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Multi-constraint instruction following requires verifying whether a response satisfies multiple individual requirements, yet LLM judges are often assessed only through overall-response judgments. We introduce MCJudgeBench, a benchmark for constraint-level judge evaluation in multi-constraint instruction following. Each instance includes an instruction, a candidate response, an explicit constraint list, per-constraint gold labels in {yes, partial, no}, and controlled response-side perturbations. The evaluation protocol further includes evaluation prompt variants to test judge stability. We evaluate proprietary and open-source LLM judges using both correctness and inconsistency metrics, distinguishing intrinsic inconsistency under stochastic decoding from procedural inconsistency under prompt and response perturbations. Our results show that judge reliability has multiple dimensions: strong overall performance does not guarantee equally reliable detection across label categories, especially for rarer partial and no cases. Judges with higher correctness do not always have lower inconsistency. Evaluation with reasoning improves correctness but does not uniformly improve stability. Thes

Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the success of quaternions. The most useful feature of quaternions lies in their ability to model three-dimensional rotations which, in turn, have found various industrial applications such as in aeronautics and computergraphics. Recently, we have witnessed a renaissance of quaternions due to the rise of machine learning. To equip the reader to contribute to this emerging research area, this chapter lays down the foundation for: - augmented statistics for modelling quaternion-valued random processes, - widely linear models to exploit such advanced statistics, - quaternion calculus and algebra for algorithmic derivations, - mean square estimation for practical considerations. For ease of exposure, several examples are offered to facilitate the learning, understanding, and(hopefully) the adoption of this multidimensional domain.

Accessing knowledge via multilingual natural-language interfaces is one of the emerging challenges in the field of information retrieval and related ones. Structured knowledge stored in knowledge graphs can be queried via a specific query language (e.g., SPARQL). Therefore, one needs to transform natural-language input into a query to fulfill an information need. Prior approaches mostly focused on combining components (e.g., rule-based or neural-based) that solve downstream tasks and come up with an answer at the end. We introduce mKGQAgent, a human-inspired framework that breaks down the task of converting natural language questions into SPARQL queries into modular, interpretable subtasks. By leveraging a coordinated LLM agent workflow for planning, entity linking, and query refinement - guided by an experience pool for in-context learning - mKGQAgent efficiently handles multilingual KGQA. Evaluated on the DBpedia- and Corporate-based KGQA benchmarks within the Text2SPARQL challenge 2025, our approach took first place among the other participants. This work opens new avenues for developing human-like reasoning systems in multilingual semantic parsing.

This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an effective model for representing computation and measurement operations on qubits. In turn, the derived model, serves as the foundation for formulating an adaptive learning problem on principal quantum learning units, thereby establishing quantum information processing units akin to that of neurons in classical approaches. Then, leveraging the modern HR-calculus, a comprehensive training framework for learning on quantum machines is developed. The quaternion-valued model accommodates mathematical tractability and establishment of performance criteria, such as convergence conditions.

We consider a model where the Standard Model is added to the Einstein Lagrangian together with a Jordan-Brans-Dicke(JBD) coupling. The time-dependent Higgs field has an important role in interpreting the effective gravitational constant, $G_{eff}$. This may lead to two Big Bangs, the first Big Bang characterizes the size of the universe being zero. At this Big Bang, the value of the effective gravitational constant is zero and starts decreasing in time through negative values. During this era, the JBD term is important. In the second Big Bang, the effective gravitational constant passes through infinity to positive values. The negative gravitational constant is interpreted as repulsive gravity. The Lagrangian density provides effective potentials leading to spontaneous symmetry breaking which gives cosmological expectation value of the Higgs field and the Higgs mass which depends on curvature and the Brans Dicke parameter.

Despite the growing promise of artificial intelligence (AI) in supporting decision-making across domains, fostering appropriate human reliance on AI remains a critical challenge. In this paper, we investigate the utility of exploring distance-based uncertainty scores for task delegation to AI and describe how these scores can be visualized through embedding representations for human-AI decision-making. After developing an AI-based system for physical stroke rehabilitation assessment, we conducted a study with 19 health professionals and 10 students in medicine/health to understand the effect of exploring distance-based uncertainty scores on users' reliance on AI. Our findings showed that distance-based uncertainty scores outperformed traditional probability-based uncertainty scores in identifying uncertain cases. In addition, after exploring confidence scores for task delegation and reviewing embedding-based visualizations of distance-based uncertainty scores, participants achieved an 8.20% higher rate of correct decisions, a 7.15% higher rate of changing their decisions to correct ones, and a 7.14% lower rate of incorrect changes after reviewing AI outputs than those reviewing pro

Room acoustic simulations at low frequencies often face significant uncertainties of material parameters and boundary conditions due to absorbing material. We discuss the application of Physics-Informed Neural Networks (PINNs) to solve the (forward) Helmholtz equation in three dimensions (3D), employing mini-batch stochastic gradient descent with periodic resampling every 100 iterations for memory-efficient training. Addressing the computational challenges posed by the extension of PINNs from 2D to 3D for acoustics, DeepXDE is used for implementing the forward PINN. The proposed numerical method is benchmarked against an analytical solution of a standing wave field in 3D. The PINN results are also compared to the Finite Element Method (FEM) solutions for a 3D wave field computed with openCFS. The alignment between PINN-generated solutions and analytical/FEM solutions shows the feasibility of PINNs modeling 3D acoustic applications for future inverse problems, and validating the accuracy and reliability of the proposed approach. Compared to FEM, establishing the PINN model took few hours (similar to the setup of a FEM simulation), the training took 38h to 42.8h (which is longer than

Cybercrime and the market for cyber-related compromises are becoming attractive revenue sources for state-sponsored actors, cybercriminals and technical individuals affected by financial hardships. Due to burgeoning cybercrime on new technological frontiers, efforts have been made to assist digital forensic investigators (DFI) and law enforcement agencies (LEA) in their investigative efforts. Forensic tool innovations and ontology developments, such as the Unified Cyber Ontology (UCO) and Cyber-investigation Analysis Standard Expression (CASE), have been proposed to assist DFI and LEA. Although these tools and ontologies are useful, they lack extensive information sharing and tool interoperability features, and the ontologies lack the latest Smart City Infrastructure (SCI) context that was proposed. To mitigate the weaknesses in both solutions and to ensure a safer cyber-physical environment for all, we propose the Smart City Ontological Paradigm Expression (SCOPE), an expansion profile of the UCO and CASE ontology that implements SCI threat models, SCI digital forensic evidence, attack techniques, patterns and classifications from MITRE. We showcase how SCOPE could present complex

This paper analyses the centralized fusion linear estimation problem in multi-sensor systems with multiple packet dropouts and correlated noises. Packet dropouts are modeled by independent Bernoulli distributed random variables. This problem is addressed in the tessarine domain under conditions of T1 and T2-properness, which entails a reduction in the dimension of the problem and, consequently, computational savings. The methodology proposed enables us to provide an optimal (in the least-mean-squares sense) linear fusion filtering algorithm for estimating the tessarine state with a lower computational cost than the conventional one devised in the real field. Simulation results illustrate the performance and advantages of the solution proposed in different settings.

These lecture notes have been written for courses given at École normale supérieure de Lyon and summer school 2022 in post-quantum cryptography that took place in the university of Budapest. Our objective is to give a general introduction to the foundations of code-based cryptography which is currently known to be secure even against quantum adversaries. In particular we focus our attention to the decoding problem whose hardness is at the ground of the security of many cryptographic primitives, the most prominent being McEliece and Alekhnovich' encryption schemes.

We consider SO(3) symmetric triplet of Higgs fields and SO(4) symmetric complex doublet of Higgs fields in the closed FLRW universe. For these models, Lagrangian densities provide effective potentials leading to spontaneous symmetry breaking which gives cosmological expectation value of the Higgs field and the Higgs mass. We find a relation which emerges between the size of the FLRW universe and cosmological vacuum expectation value of the Higgs field.

The fourth international workshop on Computational Models for Cell Processes (CompMod 2013) took place on June 11, 2013 at the Åbo Akademi University, Turku, Finland, in conjunction with iFM 2013. The first edition of the workshop (2008) took place in Turku, Finland, in conjunction with Formal Methods 2008, the second edition (2009) took place in Eindhoven, the Netherlands, as well in conjunction with Formal Methods 2009, and the third one took place in Aachen, Germany, in conjunction with CONCUR 2013. This volume contains the final versions of all contributions accepted for presentation at the workshop. The goal of the CompMod workshop series is to bring together researchers in Computer Science and Mathematics (both discrete and continuous), interested in the opportunities and the challenges of Systems Biology. The Program Committee of CompMod 2013 selected 3 papers for presentation at the workshop. In addition, we had two invited talks and five informal presentations. The scientific program of the workshop spans an interesting mix of approaches to systems and even synthetic biology, encompassing several different modeling approaches, ranging from quantitative to qualitative techn

From their inception, quaternions and their division algebra have proven to be advantageous in modelling rotation/orientation in three-dimensional spaces and have seen use from the initial formulation of electromagnetic filed theory through to forming the basis of quantum filed theory. Despite their impressive versatility in modelling real-world phenomena, adaptive information processing techniques specifically designed for quaternion-valued signals have only recently come to the attention of the machine learning, signal processing, and control communities. The most important development in this direction is introduction of the HR-calculus, which provides the required mathematical foundation for deriving adaptive information processing techniques directly in the quaternion domain. In this article, the foundations of the HR-calculus are revised and the required tools for deriving adaptive learning techniques suitable for dealing with quaternion-valued signals, such as the gradient operator, chain and product derivative rules, and Taylor series expansion are presented. This serves to establish the most important applications of adaptive information processing in the quaternion domain

Si$_x$Ge$_{1-x-y}$Sn$_y$ ternary alloys are a candidate material system for use in solar cells and other optoelectronic devices. We report on the direct transition energies and structural properties of Ge-rich Si$_x$Ge$_{1-x-y}$Sn$_y$ alloys with six different compositions up to 10 % Si and 3 % Sn, lattice-matched to Ge or GaAs substrates. The direct transitions occurring between 0.9 and 5.0 eV were investigated using spectroscopic ellipsometry (SE), and the resulting data was used to obtain the dielectric functions of the Si$_x$Ge$_{1-x-y}$Sn$_y$n layer by fitting a multi-layer model. Values for the $E_0$, $E_1$, $Δ_1$, $E_0'$ and $E_2$ transition energies were then found by differentiating these dielectric functions to extract the locations of critical points. Structurally, the composition of the samples was measured using energy-dispersive X-ray measurements (EDX). The lattice constants predicted from these compositions are in good agreement with reciprocal space maps obtained through X-ray diffraction (XRD). The results confirm that a 1 eV direct absorption edge can be achieved using relatively low Si and Sn fractions ($<$ 10 % and $<$ 3 % respectively), while the higher-

This volume contains the final versions of the papers presented at the 3rd International Workshop on Computational Models for Cell Processes (CompMod 2011). The workshop took place on September 10, 2011 at the University of Aachen, Germany, in conjunction with CONCUR 2011. The first edition of the workshop (2008) took place in Turku, Finland, in conjunction with Formal Methods 2008 and the second edition (2009) took place in Eindhoven, the Netherlands, as well in conjunction with Formal Methods 2009. The goal of the CompMod workshop series is to bring together researchers in Computer Science (especially in Formal Methods) and Mathematics (both discrete and continuous), interested in the opportunities and the challenges of Systems Biology.

Slime mould plasmodia can adjust their behaviour in response to chemical trails left by themselves and other Physarum plasmodia. This simple feedback process increases their foraging efficiency. We still do not know whether other factors influence plasmodium behaviour in realistic competition settings. Here we designed a competition experiment where two plasmodia had to find one food source in a common environment. As previously shown, the time it took plasmodia to find food depended on their hunger motivation. However, the time it took a plasmodium to start looking for food depended on its motivation and the motivation of its competitor. Plasmodia always initiated foraging quicker if they were in the presence of a competitor and the quickest if they were hungry and in the presence of a satiated competitor. The time it took to arrive to the food was not influenced by whether they were alone or with a competitor. Ultimately, this complex competition response benefited the hungry plasmodia as they had a 4:1 chance of finding the food first. The sensory ecology of Physarum polycephalum is more complex than previously thought and yields complex behaviour in a simple organism.

This is the history of translating Cantor's works into Russian from 1892 to 1985 in Odessa, Moscow, Tomsk, Kazan, S.-Petersburg, Leningrad. Mathematicians and philosophers in Russia took the ideas of the theory of sets enthusiastically. Such renowned scholars and scientists as Timchenko, Shatunovsky, Vasiliev, Florensky, Mlodzeevsky, Nekrasov, Zhegalkin, Yushkevich Sr., Fet, Yushkevich Jr., Kolmogorov, and Medvedev took part in their popularisation. In 1970 Academician Pontryagin rated the theory of sets as useless for young mathematicians, and the translated works of Cantor were not published. This article first describes the tragic fate of this translation.

Technological advances have enabled multiple countries to consider implementing Smart City Infrastructure to provide in-depth insights into different data points and enhance the lives of citizens. Unfortunately, these new technological implementations also entice adversaries and cybercriminals to execute cyber-attacks and commit criminal acts on these modern infrastructures. Given the borderless nature of cyber attacks, varying levels of understanding of smart city infrastructure and ongoing investigation workloads, law enforcement agencies and investigators would be hard-pressed to respond to these kinds of cybercrime. Without an investigative capability by investigators, these smart infrastructures could become new targets favored by cybercriminals. To address the challenges faced by investigators, we propose a common definition of smart city infrastructure. Based on the definition, we utilize the STRIDE threat modeling methodology and the Microsoft Threat Modeling Tool to identify threats present in the infrastructure and create a threat model which can be further customized or extended by interested parties. Next, we map offences, possible evidence sources and types of threats