搜索结果：Extended

Classical hydrodynamics rests on the point-particle idealization, leading to parabolic transport equations, infinite signal speeds, and the inability to capture finite time relaxation, anisotropic transport, or non Fourier thermal phenomena. This work introduces Extended Structural Dynamics (ESD), a kinetic framework in which constituents are described as spatially extended objects possessing orientation, angular momentum, and internal deformation modes. Starting from an extended Boltzmann equation, a Chapman Enskog expansion with BGK closure yields two hyperbolic parabolic transport laws: a dynamical spin equation coupling orientational relaxation to fluid vorticity, and a heat flux relaxation equation with structural thermal conductivity. These equations predict finite propagation speeds for momentum and heat, intrinsic shock regularization, anisotropic transport, and thermal waves. The spin equation provides a kinetic derivation of micropolar fluid theory, while the heat flux equation supplies a microscopic foundation for Cattaneo Vernotte behavior. Quantitative estimates indicate structural contributions can dominate classical transport coefficients. The BGK closure preserves t

The Hayabusa2 extended mission, nicknamed Hayabusa2# (# is pronounced SHARP, which stands for the Small Hazardous Asteroid Reconnaissance Probe), is JAXA's small body explorer to conduct science and engineering investigations in space. After the successful return to the Earth with the samples from the carbonaceous asteroid (162173) Ryugu on December 6, 2020, Hayabusa2 diverted away from Earth to start its decade-long extended mission. The major scope includes engineering demonstration of long-term maintenance strategies for spacecraft and operation systems and scientific investigations during various mission phases. Major scientific investigations include spacecraft-based telescopic observations of exoplanets and zodiacal dust observations during the cruise phase, flyby observations of the near-Earth asteroid (98943) Torifune in July 2026, and rendezvous observations of near-Earth asteroid 1998 KY26 in 2031. This study overviews Hayabusa2#'s flyby and the physical properties of Torifune. Although the flyby operation planning is still ongoing, the mission will attempt to fly by the target at a distance (from the asteroid's center) of ~1-10 km. The flyby speed is planned to be 5.25 k

Extended Reality (XR) enables immersive capture and re-experience of personal memories, yet how interface representations shape these experiences remains underexplored. We examine how users relive and share XR memories through three interaction approaches: (1) physical memory-linked objects, (2) virtual memory-linked objects, and (3) a conventional virtual gallery interface. In a within-subjects study (N=24, 12 pairs), participants captured shared experiences using 360° video and later accessed and shared these memories across the three interfaces. We analyzed open-ended qualitative responses focusing on perceived value, enjoyment, usability, emotional attachment, and social connection. The findings reveal trade-offs: physical objects fostered stronger social connection and conversation through tangible exchange; virtual objects balanced engagement and usability; and the gallery interface was efficient but less personal. These results suggest that object-based representations, physical and virtual, support key social dimensions of XR memory experiences, offering lessons for designing future systems that emphasize shared meaning and interpersonal connection.

Empirical coordination offers a way to understand how agents can coordinate actions under communication constraints. This paper investigates the finite blocklength regime of this problem, where the encoder and decoder aim to produce a sequence of action pairs that is jointly typical with respect to a target distribution. Adopting Shannon's random coding argument and leveraging the method of types, we analyze the average performance of a random codebook to establish an achievability result. The resulting bound on the optimal rate is presented both in exact form and as an asymptotic expansion, aligning with the prevailing characterizations in the finite blocklength literature. This work extends finite blocklength analysis to the empirical coordination setting, complementing existing results on strong coordination.

Diffie-Hellman groups are commonly used in cryptographic protocols. While most state-of-the-art, symbolic protocol verifiers support them to some degree, they do not support all mathematical operations possible in these groups. In particular, they lack support for exponent addition, as these tools reason about terms using unification, which is undecidable in the theory describing all Diffie-Hellman operators. In this paper we approximate such a theory and propose a semi-decision procedure to determine whether a protocol, which may use all operations in such groups, satisfies user-defined properties. We implement this approach by extending the Tamarin prover to support the full Diffie-Hellman theory, including group element multiplication and hence addition of exponents. This is the first time a state-of-the-art tool can model and reason about such protocols. We illustrate our approach's effectiveness with different case studies: ElGamal encryption and MQV. Using Tamarin, we prove security properties of ElGamal, and we rediscover known attacks on MQV.

AI-enhanced Extended Reality (XR) aims to deliver adaptive, immersive experiences-yet current systems fall short due to shallow user modeling and limited cognitive context. We introduce Perspective-Aware AI in Extended Reality (PAiR), a foundational framework for integrating Perspective-Aware AI (PAi) with XR to enable interpretable, context-aware experiences grounded in user identity. PAi is built on Chronicles: reasoning-ready identity models learned from multimodal digital footprints that capture users' cognitive and experiential evolution. PAiR employs these models in a closed-loop system linking dynamic user states with immersive environments. We present PAiR's architecture, detailing its modules and system flow, and demonstrate its utility through two proof-of-concept scenarios implemented in the Unity-based OpenDome engine. PAiR opens a new direction for human-AI interaction by embedding perspective-based identity models into immersive systems.

It is known that many modal and superintuitionistic logics are PSPACE-hard in languages with a small number of variables; however, questions about the complexity of similar fragments of many logics obtained by adding various axioms to "standard" ones remain unexplored. We investigate the complexity of fragments of modal logics obtained by adding an axiom requiring the convergence of the accessibility relation in Kripke frames: S4.2, K4.2, Grz.2, and GL.2. The main result is that S4.2 and Grz.2 are PSPACE-complete in a language with two variables, while K4.2 and GL.2* (a logic near to GL.2) are PSPACE-complete in a language with one variable. The obtained results are extended to infinite classes of logics.

We consider a generalisation of vector fields on a vector space, where the vector space is generalised to a highest-weight module over a Kac-Moody algebra. The generalised vector field is an element in a non-associative superalgebra defined by the module and the Kac-Moody algebra. Also the Lie derivative of a vector field parameterised by another is generalised and expressed in a simple way in terms of this superalgebra. It reproduces the generalised Lie derivative in the general framework of extended geometry, which in special cases reduces to the one in exceptional field theory, unifying diffeomorphisms with gauge transformations in supergravity theories.

Second-order quantifier-elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and subclasses with applications throughout computational logic. One of the most prominent algorithms for second-order quantifier elimination is the SCAN algorithm which is based on saturation theorem proving. In this paper we show how the SCAN algorithm on clause sets can be extended to solve a more general problem: namely, finding an instance of the second-order quantifiers that results in a logically equivalent first-order formula. In addition we provide a prototype implementation of the proposed method. This work paves the way for applying the SCAN algorithm to new problems in application domains such as modal correspondence theory, knowledge representation, and verification.

At its core, abstraction is the process of generalizing from specific instances to broader concepts or models, with the primary objective of reducing complexity while preserving properties essential to the intended purpose. It is a~fundamental, often implicit, principle that structures the understanding, communication, and development of both scientific knowledge and everyday beliefs. Studies on abstraction have evolved from its origins in Ancient Greek philosophy through methodological approaches in psychological and philosophical theories to modern computational frameworks. This paper presents a novel logic-based framework for modeling abstraction processes in which all components are expressed within logic. The framework extends beyond the traditional focus on the entailment of necessary conditions by making sufficient conditions first-class citizens as well. We define approximate abstractions, study their tightest and exact forms, and extend the approach to layered abstractions, enabling hierarchical simplification of complex systems and models. The computational complexity of the related reasoning tasks is also discussed. For clarity, our framework is developed within classica

We give an explicit formula for the generators of the logarithmic vector field of the coning of the extended Catalan arrangement of type $B_\ell$.

This paper studies properties of the integer sequence $\overline{\overline{G}}_n=\prod_{k=0}^n\binom{n}{k}_{\mathbb{Z},\mathbb{N}}$ which is analogous to $\overline{G}_n=\prod_{k=0}^n\binom{n}{k}$, the product of the elements of the $n$-th row of Pascal's triangle. Here $\binom{n}{k}_{\mathbb{Z},\mathbb{N}}$ is an extended binomial coefficient, defined in the paper, constructed using an extended version of M. Bhargava's theory of generalized factorials. In 1996 M. Bhargava introduced a generalization of the factorial function, $n!_S=\prod_pν_n(S,p)$ in terms of their prime factorization, and defines associated binomial coefficients. The last two authors extended Bhargava's invariants further to define such invariants attached to each integer $b\ge2$. One obtains extended factorials and extended binomial coefficients, and the maximal extension defines extended factorials $n!_{\mathbb{Z},\mathbb{N}}=\prod_{b\ge2}b^{α_n(\mathbb{Z},b)}$ including all $b\ge2$, with associated extended binomial coefficients $\binom{n}{k}_{\mathbb{Z},\mathbb{N}}$, yielding $\overline{\overline{G}}_n$. We have $\overline{\overline{G}}_n=\prod_{b=2}^nb^{\overlineν(n,b)}$ and the partial factorizations $\ove

We continue the study of extended Weyl groups $W$, which are reflection groups. Further we recall the definition of a hyperbolic cover of an extended Weyl group, and show that the hyperbolic covers of the extended Weyl groups are extended Coxeter groups, which had been introduced by Looijenga and discussed by people from different mathematical areas. More precisely the hyperbolic covers are the extended Coxeter groups of star type. We define simple reflections and Coxeter transformations in these groups, and show the transitivity of the Hurwitz action on the set of reduced reflection factorizations of a Coxeter transformation in the extended Coxeter groups of star type $\mathcal{W}$, where the reflections are the conjugates of the simple reflections in $\mathcal{W}$. We give two applications of our results. In the context of representation theory of algebras, we establish an isomorphism between the poset of thick subcategories that are generated by exceptional sequences of a hereditary connected ext-finite abelian $k$-category with a tilting object, $k$ algebraically closed of characteristic $0$, and the poset of elements in the extended Weyl group that are below a Coxeter transfor

The extended source effect on microlensing magnification is non-negligible and must be taken into account for in an analysis of microlensing. However, the evaluation of the extended source magnification is numerically expensive because it includes the two-dimensional integral over source profile. Various studies have developed methods to reduce this integral down to the one-dimensional-integral or integral-free form, which adopt some approximations or depend on the exact form of the source profile, e.g. disk, linear/quadratic limb-darkening profile. In this paper, we develop a new method to evaluate the extended source magnification based on fast Fourier transformation (FFT), which does not adopt any approximations and is applicable to any source profiles. Our implementation of the FFT based method enables the fast evaluation of the extended source magnification as fast as $\sim1$ msec (CPU time on a laptop) and guarantees an accuracy better than 0.3%. The FFT based method can be used for the template fitting to a huge data set of light curves from the existing and upcoming surveys.

This paper proposes a Poisson multi-Bernoulli mixture (PMBM) filter for coexisting point and extended targets, i.e., for scenarios where there may be simultaneous point and extended targets. The PMBM filter provides a recursion to compute the multi-target filtering posterior based on probabilistic information on data associations, and single-target predictions and updates. In this paper, we first derive the PMBM filter update for a generalised measurement model, which can include measurements originated from point and extended targets. Second, we propose a single-target space that accommodates both point and extended targets and derive the filtering recursion that propagates Gaussian densities for point targets and gamma Gaussian inverse Wishart densities for extended targets. As a computationally efficient approximation of the PMBM filter, we also develop a Poisson multi-Bernoulli (PMB) filter for coexisting point and extended targets. The resulting filters are analysed via numerical simulations.

This paper introduces a hybrid dynamical system methodology for managing impulsive control in spacecraft rendezvous and proximity operations under the Hill-Clohessy-Wiltshire model. We address the control design problem by isolating the out-of-plane from the in-plane dynamics and present a feedback control law for each of them. This law is based on a Lyapunov function tailored to each of the dynamics, capable of addressing thruster saturation and also a minimum impulse bit. These Lyapunov functions were found by reformulating the system's dynamics into coordinates that more intuitively represent their physical behavior. The effectiveness of our control laws is then shown through numerical simulation. This is an extended version of an ECC24 article of the same name, which includes the proofs omitted for lack of space.

We introduce a modification of the Press-Schechter formalism aimed to derive general mass functions for primordial black holes (PBHs). In this case, we start from primordial power spectra (PPS) which include a monochromatic spike, typical of ultra slow-roll inflation models. We consider the PBH formation as being associated to the amplitude of the spike on top of the linear energy density fluctuations, coming from a PPS with a blue index. By modelling the spike with a log-normal function, we study the properties of the resulting mass function spikes, and compare these to the underlying extended mass distributions. When the spike is at PBH masses which are much lower than the exponential cutoff of the extended distribution, very little mass density is held by the PBHs within the spike, and it is not ideal to apply the Press-Schechter formalism in this case as the resulting characteristic overdensity is too different from the threshold for collapse. It is more appropriate to do so when the spike mass is similar to, or larger than the cutoff mass. Additionally, it can hold a similar mass density as the extended part. Such particular mass functions also contain large numbers of small P

The Poisson multi-Bernoulli mixture (PMBM) is a multi-target distribution for which the prediction and update are closed. By applying the random finite set (RFS) framework to multi-target tracking with sets of trajectories as the variable of interest, the PMBM trackers can efficiently estimate the set of target trajectories. This paper derives two trajectory RFS filters for extended target tracking, called extended target PMBM trackers. Compared to the extended target PMBM filter based on sets on targets, explicit track continuity between time steps is provided in the extended target PMBM trackers.

Building up on our previous works regarding $q$-deformed $P$-partitions, we introduce a new family of subalgebras for the ring of quasisymmetric functions. Each of these subalgebras admits as a basis a $q$-analogue to Gessel's fundamental quasisymmetric functions where $q$ is equal to a complex root of unity. Interestingly, the basis elements are indexed by sets corresponding to an intermediary statistic between peak and descent sets of permutations that we call extended peak.