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The CMS Submission Infrastructure (SI) is the main computing resource provisioning system for CMS workloads. A number of HTCondor pools are employed to manage this infrastructure, which aggregates geographically distributed resources from the WLCG and other providers. Historically, the model of authentication among the diverse components of this infrastructure has relied on the Grid Security Infrastructure (GSI), based on identities and X509 certificates. In contrast, commonly used modern authentication standards are based on capabilities and tokens. The WLCG has identified this trend and aims at a transparent replacement of GSI for all its workload management, data transfer and storage access operations, to be completed during the current LHC Run 3. As part of this effort, and within the context of CMS computing, the Submission Infrastructure group is in the process of phasing out the GSI part of its authentication layers, in favor of IDTokens and Scitokens. The use of tokens is already well integrated into the HTCondor Software Suite, which has allowed us to fully migrate the authentication between internal components of SI. Additionally, recent versions of the HTCondor-CE support tokens as well, enabling CMS resource requests to Grid sites employing this CE technology to be granted by means of token exchange. After a rollout campaign to sites, successfully completed by the third quarter of 2022, the totality of HTCondor CEs in use by CMS are already receiving Scitoken-based pilot jobs. On the ARC CE side, a parallel campaign was launched to foster the adoption of the REST interface at CMS sites (required to enable token-based job submission via HTCondor-G), which is nearing completion as well. In this contribution, the newly adopted authentication model will be described. We will then report on the migration status and final steps towards complete GSI phase out in the CMS SI.

The computing resource needs of LHC experiments are expected to continue growing significantly during the Run 3 and into the HL-LHC era. The landscape of available resources will also evolve, as High Performance Computing (HPC) and Cloud resources will provide a comparable, or even dominant, fraction of the total compute capacity. The future years present a challenge for the experiments' resource provisioning models, both in terms of scalability and increasing complexity. The CMS Submission Infrastructure (SI) provisions computing resources for CMS workflows. This infrastructure is built on a set of federated HTCondor pools, currently aggregating 400k CPU cores distributed worldwide and supporting the simultaneous execution of over 200k computing tasks. Incorporating HPC resources into CMS computing represents firstly an integration challenge, as HPC centers are much more diverse compared to Grid sites. Secondly, evolving the present SI, dimensioned to harness the current CMS computing capacity, to reach the resource scales required for the HLLHC phase, while maintaining global flexibility and efficiency, will represent an additional challenge for the SI. To preventively address future potential scalability limits, the SI team regularly runs tests to explore the maximum reach of our infrastructure. In this note, the integration of HPC resources into CMS offline computing is summarized, the potential concerns for the SI derived from the increased scale of operations are described, and the most recent results of scalability test on the CMS SI are reported.

We propose a new simple and explicit numerical scheme for time-homogeneous stochastic differential equations. The scheme is based on sampling increments at each time step from a skew-symmetric probability distribution, with the level of skewness determined by the drift and volatility of the underlying process. We show that as the step-size decreases the scheme converges weakly to the diffusion of interest. We then consider the problem of simulating from the limiting distribution of an ergodic diffusion process using the numerical scheme with a fixed step-size. We establish conditions under which the numerical scheme converges to equilibrium at a geometric rate, and quantify the bias between the equilibrium distributions of the scheme and of the true diffusion process. Notably, our results do not require a global Lipschitz assumption on the drift, in contrast to those required for the Euler--Maruyama scheme for long-time simulation at fixed step-sizes. Our weak convergence result relies on an extension of the theory of Milstein \& Tretyakov to stochastic differential equations with non-Lipschitz drift, which could also be of independent interest. We support our theoretical results with numerical simulations.

In this work, we consider the numerical computation of ground states and dynamics of single-component Bose-Einstein condensates (BECs). The corresponding models are spatially discretized with a multiscale finite element approach known as Localized Orthogonal Decomposition (LOD). Despite the outstanding approximation properties of such a discretization in the context of BECs, taking full advantage of it without creating severe computational bottlenecks can be tricky. In this paper, we therefore present two fully-discrete numerical approaches that are formulated in such a way that they take special account of the structure of the LOD spaces. One approach is devoted to the computation of ground states and another one for the computation of dynamics. A central focus of this paper is also the discussion of implementation aspects that are very important for the practical realization of the methods. In particular, we discuss the use of suitable data structures that keep the memory costs economical. The paper concludes with various numerical experiments in 1d, 2d and 3d that investigate convergence rates and approximation properties of the methods and which demonstrate their performance and computational efficiency, also in comparison to spectral and standard finite element approaches.

Characteristic formulae give a complete logical description of the behaviour of processes modulo some chosen notion of behavioural semantics. They allow one to reduce equivalence or preorder checking to model checking, and are exactly the formulae in the modal logics characterizing classic behavioural equivalences and preorders for which model checking can be reduced to equivalence or preorder checking. This paper studies the complexity of determining whether a formula is characteristic for some finite, loop-free process in each of the logics providing modal characterizations of the simulation-based semantics in van Glabbeek's branching-time spectrum. Since characteristic formulae in each of those logics are exactly the consistent and prime ones, it presents complexity results for the satisfiability and primality problems, and investigates the boundary between modal logics for which those problems can be solved in polynomial time and those for which they become computationally hard. Amongst other contributions, this article also studies the complexity of constructing characteristic formulae in the modal logics characterizing simulation-based semantics, both when such formulae are presented in explicit form and via systems of equations.

We present a novel formal system for proving quantitative-leakage properties of programs. Based on a theory of Quantitative Information Flow (QIF) that models information leakage as a noisy communication channel, it uses "gain-functions" for the description and measurement of expected leaks. We use a small imperative programming language, augmented with leakage features, and with it express adversaries' activities in the style of, but more generally than, the Hoare triples or expectation transformers that traditionally express deterministic or probabilistic correctness but without information flow. The programs are annotated with "gain-expressions" that capture simple adversarial settings such as "Guess the secret in one try." but also much more general ones; and our formal syntax and logic -based framework enables us to transform such gain-expressions that apply after a program has finished to ones that equivalently apply before the program has begun. In that way we enable a formal proof-based reasoning system for QIF at the source level. We apply it to the %programming language we have chosen, and demonstrate its effectiveness in a number of small but sometimes intricate situations.

We consider the fundamental problem of constructing fast and small circuits for binary addition. We propose a new algorithm with running time $\mathcal O(n \log_2 n)$ for constructing linear-size $n$-bit adder circuits with a significantly better depth guarantee compared to previous approaches: Our circuits have a depth of at most $\log_2 n + \log_2 \log_2 n + \log_2 \log_2 \log_2 n + \text{const}$, improving upon the previously best circuits by [12] with a depth of at most $\log_2 n + 8 \sqrt{\log_2 n} + 6 \log_2 \log_2 n + \text{const}$. Hence, we decrease the gap to the lower bound of $\log_2 n + \log_2 \log_2 n + \text{const}$ by [5] significantly from $\mathcal O (\sqrt{\log_2 n})$ to $\mathcal O(\log_2 \log_2 \log_2 n)$. Our core routine is a new algorithm for the construction of a circuit for a single carry bit, or, more generally, for an And-Or path, i.e., a Boolean function of type $t_0 \lor ( t_1 \land (t_2 \lor ( \dots t_{m-1}) \dots ))$. We compute linear-size And-Or path circuits with a depth of at most $\log_2 m + \log_2 \log_2 m + 0.65$ in time $\mathcal O(m \log_2 m)$. These are the first And-Or path circuits known that, up to an additive constant, match the lower bound by [5] and at the same time have a linear size. The previously fastest And-Or path circuits are only by an additive constant worse in depth, but have a much higher size in the order of $\mathcal O (m \log_2 m)$.

We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker common-sense criteria for solutions to inference problems, all failed by these frequentist methods but satisfied by any admissible method. We note that pseudo-Bayesian methods made by handicapping Bayesian methods to satisfy criteria on type I error rate makes them frequentist not Bayesian in nature. We give five examples showing the differences between Bayesian and frequentist methods; the first requiring little calculus, the second showing in abstract what is wrong with these frequentist methods, the third to illustrate information conservation, the fourth to show that the same problems arise in everyday statistical problems, and the fifth to illustrate how on some real-life inference problems Bayesian methods require less data than fixed sample-size (resp. pseudo-Bayesian) frequentist hypothesis testing by factors exceeding 3000 (resp 300) without recourse to informative priors. To address the issue of different parties with opposing interests reaching agreement on a prior, we illustrate the beneficial effects of a Bayesian "Let the data decide" policy both on results under a wide variety of conditions and on motivation to reach a common prior by consent. We show that in general the frequentist confidence level contains less relevant Shannon information than the Bayesian posterior, and give an example where no deterministic frequentist critical regions give any relevant information even though the Bayesian posterior contains up to the maximum possible amount. In contrast use of the Bayesian prior allows construction of non-deterministic critical regions for which the Bayesian posterior can be recovered from the frequentist confidence.

In this paper we continue the work on implicit-explicit (IMEX) time discretizations for the incompressible Oseen equations that we started in \cite{BGG23} (E. Burman, D. Garg, J. Guzm\`an, {\emph{Implicit-explicit time discretization for Oseen's equation at high Reynolds number with application to fractional step methods}}, SIAM J. Numer. Anal., 61, 2859--2886, 2023). The pressure velocity coupling and the viscous terms are treated implicitly, while the convection term is treated explicitly using extrapolation. Herein we focus on the implicit-explicit Crank-Nicolson method for time discretization. For the discretization in space we consider finite element methods with stabilization on the gradient jumps. The stabilizing terms ensures inf-sup stability for equal order interpolation and robustness at high Reynolds number. Under suitable Courant conditions we prove stability of the implicit-explicit Crank-Nicolson scheme in this regime. The stabilization allows us to prove error estimates of order $O(h^{k+\frac12} + \tau^2)$. Here $h$ is the mesh parameter, $k$ the polynomial order and $\tau$ the time step. Finally we discuss some fractional step methods that are implied by the IMEX scheme. Numerical examples are reported comparing the different methods when applied to the Navier-Stokes' equations.

General purpose optimization routines such as nlminb, optim (R) or nlmixed (SAS) are frequently used to estimate model parameters in nonstandard distributions. This paper presents Particle Swarm Optimization (PSO), as an alternative to many of the current algorithms used in statistics. We find that PSO can not only reproduce the same results as the above routines, it can also produce results that are more optimal or when others cannot converge. In the latter case, it can also identify the source of the problem or problems. We highlight advantages of using PSO using four examples, where: (1) some parameters in a generalized distribution are unidentified using PSO when it is not apparent or computationally manifested using routines in R or SAS; (2) PSO can produce estimation results for the log-binomial regressions when current routines may not; (3) PSO provides flexibility in the link function for binomial regression with LASSO penalty, which is unsupported by standard packages like GLM and GENMOD in Stata and SAS, respectively, and (4) PSO provides superior MLE estimates for an EE-IW distribution compared with those from the traditional statistical methods that rely on moments.