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Auto-encoders (AEs) have the potential to be effective and generic tools for new physics searches at colliders, requiring little to no model-dependent assumptions. New hypothetical physics signals can be considered anomalies that deviate from the well-known background processes generally expected to describe the whole dataset. We present a search formulated as an anomaly detection (AD) problem, using an AE to define a criterion to decide about the physics nature of an event. In this work, we perform an AD search for manifestations of a dark version of strong force using raw detector images, which are large and very sparse, without leveraging any physics-based pre-processing or assumption on the signals. We propose a dual-encoder design which can learn a compact latent space through conditioning. In the context of multiple AD metrics, we present a clear improvement over competitive baselines and prior approaches. It is the first time that an AE is shown to exhibit excellent discrimination against multiple dark shower models, illustrating the suitability of this method as a performant, model-independent algorithm to deploy, e.g., in the trigger stage of LHC experiments such as ATLAS and CMS.

This paper presents a novel, efficient, high-order accurate, and stable spectral element-based model for computing the complete three-dimensional linear radiation and diffraction problem for floating offshore structures. We present a solution to a pseudo-impulsive formulation in the time domain, where the frequency-dependent quantities, such as added mass, radiation damping, and wave excitation force for arbitrary heading angle, $\beta$, are evaluated using Fourier transforms from the tailored time-domain responses. The spatial domain is tessellated by an unstructured high-order hybrid configured mesh and represented by piece-wise polynomial basis functions in the spectral element space. Fourth-order accurate time integration is employed through an explicit four-stage Runge-Kutta method and complemented by fourth-order finite difference approximations for time differentiation. To reduce the computational burden, the model can make use of symmetry boundaries in the domain representation. The key piece of the numerical model -- the discrete Laplace solver -- is validated through $p$- and $h$-convergence studies. Moreover, to highlight the capabilities of the proposed model, we present prof-of-concept examples of simple floating bodies (a sphere and a box). Lastly, a much more involved case is performed of an oscillating water column, including generalized modes resembling the piston motion and wave sloshing effects inside the wave energy converter chamber. In this case, the spectral element model trivially computes the infinite-frequency added mass, which is a singular problem for conventional boundary element type solvers.

The optimal branch number of MDS matrices makes them a preferred choice for designing diffusion layers in many block ciphers and hash functions. Consequently, various methods have been proposed for designing MDS matrices, including search and direct methods. While exhaustive search is suitable for small order MDS matrices, direct constructions are preferred for larger orders due to the vast search space involved. In the literature, there has been extensive research on the direct construction of MDS matrices using both recursive and nonrecursive methods. On the other hand, in lightweight cryptography, Near-MDS (NMDS) matrices with sub-optimal branch numbers offer a better balance between security and efficiency as a diffusion layer compared to MDS matrices. However, no direct construction method is available in the literature for constructing recursive NMDS matrices. This paper introduces some direct constructions of NMDS matrices in both nonrecursive and recursive settings. Additionally, it presents some direct constructions of nonrecursive MDS matrices from the generalized Vandermonde matrices. We propose a method for constructing involutory MDS and NMDS matrices using generalized Vandermonde matrices. Furthermore, we prove some folklore results that are used in the literature related to the NMDS code.

We consider Biot model with block preconditioners and generalized eigenvalue problems for scalability and robustness to parameters. A discontinuous Galerkin discretization is employed with the displacement and Darcy flow flux discretized as piecewise continuous in $P_1$ elements, and the pore pressure as piecewise constant in the $P_0$ element with a stabilizing term. Parallel algorithms are designed to solve the resulting linear system. Specifically, the GMRES method is employed as the outer iteration algorithm and block-triangular preconditioners are designed to accelerate the convergence. In the preconditioners, the elliptic operators are further approximated by using incomplete Cholesky factorization or two-level additive overlapping Schwartz method where coarse grids are constructed by generalized eigenvalue problems in the overlaps (GenEO). Extensive numerical experiments show a scalability and parametric robustness of the resulting parallel algorithms.

The optimal branch number of MDS matrices makes them a preferred choice for designing diffusion layers in many block ciphers and hash functions. However, in lightweight cryptography, Near-MDS (NMDS) matrices with sub-optimal branch numbers offer a better balance between security and efficiency as a diffusion layer, compared to MDS matrices. In this paper, we study NMDS matrices, exploring their construction in both recursive and nonrecursive settings. We provide several theoretical results and explore the hardware efficiency of the construction of NMDS matrices. Additionally, we make comparisons between the results of NMDS and MDS matrices whenever possible. For the recursive approach, we study the DLS matrices and provide some theoretical results on their use. Some of the results are used to restrict the search space of the DLS matrices. We also show that over a field of characteristic 2, any sparse matrix of order $n\geq 4$ with fixed XOR value of 1 cannot be an NMDS when raised to a power of $k\leq n$. Following that, we use the generalized DLS (GDLS) matrices to provide some lightweight recursive NMDS matrices of several orders that perform better than the existing matrices in terms of hardware cost or the number of iterations. For the nonrecursive construction of NMDS matrices, we study various structures, such as circulant and left-circulant matrices, and their generalizations: Toeplitz and Hankel matrices. In addition, we prove that Toeplitz matrices of order $n>4$ cannot be simultaneously NMDS and involutory over a field of characteristic 2. Finally, we use GDLS matrices to provide some lightweight NMDS matrices that can be computed in one clock cycle. The proposed nonrecursive NMDS matrices of orders 4, 5, 6, 7, and 8 can be implemented with 24, 50, 65, 96, and 108 XORs over $\mathbb{F}_{2^4}$, respectively.

Investigating deep learning language models has always been a significant research area due to the ``black box" nature of most advanced models. With the recent advancements in pre-trained language models based on transformers and their increasing integration into daily life, addressing this issue has become more pressing. In order to achieve an explainable AI model, it is essential to comprehend the procedural steps involved and compare them with human thought processes. Thus, in this paper, we use simple, well-understood non-language tasks to explore these models' inner workings. Specifically, we apply a pre-trained language model to constrained arithmetic problems with hierarchical structure, to analyze their attention weight scores and hidden states. The investigation reveals promising results, with the model addressing hierarchical problems in a moderately structured manner, similar to human problem-solving strategies. Additionally, by inspecting the attention weights layer by layer, we uncover an unconventional finding that layer 10, rather than the model's final layer, is the optimal layer to unfreeze for the least parameter-intensive approach to fine-tune the model. We support these findings with entropy analysis and token embeddings similarity analysis. The attention analysis allows us to hypothesize that the model can generalize to longer sequences in ListOps dataset, a conclusion later confirmed through testing on sequences longer than those in the training set. Lastly, by utilizing a straightforward task in which the model predicts the winner of a Tic Tac Toe game, we identify limitations in attention analysis, particularly its inability to capture 2D patterns.

Digital twins (DT) are often defined as a pairing of a physical entity and a corresponding virtual entity mimicking certain aspects of the former depending on the use-case. In recent years, this concept has facilitated numerous use-cases ranging from design to validation and predictive maintenance of large and small high-tech systems. Although growing in popularity in both industry and academia, digital twins and the methodologies for developing and maintaining them differ vastly. To better understand these differences and similarities, we performed a semi-structured interview research study with 19 professionals from industry and academia who are closely associated with different lifecycle stages of the corresponding digital twins. In this paper, we present our analysis and findings from this study, which is based on eight research questions (RQ). We present our findings per research question. In general, we identified an overall lack of uniformity in terms of the understanding of digital twins and used tools, techniques, and methodologies for their development and maintenance. Furthermore, considering that digital twins are software intensive systems, we recognize a significant growth potential for adopting more software engineering practices, processes, and expertise in various stages of a digital twin's lifecycle.

The construction of self-dual codes over small fields such that their minimum distances are as large as possible is a long-standing challenging problem in the coding theory. In 2009, a family of binary self-dual cyclic codes with lengths $n_i$ and minimum distances $d_i \geq \frac{1}{2} \sqrt{n_i}$, $n_i$ goes to the infinity for $i=1,2, \ldots$, was constructed. In this paper, we construct a family of (repeated-root) binary self-dual cyclic codes with lengths $n$ and minimum distances at least $\sqrt{n}-2$. New families of lengths $n=q^m-1$, $m=3, 5, \ldots$, self-dual codes over ${\bf F}_q$, $q \equiv 1$ $mod$ $4$, with their minimum distances larger than or equal to $\sqrt{\frac{q}{2}}\sqrt{n}-q$ are also constructed.

The additive codes may have better parameters than linear codes. However, it is still a challenging problem to efficiently construct additive codes that outperform linear codes, especially those with greater distances than linear codes of the same lengths and dimensions. This paper focuses on constructing additive codes that outperform linear codes based on quasi-cyclic codes and combinatorial methods. Firstly, we propose a lower bound on the symplectic distance of 1-generator quasi-cyclic codes of index even. Secondly, we get many binary quasi-cyclic codes with large symplectic distances utilizing computer-supported combination and search methods, all of which correspond to good quaternary additive codes. Notably, some additive codes have greater distances than best-known quaternary linear codes in Grassl's code table (bounds on the minimum distance of quaternary linear codes //www.codetables.de) for the same lengths and dimensions. Moreover, employing a combinatorial approach, we partially determine the parameters of optimal quaternary additive 3.5-dimensional codes with lengths from $28$ to $254$. Finally, as an extension, we also construct some good additive complementary dual codes with larger distances than the best-known quaternary linear complementary dual codes in the literature.

Non-overlapping codes have been studied for almost 60 years. In such a code, no proper, non-empty prefix of any codeword is a suffix of any codeword. In this paper, we study codes in which overlaps of certain specified sizes are forbidden. We prove some general bounds and we give several constructions in the case of binary codes. Our techniques also allow us to provide an alternative, elementary proof of a lower bound on non-overlapping codes due to Levenshtein in 1964.