution and a three-branch convolution, which not only increase the number of channels but also extract more features. For the last two layers, they employ the same structure, but different convolution kernels. The proposed SI-CNN prediction algorithm is shown to provide better NSCP performance prediction than other state-of-the-art methods. In particular, compared with wavelet neural network, the prediction precision of SI-CNN is improved by 26.8%.

Using quantum amplitude amplification in genetic algorithms

The selection mechanism of genetic algorithms can play a key role in leading the optimization process towards suitable solutions of a given problem, as their application can affect the trade-off between exploration and exploitation. However, some selection operators suffer from an excessive exploitation that may lead to the loss of population diversity and to a premature convergence, and others present an excessive exploration that may cause genetic algorithms to produce poor results near to random. As a consequence, there is a strong need to rethink how a mating pool is created and introduce alternative approaches to genetic selection. In this paper, a quantum algorithm, named Quantum Genetic Sampling (QGS), has been designed to replace selection operators so as to provide an increased population diversity in genetic evolution and reduce the possibility that the optimization process converge to low quality solutions. The proposed approach is based on two sequential steps. In the first step, QGS models a problem’s search space through a quantum state, where each quantum basis state is related to a possible solution of the problem. In the second step, QGS uses quantum amplitude amplification to properly adjust the probability of measuring an individual and placing it in the mating pool according to its fitness value. Unlike conventional selection operators, the quantum mechanical nature of the proposed approach allows for a non-zero probability of introducing new genetic material into the mating pool. Experiments based on well-known benchmark functions show the suitability of the proposed quantum operator for embedding in genetic algorithms, both in terms of accuracy and population diversity.

A Classical Search Game in Discrete Locations

Consider a two-person zero-sum search game between a hider and a searcher. The hider hides among n discrete locations, and the searcher successively visits individual locations until finding the hider. Known to both players, a search at location i takes ti time units and detects the hider—if hidden there—independently with probability [Formula: see text] for [Formula: see text]. The hider aims to maximize the expected time until detection, whereas the searcher aims to minimize it. We prove the existence of an optimal strategy for each player. In particular, any optimal mixed hiding strategy hides in each location with a nonzero probability, and there exists an optimal mixed search strategy that can be constructed with up to n simple search sequences. Funding: This work was supported by the Engineering and Physical Sciences Research Council [Grant EP/L015692/1] STOR-i Centre for Doctoral Training.

Temporally auto-correlated predator attacks structure ecological communities.

For species primarily regulated by a common predator, the P* rule of Holt & Lawton (Holt & Lawton, 1993. Am. Nat. 142, 623–645. (doi:10.1086/285561)) predicts that the prey species that supports the highest mean predator density (P*) excludes the other prey species. This prediction is re-examined in the presence of temporal fluctuations in the vital rates of the interacting species including predator attack rates. When the fluctuations in predator attack rates are temporally uncorrelated, the P* rule still holds even when the other vital rates are temporally auto-correlated. However, when temporal auto-correlations in attack rates are positive but not too strong, the prey species can coexist due to the emergence of a positive covariance between predator density and prey vulnerability. This coexistence mechanism is similar to the storage effect for species regulated by a common resource. Negative or strongly positive auto-correlations in attack rates generate a negative covariance between predator density and prey vulnerability and a stochastic priority effect can emerge: with non-zero probability either prey species is excluded. These results highlight how temporally auto-correlated species’ interaction rates impact the structure and dynamics of ecological communities.

Reaching Long-Term Stability in CP-ϕOTDR

Distributed Acoustic Sensing (DAS) based on coherent reflectometry with chirped pulses (CP-ϕOTDR) is a recent, yet widely recognized technique in providing spatially-resolved distributed measurements of certain physical quantities over the length of an optical fiber. Any given perturbation along the cable can be retrieved as a local temporal shift of the backscattered optical power trace, and recovered using sequential trace-to-trace correlations. However, as a technique that relies on a General Cross-correlation (GCC) estimation function, it displays a non-zero probability of obtaining anomalous estimations, which can fundamentally limit the long-term performance. Furthermore, some demonstrated strategies proposed to mitigate this effect can directly lead to the emergence of cumulative errors, which become as critical as the measurement time increases. Here, we analyze the errors affecting the long-term stability in CP-ϕOTDR systems, and we propose several strategies and processing methods to mitigate their effect. We demonstrate a ∼3 mK error after a one-month continuous temperature experiment performed to a SMF, reaching unprecedented temperature stability in CP-ϕOTDR systems with important implications in emerging fields such as DAS seismology or oceanography.

Light Isotope Separation through the Compound Membrane of Graphdiyne

The separation of isotopes of one substance is possible within the framework of the quantum mechanical model. The tunneling effect allows atoms and molecules to overcome the potential barrier with a nonzero probability. The membranes of two monoatomic layers enhance the differences in the components’ passage through the membrane, thereby providing a high separation degree of mixtures. The probability of overcoming the potential barrier by particles is found from the solving of the Schrödinger integral equation. Hermite polynomials are used to expand all the terms of the Schrödinger integral equation in a series to get a wave function. A two-layer graphdiyne membrane is used to separate the mixture.