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Self-propelled particles, like motile cells and artificial colloids, can spontaneously form macroscopic clusters. This phenomenon is called motility-induced phase separation (MIPS) and occurs even without attractive forces, provided that the self-propulsion direction fluctuates slowly. In addition to rotational noise, these particles may experience translational noise, not coupled to rotational noise, due to environmental fluctuations. We study the role of translational noise in the clustering of active Brownian hard disks. To tease apart the contribution of translational noise, we model excluded-volume interactions through a Monte-Carlo-like overlap rejection approach. We find that increasing translational diffusivity has a non-monotonic effect on clustering. At low values, it makes clusters more compact and rounded (less filamentous), eventually promoting genuine MIPS. For sufficiently higher translational diffusivity, clusters evaporate. We develop a theory for the cluster mass distribution, and employ a hydrodynamic approach with parameters taken from the simulation, that explains the clustering phase diagram.

The translational tiling problem, dated back to Wang's domino problem in the 1960s, is one of the most representative undecidable problems in the field of discrete geometry and combinatorics. Ollinger initiated the study of the undecidability of translational tiling with a fixed number of tiles in 2009, and proved that translational tiling of the plane with a set of $11$ polyominoes is undecidable. The number of polyominoes needed to obtain undecidability was reduced from $11$ to $7$ by Yang and Zhang, and then to $5$ by Kim. We show that translational tiling of the plane with a set of $4$ (disconnected) polyominoes is undecidable in this paper.

Recently, Greenfeld and Tao disprove the conjecture that translational tilings of a single tile can always be periodic [Ann. Math. 200(2024), 301-363]. In another paper [to appear in J. Eur. Math. Soc.], they also show that if the dimension $n$ is part of the input, the translational tiling for subsets of $\mathbb{Z}^n$ with one tile is undecidable. These two results are very strong pieces of evidence for the conjecture that translational tiling of $\mathbb{Z}^n$ with a monotile is undecidable, for some fixed $n$. This paper shows that translational tiling of the $3$-dimensional space with a set of $5$ polycubes is undecidable. By introducing a technique that lifts a set of polycubes and its tiling from $3$-dimensional space to $4$-dimensional space, we manage to show that translational tiling of the $4$-dimensional space with a set of $4$ tiles is undecidable. This is a step towards the attempt to settle the conjecture of the undecidability of translational tiling of the $n$-dimensional space with a monotile, for some fixed $n$.

The first undecidability result on the tiling is the undecidability of translational tiling of the plane with Wang tiles, where there is an additional color matching requirement. Later, researchers obtained several undecidability results on translational tiling problems where the tilings are subject to the geometric shapes of the tiles only. However, all these results are proved by constructing tiles with extremely concave shapes. It is natural to ask: can we obtain undecidability results of translational tiling with convex tiles? Towards answering this question, we prove the undecidability of translational tiling of the plane with a set of 7 orthogonally convex polyominoes.

Recently, two extraordinary results on aperiodic monotiles have been obtained in two different settings. One is a family of aperiodic monotiles in the plane discovered by Smith, Myers, Kaplan and Goodman-Strauss in 2023, where rotation is allowed, breaking the 50-year-old record (aperiodic sets of two tiles found by Roger Penrose in the 1970s) on the minimum size of aperiodic sets in the plane. The other is the existence of an aperiodic monotile in the translational tiling of $\mathbb{Z}^n$ for some huge dimension $n$ proved by Greenfeld and Tao. This disproves the long-standing periodic tiling conjecture. However, it is known that there is no aperiodic monotile for translational tiling of the plane. The smallest size of known aperiodic sets for translational tilings of the plane is $8$, which was discovered more than $30$ years ago by Ammann. In this paper, we prove that translational tiling of the plane with a set of $7$ polyominoes is undecidable. As a consequence of the undecidability, we have constructed a family of aperiodic sets of size $7$ for the translational tiling of the plane. This breaks the 30-year-old record of Ammann.

In this study, we investigate the thermocapillary rotation of microgears at fluid interfaces and extend the concept of geometric asymmetry to the translational propulsion of micron-sized particles. We introduce a transient numerical model that couples the Navier-Stokes equations with heat transfer, displaying particle motion through a moving mesh interface. The model incorporates absorbed light illumination as a heat source and predicts both rotational and translational speeds of particles. Our simulations explore the influence of microgear design geometry and determine the scale at which thermocapillary Marangoni motion could serve as a viable propulsion method. A clear correlation between Reynolds number and propulsion efficiency can be recognized. To transfer the asymmetry-based propulsion principle from rotational to directed translational motion, various particle geometries are considered. The exploration of breaking geometric symmetry for translational propulsion is mostly ignored in the existing literature, thus warranting further discussion. Therefore, we analyse expected translational speeds in comparison to corresponding microgears to provide insights into this promising

In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here we propose a systematic method of constructing the topological band insulators without translational symmetry in the amorphous systems. By way of the isospectral reduction approach from spectral graph theory, we reduce the structural-disordered systems formed by different multi-atomic cells into the isospectral effective periodic systems with the energy-dependent hoppings and potentials. We identify the topological band insulating phases with extended bulk states and topological in-gap edge states by the topological invariants of the reduced systems, density of states, and the commutation of the transfer matrix. In addition, when the building blocks of the two multi-atomic cells have different number of the lattice sites, our numerical calculations demonstrate that the existences of the flat band and the macroscopic bound states in the continuum in the amorphous systems. Our findings uncover an arena for the exploration of the topological band s

The eukaryotic protein synthesis process entails intricate stages governed by diverse mechanisms to tightly regulate translation. Translational regulation during stress is pivotal for maintaining cellular homeostasis, ensuring the accurate expression of essential proteins crucial for survival. This selective translational control mechanism is integral to cellular adaptation and resilience under adverse conditions. This review manuscript explores various mechanisms involved in selective translational regulation, focusing on mRNA-specific and global regulatory processes. Key aspects of translational control include translation initiation, which is often a rate-limiting step, and involves the formation of the eIF4F complex and recruitment of mRNA to ribosomes. Regulation of translation initiation factors, such as eIF4E, eIF4E2, and eIF2, through phosphorylation and interactions with binding proteins, modulates translation efficiency under stress conditions. This review also highlights the control of translation initiation through factors like the eIF4F complex and the ternary complex and also underscores the importance of eIF2α phosphorylation in stress granule formation and cellular

We consider the translational hull $Ω(I)$ of an arbitrary subsemigroup $I$ of an endomorphism monoid $\mathrm{End}(A)$ where $A$ is a universal algebra. We give conditions for every bi-translation of $I$ to be realised by transformations, or by endomorphisms, of $A$. We demonstrate that certain of these conditions are also sufficient to provide natural isomorphisms between the translational hull of $I$ and the idealiser of $I$ within $\mathrm{End}(A)$, which in the case where $I$ is an ideal is simply $\mathrm{End}(A)$. We describe the connection between these conditions and work of Petrich and Gluskin in the context of densely embedded ideals. Where the conditions fail, we develop a methodology to extract information concerning $Ω(I)$ from the translational hull $Ω(I/{\approx})$ of a quotient $I/{\approx}$ of $I$. We illustrate these concepts in detail in the cases where $A$ is: a free algebra; an independence algebra; a finite symmetric group.

Drug research and development are embracing translational research for its potential to increase the number of drugs successfully brought to clinical applications. Using the publicly available PubMed database, we sought to describe the status of drug translational research, the distribution of translational lags for all drugs as well as the collaborations between basic science and clinical science in drug research. For each drug, an indicator called Translational Lag was proposed to quantify the interval time from its first PubMed article to its first clinical article. Meanwhile, the triangle of biomedicine was also used to visualize the status and multidisciplinary collaboration of drug translational research. The results showed that only 18.1% (24,410) of drugs/compounds had been successfully entering clinical research. It averagely took 14.38 years (interquartile range, 4 to 21 years) for a drug from the initial basic discovery to its first clinical research. In addition, the results also revealed that, in drug research, there was rare cooperation between basic science and clinical science, which were more inclined to cooperate within disciplines.

This paper focuses on the undecidability of translational tiling of $n$-dimensional space $\mathbb{Z}^n$ with a set of $k$ tiles. It is known that tiling $\mathbb{Z}^2$ with translated copies with a set of $8$ tiles is undecidable. Greenfeld and Tao gave strong evidence in a series of works that for sufficiently large dimension $n$, the translational tiling problem for $\mathbb{Z}^n$ might be undecidable for just one tile. This paper shows the undecidability of translational tiling of $\mathbb{Z}^3$ with a set of $6$ tiles.

ODNP (Overhauser Dynamic Nuclear Polarization) detects an experimental measurable associated directly with translational motion of water at the nanoscale, a quantity that few other methods can detect. This study offers a unique insight into the translational diffusion of water inside RMs (reverse micelles). It finds that simply adjusting the "water loading" ($w_0$, i.e. the mole ratio of surfactant to water) to tune the size of the RMs achieves a near-continuous tuning of the translational diffusion of water. Furthermore, (1) water molecules in the core of relatively large RMs ($w_0=10$, diameter of water nanopool $\approx 3.5$ nm) diffuse only as fast as those on the surface of a lipid bilayer and (2) surprisingly, translational diffusion slows to a near-stop for RMs that are small, but still contain hundreds of water molecules in their core. Extrapolation to larger sized water pools implies that in order to recover bulk-like translational dynamics, tens of thousands of water molecules are required. The data from the small RMs also represent a breakthrough as the first example where a spin probe that is completely exposed to water (as opposed to buried inside a macromolecule) obse

Is there a fixed dimension $n$ such that translational tiling of $\mathbb{Z}^n$ with a monotile is undecidable? Several recent results support a positive answer to this question. Greenfeld and Tao disprove the periodic tiling conjecture by showing that an aperiodic monotile exists in sufficiently high dimension $n$ [Ann. Math. 200(2024), 301-363]. In another paper [to appear in J. Eur. Math. Soc.], they also show that if the dimension $n$ is part of the input, then the translational tiling for subsets of $\mathbb{Z}^n$ with one tile is undecidable. These two results are very strong pieces of evidence for the conjecture that translational tiling of $\mathbb{Z}^n$ with a monotile is undecidable, for some fixed $n$. This paper gives another supportive result for this conjecture by showing that translational tiling of the $4$-dimensional space with a set of three connected tiles is undecidable.

In the 60's, Berger famously showed that translational tilings of $\mathbb{Z}^2$ with multiple tiles are algorithmically undecidable. Recently, Bhattacharya proved the decidability of translational monotilings (tilings by translations of a single tile) in $\mathbb{Z}^2$. The decidability of translational monotilings in higher dimensions remained unsolved. In this paper, by combining our recently developed techniques with ideas introduced by Aanderaa and Lewis, we finally settle this problem, achieving the undecidability of translational monotilings of (periodic subsets of) virtually $\mathbb{Z}^2$ spaces, namely, spaces of the form $\mathbb{Z}^2\times G_0$, where $G_0$ is a finite Abelian group. This also implies the undecidability of translational monotilings in $\mathbb{Z}^d$, $d\geq 3$.

The study of the structure of translational tilings has captivated mathematicians, scientists, and the general public for centuries and continues to thrive at the crossroads of analysis, combinatorics, dynamics, logic, number theory, and geometry. This vibrant field seeks to uncover the delicate divide between rigid structures and unpredictable, ``wild'' behaviors that arise when sets fill space by translations without gaps or overlaps. We provide an overview of this study and recent developments, highlighting its multidisciplinary nature and offering a glimpse into the process behind the results.

Keeping track of translational research is essential to evaluating the performance of programs on translational medicine. Despite several indicators in previous studies, a consensus measure is still needed to represent the translational features of biomedical research at the article level. In this study, we first trained semantic representations of biomedical entities and documents (i.e., bio entity2vec and bio doc2vec) based on over 30 million PubMed articles. With these vectors, we then developed a new measure called Translational Progression (TP) for tracking biomedical articles along the translational continuum. We validated the effectiveness of TP from two perspectives (Clinical trial phase identification and ACH classification), which showed excellent consistency between TP and other indicators. Meanwhile, TP has several advantages. First, it can track the degree of translation of biomedical research dynamically and in real time. Second, it is straightforward to interpret and operationalize. Third, it doesn%u2019t require labor-intensive MeSH labeling and it is suitable for big scholarly data as well as papers that are not indexed in PubMed. In addition, we examined the trans

We present an aerial vehicle composed of a custom quadrotor with tilted rotors and a helium balloon, called SBlimp. We propose a novel control strategy that takes advantage of the natural stable attitude of the blimp to control translational motion. Different from cascade controllers in the literature that controls attitude to achieve desired translational motion, our approach directly controls the linear velocity regardless of the heading orientation of the vehicle. As a result, the vehicle swings during the translational motion. We provide a planar analysis of the dynamic model, demonstrating stability for our controller. Our design is evaluated in numerical simulations with different physical factors and validated with experiments using a real-world prototype, showing that the SBlimp is able to achieve stable translation regardless of its orientation.

The planning and conduct of animal experiments in the European Union is subject to strict legal conditions. Still, many preclinical animal experiments are only poorly designed. As a consequence, discoveries that are made in one animal experiment, cannot be reproduced in another animal experiment or discoveries in translational animal research fail to be translated to humans. When designing new experiments in a classical frequentist framework, the sample size for the new experiment is chosen with the goal to achieve at least a certain statistical power, given a statistical test for a null hypothesis, a significance threshold and a minimally relevant effect size. In a Bayesian framework, inference is made by a combination of both the information from newly observed data and also by a prior distribution, that represents a priori information on the parameters. In translational animal experiments, a priori information is present in previously conducted experiments to the same outcome in similar animals. The prior information can be incorporated in a systematic way in the design and analysis of a new animal experiment by summarizing the historical data in a (Bayesian) meta-analysis model

The Lorentz symmetry and the space and time translational symmetry are fundamental symmetries of nature. Crystals are the manifestation of the continuous space translational symmetry being spontaneously broken into a discrete one. We argue that, following the space translational symmetry, the continuous Lorentz symmetry should also be broken into a discrete one, which further implies that the continuous time translational symmetry is broken into a discrete one. We deduce all the possible discrete Lorentz and discrete time translational symmetries in 1+1-dimensional spacetime, and show how to build a field theory or a lattice field theory that has these symmetries.