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Time series data are collected in temporal order and are widely used to train systems for prediction, modeling and classification to name a few. These systems require large amounts of data to improve generalization and prevent over-fitting. However there is a comparative lack of time series data due to operational constraints. This situation is alleviated by synthesizing data which have a suitable spread of features yet retain the distinctive features of the original data. These would be its basic statistical properties and overall shape which are important for short time series such as in rehabilitative applications or in quickly changing portions of lengthy data. In our earlier work synthesized surrogate time series were used to augment rehabilitative data. This gave good results in classification but the resulting waveforms did not preserve the original signal shape. To remedy this, we use singular spectrum analysis (SSA) to separate a signal into trends and cycles to describe the shape of the signal and low level components. In a novel way we subject the low level component to randomizing processes then recombine this with the original trend and cycle components to form a synthetic time series. We compare our approach with other methods, using statistical and shape measures and demonstrate its effectiveness in classification., Comment: This version of the paper under the same title, acknowledges the data source and the funding for current research using this data. arXiv admin note: substantial text overlap with arXiv:2404.14211

We study the Casimir-Lifshitz force (CLF) between a gold plate and a graphene-covered dielectric grating. Using a scattering matrix (S-matrix) approach derived from the Fourier Modal Method (FMM), we find a significant enhancement in the CLF as compared to a mere dielectric slab coated with graphene, over a wide range of temperatures. Additionally, we demonstrate that the CLF depends strongly on the chemical potential of graphene, with maximal effects observed at lower filling fractions. Finally, we analyse the Casimir force gradient between a gold sphere and a graphene-coated dielectric grating, highlighting potential avenues for experimental measurements., Comment: 11 pages, 10 figures

We present a method to stabilize the frequency of self-sustained vibrations in micro- and nanomechanical resonators. The method refers to a two-mode system with the vibrations at significantly different frequencies. The signal from one mode is used to control the other mode. In the experiment, self-sustained oscillations of micromechanical modes are excited by pumping at the blue-detuned sideband of the higher-frequency mode. Phase fluctuations of the two modes show near perfect anti-correlation. They can be compensated in either one of the modes by a stepwise change of the pump phase. The phase change of the controlled mode is proportional to the pump phase change, with the proportionality constant independent of the pump amplitude and frequency. This finding allows us to stabilize the phase of one mode against phase diffusion using the measured phase of the other mode. We demonstrate that phase fluctuations of either the high or low frequency mode can be significantly reduced. The results open new opportunities in generating stable vibrations in a broad frequency range via parametric downconversion in nonlinear resonators.

Time series (TS) data have consistently been in short supply, yet their demand remains high for training systems in prediction, modeling, classification, and various other applications. Synthesis can serve to expand the sample population, yet it is crucial to maintain the statistical characteristics between the synthesized and the original TS : this ensures consistent sampling of data for both training and testing purposes. However the time domain features of the data may not be maintained. This motivates for our work, the objective which is to preserve the following features in a synthesized TS: its fundamental statistical characteristics and important time domain features like its general shape and prominent transients. In a novel way, we first isolate important TS features into various components using a spectrogram and singular spectrum analysis. The residual signal is then randomized in a way that preserves its statistical properties. These components are then recombined for the synthetic time series. Using accelerometer data in a clinical setting, we use statistical and shape measures to compare our method to others. We show it has higher fidelity to the original signal features, has good diversity and performs better data classification in a deep learning application.

Asymmetric Ising model, in which coupled spins affect each other differently, plays an important role in diverse fields, from physics to biology to artificial intelligence. We show that coupled parametric oscillators provide a well-controlled and fully characterizable physical system to implement the model. Such oscillators are bistable. The coupling changes the rate of interstate switching of an oscillator depending on the state of other oscillators. Our experiment on two coupled micromechanical resonators reveals unusual features of asymmetric Ising systems, including the onset of a probability current that circulates in the stationary state. We relate the asymmetry to the exponentially strong effect of a periodic force on the switching rates of an individual parametric oscillator, which we measure. Our findings open the possibilities of constructing and exploring asymmetric Ising systems with controlled parameters and connectivity.

We investigate the Casimir-Lifshitz force (CLF) between two identical graphene strip gratings, laid on finite dielectric substrates, by using the scattering matrix (S-matrix) approach derived from the Fourier Modal Method with Local Basis Functions (FMM-LBF). We fully take into account the high-order electromagnetic diffractions, the multiple scattering and the exact 2D feature of the graphene strips. We show that the non-additivity, which is one of the most interesting features of the CLF in general, is significantly high and can be modulated in situ, without any change in the actual material geometry and this by varying the graphene chemical potential. We discuss the nature of the geometrical effects and show the relevance of the geometric parameter d/D (i.e. the ratio between separation and grating period), which allows to explore the regions of parameters where the additive result is fully acceptable or where the full calculation is needed. This study can open to deeper experimental exploration of the non-additive features of the CLF with micro- or nano-electromechanical graphene-based systems., Comment: 11 pages, 6 figures

We study the non equilibrium Casimir-Lifshitz force between graphene-based parallel structures held at different temperatures and in presence of an external thermal bath at a third temperature. The graphene conductivity, which is itself a function of temperature, as well as of chemical potential, allows us to tune in situ the Casimir-Lifshitz force. We explore different non equilibrium configurations while considering different values of the graphene chemical potential. Particularly interesting cases are investigated, where the force can change sign going from attractive to repulsive or where the force becomes non monotonic with respect to chemical potential variations, contrary to the behaviour under thermal equilibrium., Comment: 10 pages, 18 figures

In this work we demonstrate that ultra-thin (5 and 15 nm) MgO transmission dynodes (tynodes) with sufficient high transmission electron yield (TEY) can be constructed. These tynodes act as electron amplification stages in a novel vacuum electron multiplier: the Timed Photon Counter (TiPC). The ultra-thin membranes with a diameter of 30 {\mu}m are arranged in a square 64-by-64-array. The TEY was determined with a scanning electron microscope (SEM) using primary electrons with primary energies of 0.75 - 5 keV. The method allow us to make a TEY map of the surface while simultaneously imaging the surface. The TEY of individual membranes can be extracted from the TEY map. An averaged maximum TEY of 4.6 +/- 0.2 was achieved by using 1.35 keV primary electrons on a TiN/MgO bi-layer membrane with a layer thickness of 2 and 5 nm, respectively. The TiN/MgO membrane with a layer thickness of 2 and 15 nm, respectively, has a maximum TEY of 3.3 +/- 0.1 (2.35 keV). Furthermore, the effect of the electric field strength on transmission (secondary) electron emission was investigated by placing the emission surface of a tynode in close proximity to a planar collector. By increasing the electric potential between the tynode and the collector, from -50 V to -100 V, the averaged maximum TEY improved from 4.6 +/- 0.2 to 5.0 +/- 0.3 at a primary energy of 1.35 keV with an upper limit of 5.5 on one of the membranes.

A microelectromechanical oscillator with a 0.73 $\mu$m gap structure is employed to probe the surface Andreev bound states in superfluid $^3$He-B. The surface specularity of the oscillator is increased by preplating it with 1.6 monolayers of $^4$He. In the linear regime, the temperature dependence of the damping coefficient is measured at various pressures, and the normalized energy gap is extracted. The damping coefficient increases after preplating at lower pressures, which is attributed to the decreased energy minigap of the surface bound states. The device is also driven into the nonlinear regime, where the temperature independent critical velocity at each pressure is measured. The critical velocity is observed to increase after preplating at all pressures, which might be related to the increased average energy gap. The observed behavior warrants a microscopic theory beyond a single parameter characterization of the surface., Comment: 10 pages, 15 figures, to be submitted to Physical Review B

Have you ever thought that you can be an intelligent painter? This means that you can paint a picture with a few expected objects in mind, or with a desirable scene. This is different from normal inpainting approaches for which the location of specific objects cannot be determined. In this paper, we present an intelligent painter that generate a person's imaginary scene in one go, given explicit hints. We propose a resampling strategy for Denoising Diffusion Probabilistic Model (DDPM) to intelligently compose unconditional harmonized pictures according to the input subjects at specific locations. By exploiting the diffusion property, we resample efficiently to produce realistic pictures. Experimental results show that our resampling method favors the semantic meaning of the generated output efficiently and generates less blurry output. Quantitative analysis of image quality assessment shows that our method produces higher perceptual quality images compared with the state-of-the-art methods., Comment: ICIP 2023

The SoccerNet 2022 challenges were the second annual video understanding challenges organized by the SoccerNet team. In 2022, the challenges were composed of 6 vision-based tasks: (1) action spotting, focusing on retrieving action timestamps in long untrimmed videos, (2) replay grounding, focusing on retrieving the live moment of an action shown in a replay, (3) pitch localization, focusing on detecting line and goal part elements, (4) camera calibration, dedicated to retrieving the intrinsic and extrinsic camera parameters, (5) player re-identification, focusing on retrieving the same players across multiple views, and (6) multiple object tracking, focusing on tracking players and the ball through unedited video streams. Compared to last year's challenges, tasks (1-2) had their evaluation metrics redefined to consider tighter temporal accuracies, and tasks (3-6) were novel, including their underlying data and annotations. More information on the tasks, challenges and leaderboards are available on https://www.soccer-net.org. Baselines and development kits are available on https://github.com/SoccerNet., Comment: Accepted at ACM MMSports 2022

Efficient energy transfer often occurs between oscillation modes in a resonator when they are tuned to internal resonance. We design the eigenfrequencies of two vibrational modes of an electromechanical resonator to be close to a ratio of 3:1 and demonstrate that the energy supplied to the upper mode can be controllably transferred to the lower mode. With the lower mode vibrating with a period tripled that of the upper mode, the discrete time-translation symmetry imposed by the periodic drive is broken. The lower mode settles into one of three stable period-tripled states with different phases. This channel for energy transfer from the upper mode can be turned on or off without changing system parameters. When the upper mode itself becomes multistable under strong resonant or parametric drive, additional sets of coexisting period-tripled states emerge in the lower mode. In the latter case, we measure a total of 6 coexisting vibration states with identical amplitude but phases differing by $\pi$/3. Excitation of coexisting states with three different phases could open new opportunities in designing mechanical memory based on ternary logic. Coupled resonators with period-tripled states can also be used to model complex interacting systems with spin equals one.

Periodic variables illuminate the physical processes of stars throughout their lifetime. Wide-field surveys continue to increase our discovery rates of periodic variable stars. Automated approaches are essential to identify interesting periodic variable stars for multi-wavelength and spectroscopic follow-up. Here, we present a novel unsupervised machine learning approach to hunt for anomalous periodic variables using phase-folded light curves presented in the Zwicky Transient Facility Catalogue of Periodic Variable Stars by \citet{Chen_2020}. We use a convolutional variational autoencoder to learn a low dimensional latent representation, and we search for anomalies within this latent dimension via an isolation forest. We identify anomalies with irregular variability. Most of the top anomalies are likely highly variable Red Giants or Asymptotic Giant Branch stars concentrated in the Milky Way galactic disk; a fraction of the identified anomalies are more consistent with Young Stellar Objects. Detailed spectroscopic follow-up observations are encouraged to reveal the nature of these anomalies., Comment: 26 pages, 17 figures. The full version of Table 4 and Table 5 are available upon request

The periodic pulsations of stars teach us about their underlying physical process. We present a convolutional autoencoder-based pipeline as an automatic approach to search for out-of-distribution anomalous periodic variables within The Zwicky Transient Facility Catalog of Periodic Variable Stars (ZTF CPVS). We use an isolation forest to rank each periodic variable by its anomaly score. Our overall most anomalous events have a unique physical origin: they are mostly highly variable and irregular evolved stars. Multiwavelength data suggest that they are most likely Red Giant or Asymptotic Giant Branch stars concentrated in the Milky Way galactic disk. Furthermore, we show how the learned latent features can be used for the classification of periodic variables through a hierarchical random forest. This novel semi-supervised approach allows astronomers to identify the most anomalous events within a given physical class, significantly increasing the potential for scientific discovery., Comment: 7 pages, 4 figures

The discoveries of anomalous compact objects challenge our understanding of the standard theory of stellar structures and evolution. They serve as an excellent laboratory to search for new physics. Earlier studies on spherically symmetric dark matter-admixed compact stars could explain a handful of anomalies. In this paper, we investigate the observational signatures of dark matter (DM)-admixed rotating white dwarfs and make connections to observed peculiar white dwarfs. We compute the equilibrium structures of DM-admixed rotating white dwarfs using a self-consistent, two-fluid method, with the DM component being a non-rotating degenerate fermi gas. We find that the admixture of DM in rotating white dwarfs could: (1) account for some peculiar white dwarfs that do not follow their usual mass-radius relation, (2) allow the existence of stable, rapid-rotating white dwarfs that are free from thermonuclear runaway, which could explain some anomalous x-ray pulsars/soft gamma-ray repeaters, and (3) produce universal $I$ (moment of inertia)-Love (tidal Love number)-$Q$ (quadrupole moment) relations that span bands above those without DM admixture, thus providing an indirect way to search for DM in white dwarfs through gravitational-wave detection. DM-admixed rotating white dwarfs can account for some peculiar compact objects. Our results suggest a systematic approach to account for unusual compact objects that could be discovered by upcoming surveys., Comment: Accepted for publications. 18 pages, 11 figures

A unified treatment of CP physics for quarks and leptons in the framed standard model (FSM) is extended to include the predicted hidden sector giving as consequences: (i) that an earlier part-estimate of the Jarlskog invariant $J'$ for leptons is turned into a prediction for its actual value, i.e., $J' \sim -0.012$ ($\delta'_{CP} \sim 1.11 \pi$), which is of the right order of magnitude, of the right sign, and in the range of values favoured by present experiment, (ii) some novel twists to the effects of CP-violation on the material content of the universe.

Underneath the ear skin there are richly branching vascular and neural networks that ultimately connecting to our heart and brain. Hence, the three-dimensional (3D) mapping of auricular electrophysiological signals could provide a new perspective for biomedical studies such as diagnosis of cardiovascular diseases and neurological disorders. However, it is still extremely challenging for current sensing techniques to cover the entire ultra-curved auricle. Here, we report a graphene-based ear-conformable sensing device with embedded and distributed 3D electrodes which enable full-auricle physiological monitoring. The sensing device, which incorporates programable 3D electrode thread array and personalized auricular mold, has 3D-conformable sensing interfaces with curved auricular skin, and was developed using one-step multi-material 3D-printing process. As a proof-of-concept, spatiotemporal auricular electrical skin resistance (AESR) mapping was demonstrated. For the first time, 3D AESR contours were generated and human subject-specific AESR distributions among a population were observed. From the data of 17 volunteers, the auricular region-specific AESR changes after cycling exercise were observed in 98% of the tests and were validated via machine learning techniques. Correlations of AESR with heart rate and blood pressure were also studied using statistical analysis. This 3D electronic platform and AESR-based new biometrical findings show promising biomedical applications., Comment: 23 pages, 6 figures

We present simulations of thermonuclear supernovae admixed with an extended component of fermionic cold dark matter. We consider the explosion of a Chandrasekhar-mass white dwarf using the deflagration model with deflagration-detonation transition with spherical symmetry. The dark matter component is comparable in size with that of the normal matter, and so the system is described by two-fluid, one-dimensional Eulerian hydrodynamics. The explosion leaves all the dark matter trapped as a remnant compact dark star in all of our considered models. The presence of dark matter lengthens the deflagration phase to produce more thermo-neutrinos and similar amounts of iron-group elements compared to those of ordinary explosions with no dark matter admixture. The dark matter admixed models produce dimmer and broader light curves, which challenge the role of thermonuclear supernovae as standard candles in cosmic distance measurement. Our results also suggest a formation path of dark compact objects which mimic sub-solar-mass black holes as dark gravitational sources, through near-solar-mass dark matter admixed thermonuclear supernovae., Comment: 17 pages, 17 figures

We measure the transmission secondary electron yield of nanometer-thick Al$_2$O$_3$/TiN/Al$_2$O$_3$ films using a prototype version of a Timed Photon Counter (TiPC). We discuss the method to measure the yield extensively. The yield is then measured as a function of landing energy between $1.2$ and $1.8$ keV and found to be in the range of $0.1$ ($1.2$ keV) to $0.9$ ($1.8$ keV). These results are in agreement to data obtained by a different, independent method. We therefore conclude that the prototype TiPC is able to characterise the thin films in terms of transmission secondary electron yield. Additionally, observed features which are unrelated to the yield determination are interpreted., Comment: This is the Accepted Manuscript version of an article accepted for publication in Journal of Instrumentation. Neither SISSA Medialab Srl nor IOP Publishing Ltd is responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1748-0221/15/10/P10022

Quantum fluctuations give rise to Casimir forces between two parallel conducting plates, the magnitude of which increases monotonically as the separation decreases. By introducing nanoscale gratings to the surfaces, recent advances have opened opportunities for controlling the Casimir force in complex geometries. Here, we measure the Casimir force between two rectangular gratings in regimes not accessible before. Using an on-chip detection platform, we achieve accurate alignment between the two gratings so that they interpenetrate as the separation is reduced. Just before interpenetration occurs, the measured Casimir force is found to have a geometry dependence that is much stronger than previous experiments, with deviations from the proximity force approximation reaching a factor of ~500. After the gratings interpenetrate each other, the Casimir force becomes non-zero and independent of displacement. This work shows that the presence of gratings can strongly modify the Casimir force to control the interaction between nanomechanical components., Comment: 31 pages, 7 figures

Large-area transmission dynodes were fabricated by depositing an ultra-thin continuous film on a silicon wafer with a 3-dimensional pattern. After removing the silicon, a corrugated membrane with enhanced mechanical properties was formed. Mechanical materials, such as this corrugated membrane, are engineered to improve its strength and robustness, which allows it to span a larger surface in comparison to flat membranes while the film thickness remains constant. The ultra-thin film consists of three layers (Al$_2$O$_3$ /TiN/Al$_2$O$_3$) and is deposited by atomic layer deposition (ALD). The encapsulated TiN layer provides in-plane conductivity, which is needed to sustain secondary electron emission. Two types of corrugated membranes were fabricated: a hexagonal honeycomb and an octagonal pattern. The latter was designed to match the square pitch of a CMOS pixel chip. The transmission secondary electron yield was determined with a collector-based method using a scanning electron microscope. The highest transmission electron yield was measured on a membrane with an octagonal pattern. A yield of 2.15 was achieved for 3.15 keV incident electrons for an Al$_2$O$_3$ /TiN/Al$_2$O$_3$ tri-layer film with layer thicknesses of 10/5/15 nm. The variation in yield across the surface of the corrugated membrane was determined by constructing a yield map. The active surface for transmission secondary electron emission is near 100%, i.e. a primary electron generates transmission secondary electrons regardless of the point of impact on the corrugated membrane.

The (secondary) electron emission from multilayered Al$_2$O$_3$/TiN membranes has been investigated with a hemispherical collector system in a scanning electron microscope for electrons with energies between 0.3 and 10 keV. These ultra-thin membranes are designed to function as transmission dynodes in novel vacuum electron multipliers. Two different types, a bi-layer and a tri-layer, have been manufactured by means of atomic-layer deposition (ALD) of aluminum oxide and sputtering of titanium nitride. The reflection and transmission electron yield ($\sigma_R$, $\sigma_T$) have been measured for both types of membranes. In comparison, the tri-layer membranes outperformed the bi-layer membranes in terms of transmission electron yield for films with the same effective thickness. The highest transmission electron yield was measured on an Al$_2$O$_3$/TiN/Al$_2$O$_3$ film with layer thicknesses of 5/2.5/5 nm, which had a maximum transmission electron yield $\sigma_\text{T}^\text{max}(E_0)$ of 3.1 (1.55 keV). Furthermore, the bi-layer membranes have been investigated more in-depth by performing an additional measurement using a positive sample bias to separate the transmitted fraction $\eta_T$ and the transmission secondary electron yield $\delta_T$. The transmitted fraction was used to determine the transmission parameter $p$, which characterizes the interaction of primary electrons (PEs) in thin films. The transmission secondary electron yield was used to compare the energy transfer of PEs in films with different thicknesses.

We report a comprehensive investigation of the effects of quantum turbulence and quantized vorticity in superfluid $^4$He on the motion of a micro-electromechanical systems (MEMS) resonator. We find that the MEMS is uniquely sensitive to quantum turbulence present in the fluid. To generate turbulence in the fluid, a quartz tuning fork (TF) is placed in proximity to the MEMS and driven at large amplitude. We observe that at low velocity, the MEMS is damped by the turbulence, and that above a critical velocity, $v_c \simeq 5\,$mm\,s$^{-1}$, the turbulent damping is greatly reduced. We find that above $v_c$, the damping of the MEMS is reduced further for increasing velocity, indicating a velocity dependent coupling between the surface of the MEMS and the quantized vortices constituting the turbulence. We propose a model of the interaction between vortices in the fluid and the surface of the MEMS. The sensitivity of these devices to a small number of vortices and the almost unlimited customization of MEMS open the door to a more complete understanding of the interaction between quantized vortices and oscillating structures, which in turn provides a new route for the investigation of the dynamics of single vortices., Comment: 14 pages, 10 figures

We develop a protocol for continuous operation of a quantum error correcting code for protection of coherent evolution due to an encoded Hamiltonian against environmental errors, using the three qubit bit flip code and bit flip errors as a canonical example. To detect errors in real time, we filter the output signals from continuous measurement of the error syndrome operators and use a double thresholding protocol for error diagnosis, while correction of errors is done as in the conventional operation. We optimize our continuous operation protocol for evolution under quantum memory and under quantum annealing, by maximizing the fidelity between the target and actual logical states at a specified final time. In the case of quantum memory we show that our continuous operation protocol yields a logical error rate that is slightly larger than the one obtained from using the optimal Wonham filter for error diagnosis. The advantage of our protocol is that it can be simpler to implement. For quantum annealing, we show that our continuous quantum error correction protocol can significantly reduce the final logical state infidelity when the continuous measurements are sufficiently strong relative to the strength of the time-dependent Hamiltonian, and that it can also significantly reduces the run time relative to that of a classical encoding. These results suggest that a continuous implementation is suitable for quantum error correction in the presence of encoded time-dependent Hamiltonians, opening the possibility of many applications in quantum simulation and quantum annealing., Comment: 22 pages, 12 figures

Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors ranging from thermal noise and frequency noise of the resonator to noise in the feedback circuitry. Increasing the vibration amplitude can mitigate some of these effects but the improvements are limited by nonlinearities that are particularly strong for miniaturized micro- and nano-mechanical systems. Here we design a micromechanical resonator with non-monotonic dependence of the frequency of eigenoscillations on energy. Near the extremum, where the dispersion of the eigenfrequency is zero, the system regains certain characteristics of a linear resonator, albeit at large vibration amplitudes. The spectral peak undergoes counter-intuitive narrowing when the noise intensity is increased. With the resonator serving as the frequency determining element in a feedback loop, the phase noise at the extremum amplitude is three times smaller than the conventional nonlinear regime. Zero dispersion phenomena open new opportunities for improving resonant sensors and frequency references.

We study the Casimir torque between two metallic one-dimensional gratings rotated by an angle $\theta$ with respect to each other. We find that, for infinitely extended gratings, the Casimir energy is anomalously discontinuous at $\theta=0$, due to a critical zero-order geometric transition between a 2D- and a 1D-periodic system. This transition is a peculiarity of the grating geometry and does not exist for intrinsically anisotropic materials. As a remarkable practical consequence, for finite-size gratings, the torque per area can reach extremely large values, increasing without bounds with the size of the system. We show that for finite gratings with only 10 period repetitions, the maximum torque is already 60 times larger than the one predicted in the case of infinite gratings. These findings pave the way to the design of a contactless quantum vacuum torsional spring, with possible relevance to micro- and nano-mechanical devices., Comment: 7 pages, 4 figures

Deployment of Network Function Virtualization (NFV) over multiple clouds accentuates its advantages like the flexibility of virtualization, proximity to customers and lower total cost of operation. However, NFV over multiple clouds has not yet attained the level of performance to be a viable replacement for traditional networks. One of the reasons is the absence of a standard based Fault, Configuration, Accounting, Performance and Security (FCAPS) framework for the virtual network services. In NFV, faults and performance issues can have complex geneses within virtual resources as well as virtual networks and cannot be effectively handled by traditional rule-based systems. To tackle the above problem, we propose a fault detection and localization model based on a combination of shallow and deep learning structures. Relatively simpler detection of 'fault' and 'no-fault' conditions or 'manifest' and 'impending' faults have been effectively shown to be handled by shallow machine learning structures like Support Vector Machine (SVM). Deeper structure, i.e. the stacked autoencoder has been found to be useful for a more complex localization function where a large amount of information needs to be worked through, in different layers, to get to the root cause of the problem. We provide evaluation results using a dataset adapted from logs of disruption in an operator's live network fault datasets available on Kaggle and another based on multivariate kernel density estimation and Markov sampling., Comment: E-preprint

Service Function Chaining (SFC) is the problem of deploying various network service instances over geographically distributed data centers and providing inter-connectivity among them. The goal is to enable the network traffic to flow smoothly through the underlying network, resulting in an optimal quality of experience to the end-users. Proper chaining of network functions leads to optimal utilization of distributed resources. This has been a de-facto model in the telecom industry with network functions deployed over underlying hardware. Though this model has served the telecom industry well so far, it has been adapted mostly to suit the static behavior of network services and service demands due to the deployment of the services directly over physical resources. This results in network ossification with larger delays to the end-users, especially with the data-centric model in which the computational resources are moving closer to end users. A novel networking paradigm, Network Function Virtualization (NFV), meets the user demands dynamically and reduces operational expenses (OpEx) and capital expenditures (CapEx), by implementing network functions in the software layer known as virtual network functions (VNFs). VNFs are then interconnected to form a complete end-to-end service, also known as service function chains (SFCs). In this work, we study the problem of deploying service function chains over network function virtualized architecture. Specifically, we study virtual network function placement problem for the optimal SFC formation across geographically distributed clouds. We set up the problem of minimizing inter-cloud traffic and response time in a multi-cloud scenario as an ILP optimization problem, along with important constraints such as total deployment costs and service level agreements (SLAs). We consider link delays and computational delays in our model., Comment: E-preprint