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The parameters of uniformly accelerated reference frame s three equivalent ways is calculated. The article also found explicitly transformation to uniformly accelerated reference frame and proved the assertion that Thomas precession and Wigner rotation s in opposite directions and cancel each other out.

A poset is called upper homogeneous, or "upho," if all of its principal order filters are isomorphic to the whole poset. In previous work of the first author, it was shown that each (finite-type N-graded) upho lattice has associated to it a finite graded lattice, called its core, which determines the rank generating function of the upho lattice. In that prior work the question of which finite graded lattices arise as cores was explored. Here, we study the question of in how many different ways a given finite graded lattice can be realized as the core of an upho lattice. We show that if the finite lattice has no nontrivial automorphisms, then it is the core of finitely many upho lattices. We also show that the number of ways a finite lattice can be realized as a core is unbounded, even when restricting to rank-two lattices. We end with a discussion of a potential algorithm for listing all the ways to realize a given finite lattice as a core.

Dicke states are permutation-invariant superpositions of qubit computational basis states, which play a prominent role in quantum information science. We consider here two higher-dimensional generalizations of these states: $SU(2)$ spin-$s$ Dicke states and $SU(d)$ Dicke states. We present various ways of preparing both types of qudit Dicke states on a qudit quantum computer, using two main approaches: a deterministic approach, based on exact canonical matrix product state representations; and a probabilistic approach, based on quantum phase estimation. The quantum circuits are explicit and straightforward, and are arguably simpler than those previously reported.

In early 2025, Augmented Intelligence - Christie's first AI art auction - drew criticism for showcasing a controversial genre. Amid wider legal uncertainty, artists voiced concerns over data mining practices, notably with respect to copyright. The backlash could be viewed as a microcosm of AI's contested position in the creative economy. Touching on the auction's presentation, reception, and results, this paper explores how, among social dissonance, machine learning finds its place in the artworld. Foregrounding responsible innovation, the paper provides a balanced perspective that champions creators' rights and brings nuance to this polarised debate. With a focus on exhibition design, it centres framing, which refers to the way a piece is presented to influence consumer perception. Context plays a central role in shaping our understanding of how good, valuable, and even ethical an artwork is. In this regard, Augmented Intelligence situates AI art within a surprisingly traditional framework, leveraging hallmarks of "high art" to establish the genre's cultural credibility. Generative AI has a clear economic dimension, converging questions of artistic merit with those of monetary wor

We introduce a very simple solitaire game, named Stanley Solitaire, in honor of Richard Stanley, and prove an explicit closed-form formula for the number of ways of playing it. Alas, the only proof that we know is via a deep theorem of Richard Stanley from 1984. We challenge the readers to find a more elementary proof.

The stellar halo of the Milky Way records the history of its interactions with dwarf galaxies, whose subsequent destruction results in the formation of an extended stellar component. Recent works have suggested that galaxies with masses comparable to the Large Magellanic Cloud (LMC, $M_\star \sim 10^9\,{\rm M}_\odot$) may be the primary building blocks of the stellar halo of our Galaxy. We use cosmological simulations of the $Λ$ Cold Dark Matter model to investigate LMC-mass galaxies at $z=1-2$ using a semi-analytic model of galaxy formation. We find that LMC analogues at $z=2$ evolve until the present day along three distinct pathways: (1) those that are destroyed in Milky Way-mass hosts; (2) those that are themselves the main progenitors of Milky Way-mass galaxies; and (3) those that survive until $z=0$, with stellar mass $\sim$1.0 dex lower than typical Milky Ways. We predict that the properties of these galaxies at $z=2$ (stellar metallicities, sizes, gas content etc.) are largely indistinguishable, irrespective of which of these pathways is eventually taken; a survey targeting such galaxies in this redshift range would struggle to tell apart a 'destroyed' stellar halo progenit

Learned locomotion policies can rapidly adapt to diverse environments similar to those experienced during training but lack a mechanism for fast tuning when they fail in an out-of-distribution test environment. This necessitates a slow and iterative cycle of reward and environment redesign to achieve good performance on a new task. As an alternative, we propose learning a single policy that encodes a structured family of locomotion strategies that solve training tasks in different ways, resulting in Multiplicity of Behavior (MoB). Different strategies generalize differently and can be chosen in real-time for new tasks or environments, bypassing the need for time-consuming retraining. We release a fast, robust open-source MoB locomotion controller, Walk These Ways, that can execute diverse gaits with variable footswing, posture, and speed, unlocking diverse downstream tasks: crouching, hopping, high-speed running, stair traversal, bracing against shoves, rhythmic dance, and more. Video and code release: https://gmargo11.github.io/walk-these-ways/

The web is full of guidance on a wide variety of tasks, from changing the oil in your car to baking an apple pie. However, as content is created independently, a single task could have thousands of corresponding procedural texts. This makes it difficult for users to view the bigger picture and understand the multiple ways the task could be accomplished. In this work we propose an unsupervised learning approach for summarizing multiple procedural texts into an intuitive graph representation, allowing users to easily explore commonalities and differences. We demonstrate our approach on recipes, a prominent example of procedural texts. User studies show that our representation is intuitive and coherent and that it has the potential to help users with several sensemaking tasks, including adapting recipes for a novice cook and finding creative ways to spice up a dish.

In this paper, we draw attention to a promising yet slightly underestimated measure of variability - the Gini coefficient. We describe two new ways of defining and interpreting this parameter. Using our new representations, we compute the Gini index for a few probability distributions and describe it in more detail for the negative binomial distribution. We also suggest the latter as a tool to measure overdispersion in epidemiology.

Because the problem of Apollonius is generally considered over the reals, it suffers from variance of number: there are at most eight circles simultaneously tangent to a given trio of circles, but some configurations have fewer than eight tangent circles. This issue arises over other non-closed fields as well. Using the tools of enriched enumerative geometry, we give two different ways to count the circles of Apollonius such that invariance of number holds over any field of characteristic not 2. We also pose the geometricity problem for local indices in enriched enumerative geometry.

People differ in how they attend to, interpret, and respond to their surroundings. Convergent processing of the world may be one factor that contributes to social connections between individuals. We used neuroimaging and network analysis to investigate whether the most central individuals in their communities (as measured by in-degree centrality, a notion of popularity) process the world in a particularly normative way. We found that more central individuals had exceptionally similar neural responses to their peers and especially to each other in brain regions that are associated with high-level interpretations and social cognition (e.g., in the default-mode network), whereas less-central individuals exhibited more idiosyncratic responses. Self-reported enjoyment of and interest in stimuli followed a similar pattern, but accounting for these data did not change our main results. These findings suggest that highly-central individuals process the world in exceptionally similar ways, whereas less-central individuals process the world in idiosyncratic ways.

An experimental detection of graviton is extremely hard problem, however, there are different ways to evaluate a graviton mass if it is non-vanishing. Theories of massive gravity or theories with non-vanishing graviton mass initially have a number of pathologies such as discontinuities, ghosts etc. In last years theorists found ways to overcome weaknesses of such theories meanwhile observational features are also discussed. In the first publication reporting about the discovery of gravitational waves from the binary black hole system the LIGO-Virgo collaboration obtained the graviton mass constraint around $1.2 \times 10^{-22}$ eV (later the estimate was improved with new data). A comparable and consistent graviton mass constraint around $2.9 \times 10^{-21}$ eV has been obtained from analysis of the bright star S2 trajectory near the Galactic Center.

In an age of media saturation, how can astronomers succeed in grabbing the public's attention to increase awareness and understanding of astronomy? Here I discuss some creative alternatives to press releases, public lectures, television programs, books, magazine articles, and other traditional ways of bringing astronomy to a wide audience. By thinking outside the box and employing novel tools - from truly terrible sci-fi movies, to modern Stonehenges, to music from the stars - astronomers are finding effective new ways of communicating the wonders of the universe to people of all ages.

Getting good speedup -- let alone high parallel efficiency -- for parallel-in-time (PinT) integration examples can be frustratingly difficult. The high complexity and large number of parameters in PinT methods can easily (and unintentionally) lead to numerical experiments that overestimate the algorithm's performance. In the tradition of Bailey's article "Twelve ways to fool the masses when giving performance results on parallel computers", we discuss and demonstrate pitfalls to avoid when evaluating performance of PinT methods. Despite being written in a light-hearted tone, this paper is intended to raise awareness that there are many ways to unintentionally fool yourself and others and that by avoiding these fallacies more meaningful PinT performance results can be obtained.

We construct examples of free-by-cyclic hyperbolic groups which fiber in infinitely many ways over Z. The construction involves adding a specialized square 2-cell to a non-positively curved, squared 2-complex defined by labeled oriented graphs. The fundamental groups of the resulting complexes are hyperbolic, free-by-cyclic and can be mapped onto Z in infinitely many ways.

A polyomino is called a development if it can make a box by folding edges of unit squares forming the polyomino. It is known that there are developments that can fold into a box (or boxes) in multiple ways. In this work, we conducted a computer search for finding such developments by using a SAT solver. As a result, we found thousands of such developments including a polyomino of area 52 that can fold into a box of size $1 \times 2 \times 8$ in five different ways.

We establish a theoretical understanding of the entanglement properties of a physical system that mediates a quantum information splitting protocol. We quantify the different ways in which an arbitrary $n$ qubit state can be split among a set of $k$ participants using a $N$ qubit entangled channel, such that the original information can be completely reconstructed only if all the participants cooperate. Based on this quantification, we show how to design a quantum protocol with minimal resources and define the splitting efficiency of a quantum channel which provides a way of characterizing entangled states based on their usefulness for such quantum networking protocols.