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Anomaly detection in computational workflows is critical for ensuring system reliability and security. However, traditional rule-based methods struggle to detect novel anomalies. This paper leverages large language models (LLMs) for workflow anomaly detection by exploiting their ability to learn complex data patterns. Two approaches are investigated: 1) supervised fine-tuning (SFT), where pre-trained LLMs are fine-tuned on labeled data for sentence classification to identify anomalies, and 2) in-context learning (ICL) where prompts containing task descriptions and examples guide LLMs in few-shot anomaly detection without fine-tuning. The paper evaluates the performance, efficiency, generalization of SFT models, and explores zero-shot and few-shot ICL prompts and interpretability enhancement via chain-of-thought prompting. Experiments across multiple workflow datasets demonstrate the promising potential of LLMs for effective anomaly detection in complex executions., Comment: 12 pages, 14 figures, paper is accepted by SC'24, source code, see: https://github.com/PoSeiDon-Workflows/LLM_AD

Serverless clouds promise efficient scaling, reduced toil and monetary costs. Yet, serverless-ing a complex, legacy application might require major refactoring and thus is risky. As a case study, we use Airflow, an industry-standard workflow system. To reduce migration risk, we propose to limit code modifications by relying on change data capture (CDC) and message queues for internal communication. To achieve serverless efficiency, we rely on Function-as-a-Service (FaaS). Our system, sAirflow, is the first adaptation of the control plane and workers to the serverless cloud - and it maintains the same interface and most of the code. Experimentally, we show that sAirflow delivers the key serverless benefits: scaling and cost reduction. We compare sAirflow to MWAA, a managed (SaaS) Airflow. On Alibaba benchmarks on warm systems, sAirflow performs similarly while halving the monetary cost. On highly parallel workflows on cold systems, sAirflow scales out in seconds to 125 workers, reducing makespan by 2x-7x.

The second law of equilibrium thermodynamics explains the direction of spontaneous processes in a system after removing internal constraints. When the system only exchanges energy with the environment as heat, the second law states that spontaneous processes at constant temperature satisfy: $\textrm{d} U - \delta Q \leq 0$. Here, $\textrm{d} U$ is the infinitesimal change of the internal energy, and $\delta Q$ is the infinitesimal heat exchanged in the process. We will consider three different systems in a heat flow: ideal gas, van der Waals gas, and a binary mixture of ideal gases. We will also study ideal gas and van der Waals gas in the heat flow and gravitational field. We will divide each system internally into two subsystems by a movable wall. We will show that the direction of the motion of the wall, after release, at constant boundary conditions is determined by the same inequality as in equilibrium thermodynamics. The only difference between equilibrium and non-equilibrium law is the dependence of the net heat change, $\delta Q$, on the state parameters of the system. We will also consider a wall thick and permeable to gas particles and derive Archimedes' principle in the heat flow. Finally, we will study the ideal gas's Couette flow, where the direction of the motion of the internal wall follows from the inequality $\textrm{d} E - \delta Q - \delta W_s \leq 0$, with $\textrm{d} E$ being the infinitesimal change of the total energy (internal and kinetic) and $\delta W_s$ the infinitesimal work exchanged with the environment due to shear force. Ultimately, we will synthesize all these cases in a framework of the second law of non-equilibrium thermodynamics.

We studied planar compressible flows of ideal gas as models of a non-equilibrium thermodynamic system. We demonstrate that internal energy $U(S^{*},V,N)$ of such systems in stationary and non-stationary states is the function of only three parameters of state, i.e. non-equilibrium entropy $S^{*}$, volume $V$ and number of particles $N$ in the system. Upon transition between different states, the system obeys the first thermodynamic law, i.e. $dU=T^{*}dS^{*}-p^{*}dV+{\mu}^{*}dN$, where $U=3/2 NRT^{*}$ and $p^{*}V=NRT^{*}$. Placing a cylinder inside the channel, we find that U depends on the location of the cylinder $y_{c}$ only via the parameters of state, i.e. $U(S^{*}(y_{c}),V,N(y_{c}))$ at V=const. Moreover, when the flow around the cylinder becomes unstable, and velocity, pressure, and density start to oscillate as a function of time, t, U depends on t only via the parameters of state, i.e. $U(S^{*}(t),V,N(t))$ for V=const. These examples show that such a form of internal energy is robust and does not depend on the particular boundary conditions even in the unsteady flow., Comment: 17 pages, 9 figures

This work develops a methodology for studying the effect of an offload zone on the ambulance ramping problem using a multi-server, multi-class non-preemptive priority queueing model that can be treated analytically. A prototype model for the ambulance/emergency-department interface is constructed, which is then implemented as a formal discrete event simulation, and is run as a regenerative steady-state simulation for empirical estimation of the ambulance queue-length and waiting-time distributions. The model is also solved by analytical means for explicit and exact representations of these distributions, which are subsequently tested against simulation results. A number of measures of performance is extracted, including the mean and 90th percentiles of the ambulance queue length and waiting time, as well as the average number of ambulance days lost per month due to offload delay (offload delay rate). Various easily computable approximations are proposed and tested. In particular, a closed-form, purely algebraic expression that approximates the dependence of the offload delay rate on the capacity of the offload zone is proposed. It can be evaluated directly from model input parameters and is found to be, for all practical purposes, indistinguishable from the exact result., Comment: 26 pages, 8 figures

Explicit and exact results are obtained for the joint queue-length distribution for the two-level non-preemptive Markovian priority queue. Marginal distributions are derived for the general multi-level problem. The results are based on a representation of the joint queue-length probability mass function as a single-variable complex contour integral, that reduces to a real integral on a finite interval arising from a cut on the real axis. Both numerical quadrature rules and exact finite sums, involving Legendre polynomials and their generalization, are presented for the joint and marginal distributions. A high level of accuracy is demonstrated across the entire ergodic region. Relationships are established with the waiting-time distributions. Asymptotic behaviour in the large queue-length regime is extracted., Comment: 29 pages, 7 figures

Explicit results are obtained using simple and exact methods for the joint queue-length distribution of the M/M/c queue with an arbitrary number of non-preemptive priority levels. This work is the first to provide explicit results for the joint probability generating function and joint probability mass function for a general number of priority levels. A fixed-point iteration is developed for the stationary balance equations, which enables direct computation of the joint queue-length distribution. A multi-variate probability generating function is also derived, from which the joint probability mass function can be computed by means of a multi-dimensional fast Fourier transform method., Comment: 30 pages, 8 figures

We formulate the first law of global thermodynamics for stationary states of the binary ideal gas mixture subjected to heat flow. We map the non-uniform system onto the uniform one and show that the internal energy $U(S^*,V,N_1,N_2,f_1^*,f_2^*)$ is the function of the following parameters of state: a non-equilibrium entropy $S^*$, volume $V$, number of particles of the first component, $N_1$, number of particles of the second component $N_2$ and the renormalized degrees of freedom. The parameters $f_1^*,f_2^*$, $N_1, N_2$ satisfy the relation $x_1f_1^*/f_1+x_2f_2^*/f_2=1$ ($f_1$, where $x_i$ is the fraction of $i$ component, and $f_2$ are the degrees of freedom for each component respectively). Thus only 5 parameters of state describe the non-equilibrium state of the binary mixture in the heat flow. We calculate the non-equilibrium entropy $S^{*}$ and new thermodynamic parameters of state $f_1^*, f_2^*$ explicitly. The latter are responsible for heat generation due to the concentration gradients. The theory reduces to equilibrium thermodynamics, when the heat flux goes to zero. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties., Comment: 8 pages, 1 figure

Explicit results are derived using simple and exact methods for the joint and marginal queue-length distributions for the M/M/c queue with two non-preemptive priority levels. Equal service rates are assumed. Two approaches are considered. One is based on numerically robust quadratic recurrence relations. The other is based on a complex contour-integral representation that yields exact closed-form analytical expressions, not hitherto available in the literature, that can also be evaluated numerically with very high accuracy.

Neurophysiology research has demonstrated that it is possible and valuable to investigate sensory processing in scenarios involving continuous sensory streams, such as speech and music. Over the past 10 years or so, novel analytic frameworks combined with the growing participation in data sharing has led to a surge of publicly available datasets involving continuous sensory experiments. However, open science efforts in this domain of research remain scattered, lacking a cohesive set of guidelines. This paper presents an end-to-end open science framework for the storage, analysis, sharing, and re-analysis of neural data recorded during continuous sensory experiments. We propose a data structure that builds on existing custom structures (Continuous-event Neural Data or CND), providing precise naming conventions and data types, as well as a workflow for storing and loading data in the general-purpose BIDS structure. The framework has been designed to interface with existing EEG/MEG analysis toolboxes, such as Eelbrain, NAPLib, MNE, and mTRF-Toolbox. We present guidelines by taking both the user view (rapidly re-analyse existing data) and the experimenter view (store, analyse, and share), making the process straightforward and accessible. Additionally, we introduce a web-based data browser that enables the effortless replication of published results and data re-analysis.

Exact explicit results are derived for the distribution of the partial busy period of the M/M/c multi-server queue for a general number of servers. A rudimentary spectral method leads to a representation that is amenable to efficient numerical computation across the entire ergodic region. An alternative algebraic approach yields a representation as a finite sum of Marcum Q-functions depending on the roots of certain polynomials that are explicitly determined for an arbitrary number of servers. Asymptotic forms are derived in the limit of a large number of servers under two scaling regimes, and also for the large-time limit. Connections are made with previous work. The present work is the first to offer tangible exact results for the distribution when the number of servers is greater than two.

Understanding the dynamics of electric-double-layer (EDL) charging in porous media is essential for advancements in next-generation energy storage devices. Due to the high computational demands of direct numerical simulations and a lack of interfacial boundary conditions for reduced-order models, the current understanding of EDL charging is limited to simple geometries. Here, we present a theoretical framework to predict EDL charging in arbitrary networks of long pores in the Debye-H\"uckel limit without restrictions on EDL thickness and pore radii. We demonstrate that electrolyte transport is described by Kirchhoff's laws in terms of the electrochemical potential of charge (the valence-weighted average of the ion electrochemical potentials) instead of the electric potential. By employing this equivalent circuit representation with modified Kirchhoff's laws, our methodology accurately captures the spatial and temporal dependencies of charge density and electric potential, matching results obtained from computationally intensive direct numerical simulations. Our framework provides results up to five orders of magnitude faster, enabling the efficient simulation of thousands of pores within a day. We employ the framework to study the impact of pore connectivity and polydispersity on electrode charging dynamics for pore networks and discuss how these factors affect the timescale, energy density, and power density of the capacitive charging. The scalability and versatility of our methodology make it a rational tool for designing 3D-printed electrodes and for interpreting geometric effects on electrode impedance spectroscopy measurements., Comment: 27 pages and 8 figures

In this work we consider the exponential utility maximization problem in the framework of semistatic hedging.

Equilibrium thermodynamics describes the energy exchange of a body with its environment. Here, we describe the global energy exchange of an ideal gas in the Coutte flow in a thermodynamic-like manner. We derive a fundamental relation between internal energy as a function of parameters of state. We analyze a non-equilibrium transition in the system and postulate the extremum principle, which determines stable stationary states in the system. The steady-state thermodynamic framework resembles equilibrium thermodynamics.

Quantum error correction with erasure qubits promises significant advantages over standard error correction due to favorable thresholds for erasure errors. To realize this advantage in practice requires a qubit for which nearly all errors are such erasure errors, and the ability to check for erasure errors without dephasing the qubit. We demonstrate that a "dual-rail qubit" consisting of a pair of resonantly coupled transmons can form a highly coherent erasure qubit, where transmon $T_1$ errors are converted into erasure errors and residual dephasing is strongly suppressed, leading to millisecond-scale coherence within the qubit subspace. We show that single-qubit gates are limited primarily by erasure errors, with erasure probability $p_\text{erasure} = 2.19(2)\times 10^{-3}$ per gate while the residual errors are $\sim 40$ times lower. We further demonstrate mid-circuit detection of erasure errors while introducing $< 0.1\%$ dephasing error per check. Finally, we show that the suppression of transmon noise allows this dual-rail qubit to preserve high coherence over a broad tunable operating range, offering an improved capacity to avoid frequency collisions. This work establishes transmon-based dual-rail qubits as an attractive building block for hardware-efficient quantum error correction., Comment: 9+13 pages, 16 figures

Dynamical decoupling is effective in reducing gate errors in most quantum computation platforms and is therefore projected to play an essential role in future fault-tolerant constructions. In superconducting circuits, however, it has proven difficult to utilize the benefits of dynamical decoupling. In this work, we present a theoretical proposal that incorporates a continuous version of dynamical decoupling, namely spin locking, with a coupler-based CZ gate for transmons and provide analytical and numerical results that demonstrate its effectiveness.

The aim of this short note is to present a solution to the discrete time exponential utility maximization problem in a case where the underlying asset has a multivariate normal distribution. In addition to the usual setting considered in Mathematical Finance, we also consider an investor who is informed about the risky asset's price changes with a delay. Our method of solution is based on the theory developed in [4] and guessing the optimal portfolio., Comment: 2 figures

There is a long-standing question of whether it is possible to extend the formalism of equilibrium thermodynamics to the case of non-equilibrium systems in steady states. We have made such an extension for an ideal gas in a heat flow [Ho\l{}yst \emph{et al.}, J. Chem. Phys. 157, 194108 (2022)]. Here we investigate whether such a description exists for the system with interactions: the Van der Waals gas in a heat flow. We introduce the parameters of state, each associated with a single way of changing energy. The first law of non-equilibrium thermodynamics follows from these parameters. The internal energy $U$ for the non-equilibrium states has the same form as in equilibrium thermodynamics. For the Van der Waals gas, $U(S^*, V, N, a^*,b^* )$ is a function of only 5 parameters of state (irrespective of the number of parameters characterizing the boundary conditions): the entropy $S^*$, volume $V$, number of particles $N$, and the rescaled Van der Waals parameters $a^*$, $b^*$. The state parameters, $a^*$, $b^*$, together with $S^*$, determine the net heat exchange with the environment., Comment: 7 pages, 1 figure

We derive the field-dependent masses in Fermi gauges for arbitrary scalar extensions of the Standard Model. These masses can be used to construct the effective potential for various models of new physics. We release a flexible $\texttt{Mathematica}$ notebook ($\texttt{VefFermi}$) which performs these calculations and renders large-scale phenomenological studies of various models possible. Motivated by the debate on the importance of gauge dependence, we show that, even in relatively simple models, there exist points where the global minimum is discontinuous in the gauge parameter. Such points require some care in discovering, indicating that a gauge-dependent treatment might still give reasonable results when examining the global features of a model., Comment: 12 pages, 2 figures

Modern HPC workload managers and their careful tuning contribute to the high utilization of HPC clusters. However, due to inevitable uncertainty it is impossible to completely avoid node idleness. Although such idle slots are usually too short for any HPC job, they are too long to ignore them. Function-as-a-Service (FaaS) paradigm promisingly fills this gap, and can be a good match, as typical FaaS functions last seconds, not hours. Here we show how to build a FaaS infrastructure on idle nodes in an HPC cluster in such a way that it does not affect the performance of the HPC jobs significantly. We dynamically adapt to a changing set of idle physical machines, by integrating open-source software Slurm and OpenWhisk. We designed and implemented a prototype solution that allowed us to cover up to 90\% of the idle time slots on a 50k-core cluster that runs production workloads.

Let $\prec$ be the product order on $\mathbb{R}^k$ and assume that $X_1,X_2,\ldots,X_n$ ($n\geq3$) are i.i.d. random vectors distributed uniformly in the unit hypercube $[0,1]^k$. Let $S$ be the (random) set of vectors in $\mathbb{R}^k$ that $\prec$-dominate all vectors in $\{X_3,..,X_n\}$, and let $W$ be the set of vectors that are not $\prec$-dominated by any vector in $\{X_3,..,X_n\}$. The main result of this work is the correlation inequality \begin{equation*} P(X_2\in W|X_1\in W)\leq P(X_2\in W|X_1\in S)\,. \end{equation*} For every $1\leq i \leq n$ let $E_{i,n}$ be the event that $X_i$ is not $\prec$-dominated by any of the other vectors in $\{X_1,\ldots,X_n\}$. The main inequality yields an elementary proof for the result that the events $E_{1,n}$ and $E_{2,n}$ are asymptotically independent as $n\to\infty$. Furthermore, we derive a related combinatorial formula for the variance of the sum $\sum_{i=1}^n \textbf{1}_{E_{i,n}}$, i.e. the number of maxima under the product order $\prec$, and show that certain linear functionals of partial sums of $\{\textbf{1}_{E_{i,n}};1\leq i\leq n\}$ are asymptotically normal as $n\to\infty$.

In an overloaded FaaS cluster, individual worker nodes strain under lengthening queues of requests. Although the cluster might be eventually horizontally-scaled, adding a new node takes dozens of seconds. As serving applications are tuned for tail serving latencies, and these greatly increase under heavier loads, the current workaround is resource over-provisioning. In fact, even though a service can withstand a steady load of, e.g., 70% CPU utilization, the autoscaler is triggered at, e.g., 30-40% (thus the service uses twice as many nodes as it would be needed). We propose an alternative: a worker-level method handling heavy load without increasing the number of nodes. FaaS executions are not interactive, compared to, e.g., text editors: end-users do not benefit from the CPU allocated to processes often, yet for short periods. Inspired by scheduling methods for High Performance Computing, we take a radical step of replacing the classic OS preemption by (1) queuing requests based on their historical characteristics; (2) once a request is being processed, setting its CPU limit to exactly one core (with no CPU oversubscription). We extend OpenWhisk and measure the efficiency of the proposed solutions using the SeBS benchmark. In a loaded system, our method decreases the average response time by a factor of 4. The improvement is even higher for shorter requests, as the average stretch is decreased by a factor of 18. This leads us to show that we can provide better response-time statistics with 3 machines compared to a 4-machine baseline.

Ion transport in porous media is present in a wealth of technologies, e.g., energy storage devices such as batteries and supercapacitors, and environmental technologies such as electrochemical carbon capture and capacitive deionization. Recent studies on flat-plate electrodes have demonstrated that asymmetries in ion properties, such as valences and diffusivities, lead to intriguing and counter-intuitive physical phenomena. Yet, the consequences of such asymmetries to ion transport have seldom been explored in porous geometries. To bridge this knowledge gap, we conduct a perturbation expansion of the Poisson-Nernst-Planck equations in a cylindrical pore in the limit of small potentials for a binary electrolyte with arbitrary valences and diffusivities. We obtain good agreement between the perturbation analysis and direct numerical simulations. Our analysis reveals that the charge and the salt transport are coupled with each other. Further, the coupling between the charge and salt transport processes is enhanced with an increase in valence and diffusivity asymmetries of ions. We observe that the mismatch of the ionic diffusivities induces a non-trivial salt dynamics, producing either transient depletion or enhancement of salt in the pore. In the regime of high static diffusion layer conductance, we obtain an analytical solution to our perturbation model. The solution elucidates how electrolyte asymmetry induces two charging timescales that are set by the relative pore size. In the overlapping-double-layer regime, these timescales reduce to the diffusion times of each ion such that the transport of the two ions appears to be decoupled. Overall, our work underscores that the asymmetry in cation and anion diffusivities fundamentally alters the behavior of ionic transport inside a charged cylindrical pore and opens up new avenues of research on electrolyte transport in porous materials., Comment: 20 pages, 10 figures, submitted to Electrochimica Acta

Cloud resource management is often modeled by two-dimensional bin packing with a set of items that correspond to tasks having fixed CPU and memory requirements. However, applications running in clouds are much more flexible: modern frameworks allow to (horizontally) scale a single application to dozens, even hundreds of instances; and then the load balancer can precisely divide the workload between them. We analyze a model that captures this (semi)-flexibility of cloud resource management. Each cloud application is characterized by its memory footprint and its momentary CPU load. Combining the scheduler and the load balancer, the resource manager decides how many instances of each application will be created and how the CPU load will be balanced between them. In contrast to the divisible load model, each instance of the application requires a certain amount of memory, independent of the number of instances. Thus, the resource manager effectively trades additional memory for more evenly balanced load. We study two objectives: the bin-packing-like minimization of the number of machines used; and the makespan-like minimization of the maximum load among all the machines. We prove NP-hardness of the general problems, but also propose polynomial-time exact algorithms for boundary special cases. Notably, we show that (semi)-flexibility may result in reducing the required number of machines by a tight factor of $2-\varepsilon$. For the general case, we propose heuristics that we validate by simulation on instances derived from the Azure trace.