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The non-Markovian dynamics of an open quantum system can be rigorously derived using the Feynman-Vernon influence functional approach. Although this formalism is exact, practical numerical implementations often require compromises. The time-convolutionless (TCL) master equation offers an exact framework, yet its application typically relies on a perturbative expansion of both the time forward and time backward state propagators. Due to the significant computational effort involved - and the scarcity of analytical solutions for most open quantum systems - the fourth-order perturbative TCL generator (TCL4) has only been benchmarked on a limited range of systems and parameter spaces. Recent advancements, however, have made the computation of TCL4 faster and more accessible. In this paper, we benchmark the TCL4 master equation against numerically exact methods for the biased spin-boson model. We focus on the regime near critical bath coupling where perturbative master equations are expected to become inaccurate. Our findings reveal that the TCL4 approach is most reliable at low temperature and more efficient than the numerical exact methods. This study aims to delineate the conditions under which the TCL4 perturbative master equation enhances the accuracy of the TCL2.

We give a review of brackets and interior products in bosonic string theory, in different representations, used in formulation of a theory and derived in a transformation of related mathematical structures. We consider the C-bracket, defined in double string theory, in a context of Poisson algebra of symmetry generator, and show its connection to prior brackets trough anomaly reduction, and its characteristics related to Courant algebroid definitions.

Understanding how the microscopic properties of open quantum systems affect gate functionality is essential for developing high-quality quantum gates. This work examines driven qubit evolution in a bath of linear harmonic oscillators with a fast external drive. The dynamically prepared state technique and the time-dependent Bloch-Redfield master equation allow for accurate state coherence calculations. This technique eliminates reaction delays for relaxation dynamics and corrects inaccurate dephasing rates caused by factorized initial states in traditional master equations. Furthermore, the interaction with the bath is investigated for its effect on gate fidelity. As a function of the qubit rotation angle, the gate fidelity is minimal for the {\pi}-flip and partially recovers with the 2{\pi}-flip.

We consider the problem of characterizing graphs with the maximum spectral radius among the connected graphs with given numbers of vertices and edges. It is well-known that the candidates for extremal graphs are threshold graphs, but only a few partial theoretical results have been obtained so far. Therefore, we approach to this problem from a novel perspective that involves incomplete enumeration of different threshold graphs with a given characteristic. Our methodology defines the considered problem as an optimization task and utilizes two metaheuristic methods, Variable Neighborhood Search (VNS), which relies on iterative improvements of a single current best solution and Bee Colony Optimization (BCO), a population-based metaheuristic from the Swarm Intelligence (SI) class. We use compact solution representation and several auxiliary data structures that should enable efficient search of the solution space. In addition, we define several types of transformations that preserve the feasibility of the resulting solution. The proposed methods are compared on the graphs with a moderate number of vertices. Preliminary results are in favor of the VNS approach, however, we believe that both methods could be improved., Comment: 17 pages, 3 figures, 5 algorithms

This article examines late-time resummations of perturbative master equations, and finds asymptotic inflation in quantum dynamics generators when environmental correlations decay algebraically with time. We utilize the time-convolutionless master equation (TCL), which we compute perturbatively as TCL2$n$, where 2$n$ is the order in the expansion in time-ordered cumulants. We introduce Hadamarded time-ordered cumulants and classify them by their late-time growth. In the unbiased spin boson model (SBM), we find a maximum order of the expansion $n_{\text{max}}=\lceil s+1\rceil $ above which the dynamics has {\it no} Markovian limit, resulting in the precision limit of the reduced states of $O(\lambda^{2\lceil s\rceil})$. $s$ is the exponent in the power law of the spectral density versus frequency at zero frequency and $\lambda$ is the dimensionless weak-coupling constant. We perform resummation of the leading cumulants in TCL2$n$, resulting in a new master equation with renormalized Bohr frequencies (rTCL). The frequency shifts include the imaginary decoherence rates and nonlocal spectral overlaps (F\"orsters resonances). The inflation rate in the unbiased SBM is temperature independent and equal to the decoherence rate $\nu_2$, leading to the time limit for the validity of master equations of $t_L\approx (s+1)/\nu_2$. rTCL can be regularized by analytic continuation, resulting in a highly accurate Markovian approximation respecting the precision limit. Only if the environmental correlations decay exponentially with time, the resummation generator have a Markovian limit below a threshold $\lambda$, in both biased and unbiased SBM., Comment: 46 pages, 6 figures

In this paper we present a novel algorithm developed for computing the QR factorisation of extremely ill-conditioned tall-and-skinny matrices on distributed memory systems. The algorithm is based on the communication-avoiding CholeskyQR2 algorithm and its block Gram-Schmidt variant. The latter improves the numerical stability of the CholeskyQR2 algorithm and significantly reduces the loss of orthogonality even for matrices with condition numbers up to $10^{15}$. Currently, there is no distributed GPU version of this algorithm available in the literature which prevents the application of this method to very large matrices. In our work we provide a distributed implementation of this algorithm and also introduce a modified version that improves the performance, especially in the case of extremely ill-conditioned matrices. The main innovation of our approach lies in the interleaving of the CholeskyQR steps with the Gram-Schmidt orthogonalisation, which ensures that update steps are performed with fully orthogonalised panels. The obtained orthogonality and numerical stability of our modified algorithm is equivalent to CholeskyQR2 with Gram-Schmidt and other state-of-the-art methods. Weak scaling tests performed with our test matrices show significant performance improvements. In particular, our algorithm outperforms state-of-the-art Householder-based QR factorisation algorithms available in ScaLAPACK by a factor of $6$ on CPU-only systems and up to $80\times$ on GPU-based systems with distributed memory., Comment: 12 pages, 10 figures, 2 tables

An increasing number of regulations propose AI audits as a mechanism for achieving transparency and accountability for artificial intelligence (AI) systems. Despite some converging norms around various forms of AI auditing, auditing for the purpose of compliance and assurance currently lacks agreed-upon practices, procedures, taxonomies, and standards. We propose the criterion audit as an operationalizable compliance and assurance external audit framework. We model elements of this approach after financial auditing practices, and argue that AI audits should similarly provide assurance to their stakeholders about AI organizations' ability to govern their algorithms in ways that mitigate harms and uphold human values. We discuss the necessary conditions for the criterion audit and provide a procedural blueprint for performing an audit engagement in practice. We illustrate how this framework can be adapted to current regulations by deriving the criteria on which bias audits can be performed for in-scope hiring algorithms, as required by the recently effective New York City Local Law 144 of 2021. We conclude by offering a critical discussion on the benefits, inherent limitations, and implementation challenges of applying practices of the more mature financial auditing industry to AI auditing where robust guardrails against quality assurance issues are only starting to emerge. Our discussion -- informed by experiences in performing these audits in practice -- highlights the critical role that an audit ecosystem plays in ensuring the effectiveness of audits.

This paper investigates the simultaneous twisting of the Courant bracket by a 2-form $B$ and a bi-vector $\theta$, exploring the generalized fluxes obtained in Courant algebroid relations. We define the twisted Lie bracket and demonstrate that the generalized $H$-flux can be expressed as the field strength defined on this Lie algebroid. Similarly, we show that the $f$-flux is a direct consequence of simultaneous twisting, which arises in the twisted Lie bracket relations between holonomic partial derivatives. We obtain the generalized $Q$ flux in terms of the twisted Koszul bracket, which is a quasi-Lie algebroid bracket. The action of an exterior derivative related to the twisted Koszul bracket on a bi-vector produces the generalized $R$-flux. We show that the generalized $R$-flux is also the twisted Schouten-Nijenhuis bracket, i.e. the natural graded bracket on multi-vectors defined with the twisted Lie bracket.

Scalable and effective calibration is a fundamental requirement for Low Cost Air Quality Monitoring Systems and will enable accurate and pervasive monitoring in cities. Suffering from environmental interferences and fabrication variance, these devices need to encompass sensors specific and complex calibration processes for reaching a sufficient accuracy to be deployed as indicative measurement devices in Air Quality (AQ) monitoring networks. Concept and sensor drift often force calibration process to be frequently repeated. These issues lead to unbearable calibration costs which denies their massive deployment when accuracy is a concern. In this work, We propose a zero transfer samples, global calibration methodology as a technological enabler for IoT AQ multisensory devices which relies on low cost Particulate Matter (PM) sensors. This methodology is based on field recorded responses from a limited number of IoT AQ multisensors units and machine learning concepts and can be universally applied to all units of the same type. A multi season test campaign shown that, when applied to different sensors, this methodology performances match those of state of the art methodology which requires to derive different calibration parameters for each different unit. If confirmed, these results show that, when properly derived, a global calibration law can be exploited for a large number of networked devices with dramatic cost reduction eventually allowing massive deployment of accurate IoT AQ monitoring devices. Furthermore, this calibration model could be easily embedded on board of the device or implemented on the edge allowing immediate access to accurate readings for personal exposure monitor applications as well as reducing long range data transfer needs.

Mixture fraction-based models are widely employed for predicting turbulent non-premixed combustion processes due to their cost-effectiveness and well-established subfilter closure. In these models, the transport of reactive scalars in physical space is decomposed into two components: scalar transport relative to mixture fraction and transport of mixture fraction in physical space. Conventional flamelet models do not consider that these two processes have to be formulated consistently, which can lead to scalar mass conservation errors. In the context of multiphase flows, scalar transport in mixture fraction space is governed by three conditional flow-dependent parameters: the conditional scalar dissipation rate, the conditional scalar diffusion rate, and the conditional spray source term. The evolution of mixture fraction in physical space is typically modeled using the presumed Filtered Density Function (FDF) approach. This paper introduces a novel formulation for the conditional flow parameters that aligns with the presumed FDF approach, thereby ensuring scalar mass conservation. The proposed model is applied to a Large-Eddy Simulation (LES) of the inert ECN Spray A case, with a comparison against a conventional flow parameter model that employs an inverse error function shape for the scalar dissipation rate. The results indicate that the conventional model produces similar conditional dissipation rates to the new model in regions where combustion takes place. However, significant discrepancies are observed in the conditional diffusion rate, highlighting the susceptibility of the conventional model to scalar mass conservation errors for non-unity Lewis number scalars.

Despite recent advances in quantum sciences, a quantum master equation that accurately and simply characterizes open quantum dynamics across extremely long timescales and in dispersive environments is still needed. In this study, we optimize the computation of the fourth-order time-convolutionless master equation to meet this need. Early versions of this master equation required computing a multidimensional integral, limiting its use. Our master equation accounts for simultaneous relaxation and dephasing, resulting in coefficients proportional to the system's spectral density over frequency derivative. In sub-Ohmic environments, this derivative induces infrared divergence in the master equation, invalidating the second-order Bloch-Redfield master equation findings. We analyze the approach to a ground state in a generic open quantum system and demonstrate that it is not reliably computed by the Bloch-Redfield equation alone. The optimized fourth-order equation shows that the ground-state approach is accurate to second order in bath coupling regardless of the dispersion, even though it can diverge in the fourth order at zero temperature., Comment: 28 pages, 5 figures Changes: Typos in Eq. 35 and 77 fixed. Rewording of the abstract, introduction and conclusion, in response to review. Title changed to emphasise the main result

We present a complete system for real-time rendering of scenes with complex appearance previously reserved for offline use. This is achieved with a combination of algorithmic and system level innovations. Our appearance model utilizes learned hierarchical textures that are interpreted using neural decoders, which produce reflectance values and importance-sampled directions. To best utilize the modeling capacity of the decoders, we equip the decoders with two graphics priors. The first prior -- transformation of directions into learned shading frames -- facilitates accurate reconstruction of mesoscale effects. The second prior -- a microfacet sampling distribution -- allows the neural decoder to perform importance sampling efficiently. The resulting appearance model supports anisotropic sampling and level-of-detail rendering, and allows baking deeply layered material graphs into a compact unified neural representation. By exposing hardware accelerated tensor operations to ray tracing shaders, we show that it is possible to inline and execute the neural decoders efficiently inside a real-time path tracer. We analyze scalability with increasing number of neural materials and propose to improve performance using code optimized for coherent and divergent execution. Our neural material shaders can be over an order of magnitude faster than non-neural layered materials. This opens up the door for using film-quality visuals in real-time applications such as games and live previews., Comment: Equal contribution by the first six authors. Order determined by a rock-paper-scissors tournament. Project page: https://research.nvidia.com/labs/rtr/neural_appearance_models/

It is widely accepted that the dynamic of entanglement in presence of a generic circuit can be predicted by the knowledge of the statistical properties of the entanglement spectrum. We tested this assumption by applying a Metropolis-like entanglement cooling algorithm generated by different sets of local gates, on states sharing the same statistic. We employ the ground states of a unique model, namely the one-dimensional Ising chain with a transverse field, but belonging to different macroscopic phases such as the paramagnetic, the magnetically ordered, and the topological frustrated ones. Quite surprisingly, we observe that the entanglement dynamics are strongly dependent not just on the different sets of gates but also on the phase, indicating that different phases can possess different types of entanglement (which we characterize as purely local, GHZ-like, and W-state-like) with different degree of resilience against the cooling process. Our work highlights the fact that the knowledge of the entanglement spectrum alone is not sufficient to determine its dynamics, thereby demonstrating its incompleteness as a characterization tool. Moreover, it shows a subtle interplay between locality and non-local constraints., Comment: 14 pages, 11 figures, 1 table

As modern massively parallel clusters are getting larger with beefier compute nodes, traditional parallel eigensolvers, such as direct solvers, struggle keeping the pace with the hardware evolution and being able to scale efficiently due to additional layers of communication and synchronization. This difficulty is especially important when porting traditional libraries to heterogeneous computing architectures equipped with accelerators, such as Graphics Processing Unit (GPU). Recently, there have been significant scientific contributions to the development of filter-based subspace eigensolver to compute partial eigenspectrum. The simpler structure of these type of algorithms makes for them easier to avoid the communication and synchronization bottlenecks typical of direct solvers. The Chebyshev Accelerated Subspace Eigensolver (ChASE) is a modern subspace eigensolver to compute partial extremal eigenpairs of large-scale Hermitian eigenproblems with the acceleration of a filter based on Chebyshev polynomials. In this work, we extend our previous work on ChASE by adding support for distributed hybrid CPU-multi-GPU computing architectures. Our tests show that ChASE achieves very good scaling performance up to 144 nodes with 526 NVIDIA A100 GPUs in total on dense eigenproblems of size up to $360$k., Comment: Accepted for publication on the Proceedings of the PASC22 Conference

One of the most important and commonly used operations in many linear algebra functions is matrix-matrix multiplication (GEMM), which is also a key component in obtaining high performance of many scientific codes. It is a computationally intensive function requiring $O(n^3)$ operations, and its high computational intensity makes it well-suited to be significantly accelerated with GPUs. Today, many research problems require solving a very large number of relatively small GEMM operations that cannot utilise the entire GPU. To overcome this bottleneck, special functions have been developed that pack several GEMM operations into one and then compute them simultaneously on a GPU, which is called a batch operation. In this research work, we have proposed a different approach based on linking multiple GEMM operations to MPI ranks and then binding multiple MPI ranks to a single GPU. To increase GPU utilisation, more MPI ranks (i.e. GEMM operations) are added. We implement and test this approach in the field of theoretical physics to compute entanglement properties through simulated annealing Monte Carlo simulation of quantum spin chains. For the specific use case, we were able to simulate a much larger spin system and achieve a speed-up of up to $35\times$ compared to the parallel CPU-only version.

We consider the double field formulation of the closed bosonic string theory, and calculate the Poisson bracket algebra of the symmetry generators governing both general coordinate and local gauge transformations. Parameters of both of these symmetries depend on a double coordinate, defined as a direct sum of the initial and T-dual coordinate. When no antisymmetric field is present, the $C$-bracket appears as the Lie bracket generalization in a double theory. With the introduction of the Kalb-Ramond field, the $B$-twisted $C$-bracket appears, while with the introduction of the non-commutativity parameter, the $\theta$-twisted $C$-bracket appears. We present the derivation of these brackets and comment on their relations to analogous twisted Courant brackets and T-duality.

Understanding nonsecular dynamics in open quantum systems is addressed here, with emphasis on systems with large numbers of Bohr frequencies, zero temperature, and fast driving. We employ the master equation, which replaces arithmetic averages of the decay rates in the open system, with their geometric averages, and find that it can improve the second order perturbation theory, known as the Redfield equation, while enforcing complete positivity on quantum dynamics. The characteristic frequency scale that governs the approximation is the minimax frequency: the minimum of the maximum system oscillation frequency and the bath relaxation rate; this needs to be larger than the dissipation rate for it to be valid. The concepts are illustrated on the Heisenberg ferromagnetic spin-chain model. To study the accuracy of the approximation, a Hamiltonian is drawn from the Gaussian unitary ensemble, for which we calculate the fourth order time convolutionless master equation, in the Ohmic bath at zero temperature. Enforcing the geometric average, decreases the trace distance to the exact solution. Dynamical decoupling of a qubit is examined by applying the Redfield and the geometric-arithmetic master equations, in the interaction picture of the time dependent system Hamiltonian, and the results are compared to the exact path integral solution. The geometric-arithmetic approach is significantly simpler and can be super-exponentially faster compared to the Redfield approach.

In global efforts to reduce harmful greenhouse gas emissions from the transport sector, novel bio-hybrid liquid fuels from renewable energy and carbon sources can be a major form of energy for future propulsion systems due to their high energy density. A fundamental understanding of the spray and mixing performance of the new fuel candidates in combustion systems is necessary to design and develop the fuels for advanced combustion concepts. In the fuel design process, a large number of candidates is required to be screened to arrive at potential fuels for further detailed investigations. For such a screening process, three-dimensional (3D) simulation models are computationally too expensive and hence unfeasible. Therefore, in this paper, we present a fast, reduced-order model (ROM) for inert sprays. The model is based on the cross-sectionally averaged spray (CAS) model derived by Wan (1997) from 3D multiphase equations. The original model was first tested against a wide range of conditions and different fuels. The discrepancies between the CAS model and experimental data are addressed by integrating state-of-the-art breakup and evaporation models. A transport equation for vapor mass fraction is proposed, which is important for evaporation modeling. Furthermore, the model is extended to consider polydisperse droplets by modeling the droplet size distribution by commonly used presumed probability density functions, such as Rosin-Rammler, lognormal, and gamma distributions. The improved CAS model is capable of predicting trends in the macroscopic spray characteristics for a wide range of conditions and fuels. The computational cost of the CAS model is lower than the 3D simulation methods by up to 6 orders of magnitude depending on the method. This enables the model to be used not only for the rapid screening of novel fuel candidates, but also for other applications, where ROMs are useful., Comment: 44 pages, 14 figures

Coastal water quality management is a public health concern, as poor coastal water quality can harbor pathogens that are dangerous to human health. Tourism-oriented countries need to actively monitor the condition of coastal water at tourist popular sites during the summer season. In this study, routine monitoring data of $Escherichia\ Coli$ and enterococci across 15 public beaches in the city of Rijeka, Croatia, were used to build machine learning models for predicting their levels based on environmental parameters as well as to investigate their relationships with environmental stressors. Gradient Boosting (Catboost, Xgboost), Random Forests, Support Vector Regression and Artificial Neural Networks were trained with measurements from all sampling sites and used to predict $E.\ Coli$ and enterococci values based on environmental features. The evaluation of stability and generalizability with 10-fold cross validation analysis of the machine learning models, showed that the Catboost algorithm performed best with R$^2$ values of 0.71 and 0.68 for predicting $E.\ Coli$ and enterococci, respectively, compared to other evaluated ML algorithms including Xgboost, Random Forests, Support Vector Regression and Artificial Neural Networks. We also use the SHapley Additive exPlanations technique to identify and interpret which features have the most predictive power. The results show that site salinity measured is the most important feature for forecasting both $E.\ Coli$ and enterococci levels. Finally, the spatial and temporal accuracy of both ML models were examined at sites with the lowest coastal water quality. The spatial $E. Coli$ and enterococci models achieved strong R$^2$ values of 0.85 and 0.83, while the temporal models achieved R$^2$ values of 0.74 and 0.67. The temporal model also achieved moderate R$^2$ values of 0.44 and 0.46 at a site with high coastal water quality.

Deriving quantum error correction and quantum control from the Schrodinger equation for a unified qubit-environment Hamiltonian will give insights into how microscopic degrees of freedom affect the capability to control and correct quantum information beyond that of phenomenological theory. Here, we investigate the asymptotic reduced state of two qubits coupled to each other solely via a common heat bath of linear harmonic oscillators and search for evidence of fault-tolerant excited qubit states. We vary the Hamiltonian parameters, including the qubit-qubit and qubit-bath detuning, the bath spectral density, and whether or not we use the Markov approximation in the calculation of our dynamics. In proximity to special values of these parameters, we identify these states as asymptotic reduced states that are arbitrarily pure, excited, unique, and have high singlet fidelity. We emphasize the central role of the Lamb-shift as an agent responsible for fault tolerant excitations. To learn how these parameters relate to performance, we discuss numerical studies on fidelity and error recovery time., Comment: 22 pages 17 figures

We obtain the Courant bracket twisted simultaneously by a 2-form $B$ and a bi-vector $\theta$ by calculating the Poisson bracket algebra of the symmetry generator in the basis obtained acting with the relevant twisting matrix. It is the extension of the Courant bracket that contains well known Schouten-Nijenhuis and Koszul bracket, as well as some new star brackets. We give interpretation to the star brackets as projections on isotropic subspaces.

We consider the symmetries of a closed bosonic string, starting with the general coordinate transformations. Their generator takes vector components $\xi^\mu$ as its parameter and its Poisson bracket algebra gives rise to the Lie bracket of its parameters. We are going to extend this generator in order for it to be invariant upon self T-duality, i.e. T-duality realized in the same phase space. The new generator is a function of a $2D$ double symmetry parameter $\Lambda$, that is a direct sum of vector components $\xi^\mu$, and 1-form components $\lambda_\mu$. The Poisson bracket algebra of a new generator produces the Courant bracket in a same way that the algebra of the general coordinate transformations produces Lie bracket. In that sense, the Courant bracket is T-dual invariant extension of the Lie bracket. When the Kalb-Ramond field is introduced to the model, the generator governing both general coordinate and local gauge symmetries is constructed. It is no longer self T-dual and its algebra gives rise to the $B$-twisted Courant bracket, while in its self T-dual description, the relevant bracket becomes the $\theta$-twisted Courant bracket. Next, we consider the T-duality and the symmetry parameters that depend on both the initial coordinates $x^\mu$ and T-dual coordinates $y_\mu$. The generator of these transformations is defined as an inner product in a double space and its algebra gives rise to the C-bracket.