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We prove results on existence and uniqueness of solutions of a system of equations modeling the evolution of a generalized bioconvective flow. The mathematical model considered in the present work describes the convective motion generated by the upward swimming of a culture of microorganisms under the influence of vertical gravitational forces, in an incompressible viscous fluid whose viscosity may depend on the concentration of microorganisms.

We give an effective procedure to explicitly find the decomposition of a polarized abelian variety into its simple factors if a period matrix is known. Since finding this datum is not easy, we also provide two methods to compute the period matrix for a polarized abelian variety, depending on the given geometric information about it. These results work particularly well in combination with our previous work on abelian varieties with group actions, since they allow us to fully decompose such varieties by successively decomposing their factor subvarieties, even when these no longer have a group action. We highlight that we do not require to determine the full endomorphism algebra of any of the (sub)varieties involved. We illustrate the power of our algorithms with two byproducts: we find a completely decomposable Jacobian variety of dimension 101, filling this Ekedahl-Serre gap, and we describe a new completely decomposable Jacobian variety of CM type of dimension 11., Comment: 21 pages

In this short note, we study the Jacobian variety of the Accola-Maclachlan curve of genus four and obtain explicitly its Poincar\'e isogeny decomposition. More precisely, we show that its Jacobian variety is isomorphic to the product of two abelian surfaces that are simple, and provide explicitly a Riemann matrix for each one of the involved abelian surfaces, Comment: 11 pages

Supernova remnants are the nebular leftover of defunct stellar environments, resulting from the interaction between a supernova blastwave and the circumstellar medium shaped by the progenitor throughout its life. They display a large variety of non-spherical morphologies such as ears that shine non-thermally. % We have modelled the structure and the non-thermal emission of the supernova remnant G1.9+0.3 through 3D magnetohydrodynamic numerical simulations. We propose that the peculiar ear-shaped morphology of this supernova remnant results from the interaction of the its blast wave with a magnetized circumstellar medium, which was previously asymmetrically shaped by the past stellar wind emanating from the progenitor star or its stellar companion. We created synthetic non-thermal radio and x-ray maps from our simulated remnant structure, which are in qualitative agreement with observations, forming ears on the polar directions. Our synthetic map study explains the discrepancies between the measured non-thermal radio and X-ray surface brightness distributions assuming that the Inverse Compton process produces the observed X-ray emission., Comment: Accepted for publication in MNRAS

In this article, we consider certain irreducible subvarieties of the moduli space of compact Riemann surfaces determined by the specification of actions of finite groups. We address the general problem of determining which among them are non-normal subvarieties of the moduli space., Comment: 22 pages

Tactile sensing typically involves active exploration of unknown surfaces and objects, making it especially effective at processing the characteristics of materials and textures. A key property extracted by human tactile perception is surface roughness, which relies on measuring vibratory signals using the multi-layered fingertip structure. Existing robotic systems lack tactile sensors that are able to provide high dynamic sensing ranges, perceive material properties, and maintain a low hardware cost. In this work, we introduce the reference design and fabrication procedure of a miniature and low-cost tactile sensor consisting of a biomimetic cutaneous structure, including the artificial fingerprint, dermis, epidermis, and an embedded magnet-sensor structure which serves as a mechanoreceptor for converting mechanical information to digital signals. The presented sensor is capable of detecting high-resolution magnetic field data through the Hall effect and creating high-dimensional time-frequency domain features for material texture classification. Additionally, we investigate the effects of different superficial sensor fingerprint patterns for classifying materials through both simulation and physical experimentation. After extracting time series and frequency domain features, we assess a k-nearest neighbors classifier for distinguishing between different materials. The results from our experiments show that our biomimetic tactile sensors with fingerprint ridges can classify materials with more than 8% higher accuracy and lower variability than ridge-less sensors. These results, along with the low cost and customizability of our sensor, demonstrate high potential for lowering the barrier to entry for a wide array of robotic applications, including model-less tactile sensing for texture classification, material inspection, and object recognition., Comment: To be published in ICRA 2022

Unlike conformal boundary conditions, conformal defects of Virasoro minimal models lack classification. Alternatively to the defect perturbation theory and the truncated conformal space approach, we employ open string field theory (OSFT) techniques to explore the space of conformal defects. We illustrate the method by an analysis of OSFT around the background associated to the $(1,2)$ topological defect in diagonal unitary minimal models. Numerical analysis of OSFT equations of motion leads to an identification of a nice family of solutions, recovering the picture of infrared fixed points due to Kormos, Runkel and Watts. In particular, we find a continuum of solutions in the Ising model case and 6 solutions for other minimal models. OSFT provides us with numerical estimates of the g-function and other coefficients of the boundary state., Comment: 37 pages, 8 figures, 6 tables, v2: minor typos corrected

In this article we study compact Riemann surfaces of genus $g$ with an automorphism of prime order $g+1.$ The main result provides a classification of such surfaces. In addition, we give a description of them as algebraic curves, determine and realise their full automorphism groups and compute their fields of moduli. We also study some aspects of their Jacobian varieties such as isogeny decompositions and complex multiplication. Finally, we determine the period matrix of the Accola-Maclachlan curve of genus four., Comment: To appear in Journal of Group Theory, 37 pages

In this article we determine the maximal possible order of the automorphism group of the form $ag + b$, where $a$ and $b$ are integers, of a complex three and four-dimensional family of compact Riemann surfaces of genus $g$, appearing for all genus. In addition, we construct and describe explicit complex three and four-dimensional families possessing these maximal number of automorphisms., Comment: 19 pages, To appear in Journal of Pure and Applied Algebra

In this paper we explore the potential improvements in neutrino event reconstruction that a 3D pixelated readout could offer over a 2D projective wire readout for liquid argon time projection chambers. We simulate and study events in two generic, idealized detector configurations for these two designs, classifying events in each sample with deep convolutional neural networks to compare the best 2D results to the best 3D results. In almost all cases we find that the 3D readout provides better reconstruction efficiency and purity than the 2D projective wire readout, with the advantages of 3D being particularly evident in more complex topologies, such as electron neutrino charged current events. We conclude that the use of a 3D pixelated detector could significantly enhance the reach and impact of future liquid argon TPC experiments physics program, such as DUNE.

In these notes we use the recently found relation between facets of tropical Grassmannians and generalizations of Feynman diagrams to compute all "biadjoint amplitudes" for $n=7$ and $k=3$. We also study scattering equations on $X(3,7)$, the configuration space of seven points on $\mathbb{CP}^2$. We prove that the number of solutions is $1272$ in a two-step process. In the first step we obtain $1162$ explicit solutions to high precision using near-soft kinematics. In the second step we compute the matrix of $360\times 360$ biadjoint amplitudes obtained by using the facets of ${\rm Trop}\, G(3,7)$, subtract the result from using the $1162$ solutions and compute the rank of the resulting matrix. The rank turns out to be $110$, which proves that the number of solutions in addition to the $1162$ explicit ones is exactly $110$., Comment: 13 pages, 1 figure and 6 ancillary files; minor revision

A \textit{Humbert-Edge curve of type} $n$ is a non-degenerate smooth complete intersection of $n-1$ diagonal quadrics. Such a curve has an interesting geometry since it has a natural action of the group $(\mathbb{Z}/2\mathbb{Z})^n$. We present here a decomposition of its Jacobian variety as a product of Prym-Tyurin varieties, and we compute the kernel of the corresponding isogeny., Comment: 9 pages, comments welcome! To appear in Contemporary Mathematics