Modeling, Analysis, and Hard Real-time Scheduling of Adaptive Streaming Applications

In real-time systems, the application's behavior has to be predictable at compile-time to guarantee timing constraints. However, modern streaming applications which exhibit adaptive behavior due to mode switching at run-time, may degrade system predictability due to unknown behavior of the application during mode transitions. Therefore, proper temporal analysis during mode transitions is imperative to preserve system predictability. To this end, in this paper, we initially introduce Mode Aware Data Flow (MADF) which is our new predictable Model of Computation (MoC) to efficiently capture the behavior of adaptive streaming applications. Then, as an important part of the operational semantics of MADF, we propose the Maximum-Overlap Offset (MOO) which is our novel protocol for mode transitions. The main advantage of this transition protocol is that, in contrast to self-timed transition protocols, it avoids timing interference between modes upon mode transitions. As a result, any mode transition can be analyzed independently from the mode transitions that occurred in the past. Based on this transition protocol, we propose a hard real-time analysis as well to guarantee timing constraints by avoiding processor overloading during mode transitions. Therefore, using this protocol, we can derive a lower bound and an upper bound on the earliest starting time of the tasks in the new mode during mode transitions in such a way that hard real-time constraints are respected.Comment: Accepted for presentation at EMSOFT 2018 and for publication in IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD) as part of the ESWEEK-TCAD special issu

Characteristics of temporal fluctuations in the hyperpolarized state of the cortical slow oscillation

We present evidence for the hypothesis that transitions between the low- and high-firing states of the cortical slow oscillation correspond to neuronal phase transitions. By analyzing intracellular recordings of the membrane potential during the cortical slow oscillation in rats, we quantify the temporal fluctuations in power and the frequency centroid of the power spectrum in the period of time before “down” to “up” transitions. By taking appropriate averages over such events, we present these statistics as a function of time before transition. The results demonstrate an increase in fluctuation power and time scale broadly consistent with the slowing of systems close to phase transitions. The analysis is complicated and limited by the difficulty in identifying when transitions begin, and removing dc trends in membrane potential

Testing Homogeneity of Time-Continuous Rating Transitions

Banks could achieve substantial improvements of their portfolio credit risk assessment by estimating rating transition matrices within a time-continuous Markov model, thereby using continuous-time rating transitions provided by internal rating systems instead of discrete-time rating information. A non-parametric test for the hypothesis of time-homogeneity is developed. The alternative hypothesis is multiple structural change of transition intensities, i.e. time-varying transition probabilities. The partial-likelihood ratio for the multivariate counting process of rating transitions is shown to be asymptotically c2 -distributed. A Monte Carlo simulation finds both size and power to be adequate for our example. We analyze transitions in credit-ratings in a rating system with 8 rating states and 2743 transitions for 3699 obligors observed over seven years. The test rejects the homogeneity hypothesis at all conventional levels of significance. --Portfolio credit risk,Rating transitions,Markov model,time-homogeneity,partial likelihood

Dynamical quantum phase transitions in discrete time crystals

Discrete time crystals are related to non-equilibrium dynamics of periodically driven quantum many-body systems where the discrete time translation symmetry of the Hamiltonian is spontaneously broken into another discrete symmetry. Recently, the concept of phase transitions has been extended to non-equilibrium dynamics of time-independent systems induced by a quantum quench, i.e. a sudden change of some parameter of the Hamiltonian. There, the return probability of a system to the ground state reveals singularities in time which are dubbed dynamical quantum phase transitions. We show that the quantum quench in a discrete time crystal leads to dynamical quantum phase transitions where the return probability of a periodically driven system to a Floquet eigenstate before the quench reveals singularities in time. It indicates that dynamical quantum phase transitions are not restricted to time-independent systems and can be also observed in systems that are periodically driven. We discuss how the phenomenon can be observed in ultra-cold atomic gases.Comment: version accepted for publication in Physical Review A (9 pages, 3 figs

Theory for transitions between log and stationary phases: universal laws for lag time

Quantitative characterization of bacterial growth has gathered substantial attention since Monod's pioneering study. Theoretical and experimental work has uncovered several laws for describing the log growth phase, in which the number of cells grows exponentially. However, microorganism growth also exhibits lag, stationary, and death phases under starvation conditions, in which cell growth is highly suppressed, while quantitative laws or theories for such phases are underdeveloped. In fact, models commonly adopted for the log phase that consist of autocatalytic chemical components, including ribosomes, can only show exponential growth or decay in a population, and phases that halt growth are not realized. Here, we propose a simple, coarse-grained cell model that includes inhibitor molecule species in addition to the autocatalytic active protein. The inhibitor forms a complex with active proteins to suppress the catalytic process. Depending on the nutrient condition, the model exhibits the typical transition among the lag, log, stationary, and death phases. Furthermore, the lag time needed for growth recovery after starvation follows the square root of the starvation time and is inverse to the maximal growth rate, in agreement with experimental observations. Moreover, the distribution of lag time among cells shows an exponential tail, also consistent with experiments. Our theory further predicts strong dependence of lag time upon the speed of substrate depletion, which should be examined experimentally. The present model and theoretical analysis provide universal growth laws beyond the log phase, offering insight into how cells halt growth without entering the death phase.Comment: 17 pages, 5 figure

Quantum transitions induced by the third cumulant of current fluctuations

We investigate the transitions induced by external current fluctuations on a small probe quantum system. The rates for the transitions between the energy states are calculated using the real-time Keldysh formalism for the density matrix evolution. We especially detail the effects of the third cumulant of current fluctuations inductively coupled to a quantum bit and propose a setup for detecting the frequency-dependent third cumulant through the transitions it induces.Comment: 4 pages, 3 figure

Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions

We introduce and study a class of particle hopping models consisting of a single box coupled to a pair of reservoirs. Despite being zero-dimensional, in the limit of large particle number and long observation time, the current and activity large deviation functions of the models can exhibit symmetry-breaking dynamical phase transitions. We characterize exactly the critical properties of these transitions, showing them to be direct analogues of previously studied phase transitions in extended systems. The simplicity of the model allows us to study features of dynamical phase transitions which are not readily accessible for extended systems. In particular, we quantify finite-size and finite-time scaling exponents using both numerical and theoretical arguments. Importantly, we identify an analogue of critical slowing near symmetry breaking transitions and suggest how this can be used in the numerical studies of large deviations. All of our results are also expected to hold for extended systems.Comment: 34 pages, 6 figure

Accurate estimations of circumstellar and interstellar lines of quadruply ionized vanadium using the coupled cluster approach

Accurate {\it ab initio} calculations have been carried out to study the valence electron removal energies and oscillator strengths of astrophysically important electromagnetic transitions of quadruply ionized vanadium, $V^{4+}$. Many important electron correlations are considered to all-orders using the relativistic coupled-cluster theory. Calculated ionization potentials and fine structure splittings are compared with the experimental values, wherever available. To our knowledge, oscillator strengths of electric dipole transitions are predicted for the first time for most of the transitions. The transitions span in the range of ultraviolet, visible and near infrared regions and are important for astrophysical observations.Comment: Submitted in Astrophysical

Dynamical quantum phase transitions: a brief survey

Nonequilibrium states of closed quantum many-body systems defy a thermodynamic description. As a consequence, constraints such as the principle of equal a priori probabilities in the microcanonical ensemble can be relaxed, which can lead to quantum states with novel properties of genuine nonequilibrium nature. In turn, for the theoretical description it is in general not sufficient to understand nonequilibrium dynamics on the basis of the properties of the involved Hamiltonians. Instead it becomes important to characterize time-evolution operators which adds time as an additional scale to the problem. In these Perspectives we summarize recent progress in the field of dynamical quantum phase transitions, which are phase transitions in time with temporal nonanalyticities in matrix elements of the time-evolution operator. These transitions are not driven by an external control parameter, but rather occur due to sharp internal changes generated solely by unitary real-time dynamics. We discuss the obtained insights on general properties of dynamical quantum phase transitions, their physical interpretation, potential future research directions, as well as recent experimental observations.Comment: 7 pages, 4 figure