Extreme values for the waiting time in large fork-join queues

We prove that the scaled maximum steady-state waiting time and the scaled maximum steady-state queue length among N GI/GI/1-queues in the N-server fork-join queue converge to a normally distributed random variable as N→∞. The maximum steady-state waiting time in this queueing system scales around 1γlogN, where γ is determined by the cumulant generating function Λ of the service times distribution and solves the Cramér–Lundberg equation with stochastic service times and deterministic interarrival times. This value 1γlogN is reached at a certain hitting time. The number of arrivals until that hitting time satisfies the central limit theorem, with standard deviation σAΛ′(γ)γ. By using the distributional form of Little’s law, we can extend this result to the maximum queue length. Finally, we extend these results to a fork-join queue with different classes of servers

Classifying fermionic states via many-body correlation measures

Understanding the structure of quantum correlations in a many-body system is key to its computational treatment. For fermionic systems, correlations can be defined as deviations from Slater determinant states. The link between fermionic correlations and efficient computational physics methods is actively studied but remains ambiguous. We make progress in establishing this connection mathematically. In particular, we find a rigorous classification of states relative to k-fermion correlations, which admits a computational physics interpretation. Correlations are captured by a measure ωk, a function of k-fermion reduced density matrix that we call twisted purity. A condition ωk = 0 for a given k puts the state in a class Gk of correlated states. Sets Gk are nested in k, and Slater determinants correspond to k = 1. Classes Gk=O(1) are shown to be physically relevant, as ωk vanishes or nearly vanishes for truncated configuration-interaction states, perturbation series around Slater determinants, and some nonperturbative eigenstates of the 1D Hubbard model. For each k = O(1), we give an explicit ansatz with a polynomial number of parameters that covers all states in Gk. Potential applications of this ansatz and its connections to the coupled-cluster wavefunction are discussed

VCrypt: Leveraging Vectorized and Compressed Execution for Client-side Encryption

VCrypt is a novel extension on DuckDB that enables fine-grained client-side [en/de]cryption in a performance- and storage-efficient manner, by exploiting columnar compression as well as vectorized and compressed execution. We designed VCrypt such that in analytical queries, typically (i) data can be encrypted and decrypted batch-at-a-time instead of value-at-a-time, and (ii) the extra storage for cryptographic nonces gets compressed away. We also demonstrate the use of VCrypt inside MotherDuck, leveraging its hybrid processing model that evaluates SQL queries partly on a client DuckDB and partly on a cloud DuckDB, to achieve secure hybrid execution. This provides security even if the cloud server is untrusted, by forcing the [en/de]cryption of sensitive data to happen only client-side, while still allowing useful cloud-side work like filters and joins

Semidefinite approximations for bicliques and bi-independent pairs

We investigate some graph parameters dealing with bi-independent pairs (A, B) in a bipartite graph G= (V1 ∪ V2,E), that is, pairs (A, B) where A⊆ V1, B⊆ V2, and A∪ B are independent. These parameters also allow us to study bicliques in general graphs. When maximizing the cardinality |A∪ B|, one finds the stability number α(G), well-known to be polynomial-time computable. When maximizing the product |A| · |B|, one finds the parameter g(G), shown to be NP-hard by Peeters in 2003, and when maximizing the ratio |A| · |B|=|A∪ B|, one finds h(G), introduced by Vallentin in 2020 for bounding product-free sets in finite groups. We show that h(G) is an NP-hard parameter and, as a crucial ingredient, that it is NP-complete to decide whether a bipartite graph G has a balanced maximum independent set. These hardness results motivate introducing semidefinite programming (SDP) bounds for g(G), h(G), and αbal(G) (the maximum cardinality of a balanced independent set). We show that these bounds can be seen as natural variations of the Lovász ϑ-number, a well-known semidefinite bound on α(G). In addition, we formulate closed-form eigenvalue bounds, and we show relationships among them as well as with earlier spectral parameters by Hoffman and Haemers in 2001 and Vallentin in 2020

II Zebrawriter

This is the converted file of the 5 hole papertape. The source is X1 handcode assembler

Studying exploration in RL: An optimal transport analysis of occupancy measure trajectories

The rising successes of RL are propelled by combining smart algorithmic strategies and deep architectures to optimize the distribution of returns and visitations over the state-action space. A quantitative framework to compare the learning processes of these eclectic RL algorithms is currently absent but desired in practice. We address this gap by representing the learning process of an RL algorithm as a sequence of policies generated during training, and then studying the policy trajectory induced in the manifold of state-action occupancy measures. Using an optimal transport-based metric, we measure the length of the paths induced by the policy sequence yielded by an RL algorithm between an initial policy and a final optimal policy. Hence, we first define the Effort of Sequential Learning (ESL). ESL quantifies the relative distance that an RL algorithm travels compared to the shortest path from the initial to the optimal policy. Furthermore, we connect the dynamics of policies in the occupancy measure space and regret (another metric to understand the suboptimality of an RL algorithm), by defining the Optimal Movement Ratio (OMR). OMR assesses the fraction of movements in the occupancy measure space that effectively reduce an analogue of regret. Finally, we derive approximation guarantees to estimate ESL and OMR with a finite number of samples and without access to an optimal policy. Through empirical analyses across various environments and algorithms, we demonstrate that ESL and OMR provide insights into the exploration processes of RL algorithms and the hardness of different tasks in discrete and continuous MDPs

A comprehensive academic and industrial survey of blockchain technology for the energy sector using fuzzy Einstein decision-making

The global energy sector is undergoing a significant transformation driven by decarbonization and digitalization, leading to the emergence of Distributed Ledger Technology (DLT) — particularly blockchain — as a promising tool for enhancing transparency, security, and efficiency in modern power systems. This study aims to provide a comprehensive academic and industrial survey of blockchain applications in the energy sector and develop a robust decision-making framework to identify and prioritize the most promising real-world use cases based on multidisciplinary criteria. A three-stage methodology was adopted: (i) a literature and market review encompassing over 300 academic publications and commercial blockchain initiatives in energy, (ii) an in-depth evaluation of the evolution and viability of blockchain initiatives in energy with the help of expert surveys, and (iii) a novel decision-making model using a q-rung orthopair fuzzy Multi-Attributive Border Approximation (q-ROF-MABAC) method under the Einstein operator. The results were compared with existing decision models to validate consistency and robustness. Nine key blockchain use case categories were identified and ranked based on technical, economic, and governance dimensions. The results demonstrated that integrating expert insights into a fuzzy logic framework helps filter out overhyped claims in the literature and prioritize realistic and high-impact applications such as green certificates, grid services, and peer-to-peer energy trading. The model's rankings remained stable across varying weight configurations, confirming the robustness of the methodology. This study provides an evidence-based decision-support tool for researchers, industry stakeholders, and policymakers to better understand, evaluate, and adopt blockchain technologies in the energy sector

Fault-tolerant structures for measurement-based quantum computation on a network

In this work, we introduce a method to construct fault-tolerant measurement-based quantum computation (MBQC) architectures and numerically estimate their performance over various types of networks. A possible application of such a paradigm is distributed quantum computation, where separate computing nodes work together on a fault-tolerant computation through entanglement. We gauge error thresholds of the architectures with an efficient stabilizer simulator to investigate the resilience against both circuit-level and network noise. We show that, for both monolithic (i.e., non-distributed) and distributed implementations, an architecture based on the diamond lattice may outperform the conventional cubic lattice. Moreover, the high erasure thresholds of non-cubic lattices may be exploited further in a distributed context, as their performance may be boosted through entanglement distillation by trading in entanglement success rates against erasure errors during the error-decoding process. These results highlight the significance of lattice geometry in the design of fault-tolerant measurement-based quantum computing on a network, emphasizing the potential for constructing robust and scalable distributed quantum computers

Infinite-horizon Fuk-Nagaev inequalities

We develop explicit bounds for the tail of the distribution of the all-time supremum of a random walk with negative drift, where the increments have a truncated heavy-tailed distribution. As an application, we consider a ruin problem in the presence of reinsurance

Detecting wing fractures in chickens using deep learning, photographs and computed tomography scanning

Animal welfare monitoring is a key part of veterinary surveillance in every poultry slaughterhouse. Among the animal welfare indicators routinely inspected, the prevalence of wing fractures and soft tissues injuries (e.g. bruises) is particularly relevant, because it is related to acute pain and suffering in injured birds. According to current practice, assessment corresponds to visual examination by animal welfare officers. However, taking into consideration the speed of the production line and limitations associated with human inspection (e.g. different visual perception, subjectivism and fatigue), new more objective and automated techniques are desirable. Therefore, the aim of this study was to assess the applicability of three deep learning classification models to detect fractures and/or bruises based on computed tomography (CT) scans and photographs of the wings. Namely, 1. Model_CT (two categories: 1.BROKEN and 2.NON_BROKEN) detecting fractures based on CT scans, 2.Model_Photo_Fractures (1.FRACTURES and 2.NO_FRACTURES) detecting fractures based on photographs and 3.Model_Photo_Bruises (1.BRUISES and 2.NO_BRUISES) detecting bruises based on photographs. To train, validate and test these models 306 CT scans and 285 photographs were collected. The 3D ResNet34 and 2D EfficientNetV2_s architectures were used for the CT and Photo_Models, respectively. The models reached an accuracy of 98 % (Model_CT), 96 % (Model_Photo_Fractures) and 82 % (Model_Photo_Bruises). All in all, applying deep learning to the combination of CT scanning and photography can help to objectively recognize wing fractures and bruises. Consequently, it might lead to more accurate and objective animal welfare monitoring and ultimately to raised animal welfare standards