搜索结果：Translational neurodegeneration

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 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

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 $n$.

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

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.

Neurodegeneration, characterized by the progressive loss of neuronal structure or function, is commonly assessed in clinical practice through reductions in cortical thickness or brain volume, as visualized by structural MRI. While informative, these conventional approaches lack the statistical sophistication required to fully capture the spatially correlated and heterogeneous nature of neurodegeneration, which manifests both in healthy aging and in neurological disorders. To address these limitations, brain age gap has emerged as a promising data-driven biomarker of brain health. The brain age gap prediction (BAGP) models estimate the difference between a person's predicted brain age from neuroimaging data and their chronological age. The resulting brain age gap serves as a compact biomarker of brain health, with recent studies demonstrating its predictive utility for disease progression and severity. However, practical adoption of BAGP models is hindered by their methodological obscurities and limited generalizability across diverse clinical populations. This tutorial article provides an overview of BAGP and introduces a principled framework for this application based on recent ad

INTRODUCTION: Quantification of amyloid plaques (A), neurofibrillary tangles (T2), and neurodegeneration (N) using PET and MRI is critical for Alzheimer's disease (AD) diagnosis and prognosis. Existing pipelines face limitations regarding processing time, variability in tracer types, and challenges in multimodal integration. METHODS: We developed petBrain, a novel end-to-end processing pipeline for amyloid-PET, tau-PET, and structural MRI. It leverages deep learning-based segmentation, standardized biomarker quantification (Centiloid, CenTauR, HAVAs), and simultaneous estimation of A, T2, and N biomarkers. The pipeline is implemented as a web-based platform, requiring no local computational infrastructure or specialized software knowledge. RESULTS: petBrain provides reliable and rapid biomarker quantification, with results comparable to existing pipelines for A and T2. It shows strong concordance with data processed in ADNI databases. The staging and quantification of A/T2/N by petBrain demonstrated good agreement with CSF/plasma biomarkers, clinical status, and cognitive performance. DISCUSSION: petBrain represents a powerful and openly accessible platform for standardized AD biom

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.

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 $\mathbb{Z}^d$, $d\geq 3$.

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.

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

Creating controlled methods to simulate neurodegeneration in artificial intelligence (AI) is crucial for applications that emulate brain function decline and cognitive disorders. We use IQ tests performed by Large Language Models (LLMs) and, more specifically, the LLaMA 2 to introduce the concept of ``neural erosion." This deliberate erosion involves ablating synapses or neurons, or adding Gaussian noise during or after training, resulting in a controlled progressive decline in the LLMs' performance. We are able to describe the neurodegeneration in the IQ tests and show that the LLM first loses its mathematical abilities and then its linguistic abilities, while further losing its ability to understand the questions. To the best of our knowledge, this is the first work that models neurodegeneration with text data, compared to other works that operate in the computer vision domain. Finally, we draw similarities between our study and cognitive decline clinical studies involving test subjects. We find that with the application of neurodegenerative methods, LLMs lose abstract thinking abilities, followed by mathematical degradation, and ultimately, a loss in linguistic ability, respondi

Neurodegenerative diseases are characterized by the accumulation of misfolded proteins and widespread disruptions in brain function. Computational modeling has advanced our understanding of these processes, but efforts have traditionally focused on either neuronal dynamics or the underlying biological mechanisms of disease. One class of models uses neural mass and whole-brain frameworks to simulate changes in oscillations, connectivity, and network stability. A second class focuses on biological processes underlying disease progression, particularly prion-like propagation through the connectome, and glial responses and vascular mechanisms. Each modeling tradition has provided important insights, but experimental evidence shows these processes are interconnected: neuronal activity modulates protein release and clearance, while pathological burden feeds back to disrupt circuit function. Modeling these domains in isolation limits our understanding. To determine where and why disease emerges, how it spreads, and how it might be altered, we must develop integrated frameworks that capture feedback between neuronal dynamics and disease biology. In this review, we survey the two modeling a

Alzheimer's disease (AD), the predominant form of dementia, is a growing global challenge, emphasizing the urgent need for accurate and early diagnosis. Current clinical diagnoses rely on radiologist expert interpretation, which is prone to human error. Deep learning has thus far shown promise for early AD diagnosis. However, existing methods often overlook focal structural atrophy critical for enhanced understanding of the cerebral cortex neurodegeneration. This paper proposes a deep learning framework that includes a novel structure-focused neurodegeneration CNN architecture named SNeurodCNN and an image brightness enhancement preprocessor using gamma correction. The SNeurodCNN architecture takes as input the focal structural atrophy features resulting from segmentation of brain structures captured through magnetic resonance imaging (MRI). As a result, the architecture considers only necessary CNN components, which comprises of two downsampling convolutional blocks and two fully connected layers, for achieving the desired classification task, and utilises regularisation techniques to regularise learnable parameters. Leveraging mid-sagittal and para-sagittal brain image viewpoints

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.

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

In this study, we present a technique that spans multi-scale views (global scale -- meaning brain network-level and local scale -- examining each individual ROI that constitutes the network) applied to resting-state fMRI volumes. Deep learning based classification is utilized in understanding neurodegeneration. The novelty of the proposed approach lies in utilizing two extreme scales of analysis. One branch considers the entire network within graph-analysis framework. Concurrently, the second branch scrutinizes each ROI within a network independently, focusing on evolution of dynamics. For each subject, graph-based approach employs partial correlation to profile the subject in a single graph where each ROI is a node, providing insights into differences in levels of participation. In contrast, non-linear analysis employs recurrence plots to profile a subject as a multichannel 2D image, revealing distinctions in underlying dynamics. The proposed approach is employed for classification of a cohort of 50 healthy control (HC) and 50 Mild Cognitive Impairment (MCI), sourced from ADNI dataset. Results point to: (1) reduced activity in ROIs such as PCC in MCI (2) greater activity in occipi

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.