102,080 research outputs found
A survey on abelian dynamical Galois groups
No full textLet be a number field, and . A recent conjecture
of Andrews and Petsche predicts that the dynamical Galois group of the pair
is abelian if and only if the pair is
-conjugated to , where is a power or a Chebyshev
map and is or , respectively, and is
a root of unity. We review three completely different approaches that allow to
prove several cases of the conjecture.Comment: Rendiconti Sem. Mat. Univ. Pol. Torino Vol. 80, 2022 (2022), 41 - 5
Sperm structure of Rhopalura littoralis (Orthonectida)
No full textThe fine structure of the spermatozoon in the orthonectid Rhopalura littoralis is described. This is the first fine structural description of an orthonectid sperm. The spermatozoon contains a slightly elongated nucleus and two centrioles orientated along the longitudinal axis of the sperm. The proximal centriole bears one rootlet. A single mitochondrion is present in the mid-piece region. An acrosome is absent. The sperm tail is a simple flagellum with 9 +2 structure. We consider the orthonectan spermatozoon to be closer in structure to of those of Porifera, Cnidaria, and Annelida, than to Aschelminthes and Platyhelminthes, to which they have previously been allied
On a Conjecture on Irreducible Polynomials over Finite Fields with Restricted Coefficients
No full textSequence-based imitation learning for surgical robot operations
No full textAim: This paper aims to advance autonomous surgical operations through imitation learning from video demonstrations. Methods: To address this objective, we propose two main contributions: (1) We introduce a new dataset of virtual kidney tumor environments to train our model on. The dataset is composed of video demonstrations of tumor removal from the kidney, executed in a virtual environment, and kinematic data of the robot tools; (2) We employed an imitation learning architecture composed of vision transformers (ViT) to handle the frames extracted from the videos and of a long short-term memory (LSTM) structure to process surgical motion sequences with a sliding window mechanism. This model processes video frames and prior poses to predict the poses for both robotic arms. A self-generating sequence approach was implemented, where each predicted pose served as the latest element in the sequence, subsequently used as input for the next prediction together with the current frame of the video. The choice of architecture and methodology was guided by the need to effectively model the sequential nature of surgical operations. Results: The model achieved promising results, exhibiting an average position error of 0.5 cm. The model was able to execute correctly 70% of the test tasks. This highlights the sequence-based approach's efficacy in capturing and predicting surgical trajectories. Conclusion: Our study supports imitation learning's viability for acquiring task execution policies in surgical robotics. The sequence-based model, combining ViT and LSTM architectures, successfully handles surgical trajectories
Optimal selection for good polynomials of degree up to five
No full textAn (r, l)-good polynomial is a polynomial of degree r + 1 that is constant on l subsets of F-q, each of size r + 1. For any positive integer r <= 4 we provide an (r, l)-good polynomial such that l = C(r)q + O(root q), with C-r maximal. This directly provides an explicit estimate (up to an error term of O(root q), with explict constant) for the maximal length and dimension of a Tamo-Barg LRC. Moreover, we explain how to construct good polynomials achieving these bounds. Finally, we provide computational examples to show how close our estimates are to the actual values of l, and we explain how to obtain the best possible good polynomials in degree 5. Our results complete the study by Chen et al. (Des Codes Cryptogr 89(7):1639-1660, 2021), providing (r, l)-good polynomials of degree up to 5, with l maximal (up to an error term of root q), and our methods are independent
Sperm ultrastructure in nematogenia panamensis (Annelida, oligochaeta, ocnerodrilidae). a phylogenetic approach
No full textMature spermatozoa of Nematogenia panamensis (Annelida: Oligochaeta, Ocnerodrilidae) from Madagascar were studied by electron microscopy. The spermatozoon is 35 pm long and shows the conventional clitellate sequence of acrosome, nucleus, middle piece and tail. The acrosome is asymmetric, showing an acrosome rod consistently bent to one side and probably exiting laterally for a short distance from the acrosome vesicle, only to re-enter apically. The middle piece consists of six mitochondria with the shape of a cylindrical sector and the tail is a flagellum with a 9+2 axoneme with two central tetragon fibers, surrounded for most of its length by glycogen granules. While the general features of Nematogenia spermatozoon are undoubtedly of megadrile type, some characters, like the shortness of the acrosome and the basal chamber, indicate a plesiomorphic condition within the group. This is in good agreement with the proposed phylogenetic position of Ocnerodrilidae within the Oligochaeta
Metabotropic glutamate receptors
No full textMetabotropic glutamate receptors (mGlus) are a family of G-protein-coupled receptors activated by the neurotransmitter glutamate. Molecular cloning has revealed eight different subtypes (mGlu1-8) with distinct molecular and pharmacological properties. Multiplicity in this receptor family is further generated through alternative splicing. mGlus activate a multitude of signalling pathways important for modulating neuronal excitability, synaptic plasticity and feedback regulation of neurotransmitter release. In this review, we summarize anatomical findings (from our work and that of other laboratories) describing their distribution in the central nervous system. Recent evidence regarding the localization of these receptors in peripheral tissues will also be examined. The distinct regional, cellular and subcellular distribution of mGlus in the brain will be discussed in view of their relationship to neurotransmitter release sites and of possible functional implications. © Springer-Verlag 2006
An equivariant isomorphism theorem for mod reductions of arboreal Galois representations
No full textLet be a quadratic, monic polynomial with coefficients in , where is a localization of a number ring . In this paper, we first prove that if is non-square andnon-isotrivial, then there exists an absolute, effective constant with the following property: for all primes such that the reduced polynomial \phi_\mathfrak p\in (\mathcalO_{F,D}/\mathfrak p)[t][x] is non-square and non-isotrivial, the squarefree Zsigmondy set of is bounded by . Using this result, we prove that if is non-isotrivial and geometrically stable thenoutside a finite, effective set of primes of the geometric part of the arboreal representation of is isomorphic to that of . As an application of our results we prove R. Jones' conjecture on the arboreal Galois representation attached to the polynomial .<br
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