cometadata/datacite-rtg-text-other-reclassification-records huggingface dataset:
Transitive closure in a polluted environment
Creators: name: Gravner, Janko
name: Kolesnik, Brett
Publisher: name: arXiv
Year: 2019
Subjects: subject: Probability (math.PR)
subject: Combinatorics (math.CO)
subject: FOS: Mathematics

description: We introduce and study a new percolation model, inspired by recent works on jigsaw percolation, graph bootstrap percolation, and percolation in polluted environments. Start with an oriented graph $G_0$ of initially occupied edges on $n$ vertices, and iteratively occupy additional (oriented) edges by transitivity, with the constraint that only open edges in a certain random set can ever be occupied. All other edges are closed, creating a set of obstacles for the spread of occupied edges. When $G_0$ is an unoriented linear graph, and leftward and rightward edges are open independently with possibly different probabilities, we identify three regimes in which the set of eventually occupied edges is either all open edges, the majority of open edges in one direction, or only a very small proportion of all open edges. In the more general setting where $G_0$ is a connected unoriented graph of bounded degree, we show that the transition between sparse and full occupation of open edges occurs when the probability of open edges is $(\log n)^{-1/2+o(1)}$. We conclude with several conjectures and open problems.
description: v2: final version
The Toda flow as a porous medium equation
Creators: name: Khesin, Boris
name: Modin, Klas
Publisher: name: arXiv
Year: 2022
Subjects: subject: Dynamical Systems (math.DS)
subject: Differential Geometry (math.DG)
subject: Exactly Solvable and Integrable Systems (nlin.SI)
subject: FOS: Mathematics
subject: FOS: Physical sciences
subject: 37K25, 70H06, 76S05

description: We describe the geometry of the incompressible porous medium (IPM) equation: we prove that it is a gradient dynamical system on the group of area-preserving diffeomorphisms and has a special double-bracket form. Furthermore, we show its similarities and differences with the dispersionless Toda system. The Toda flow describes an integrable interaction of several particles on a line with an exponential potential between neighbours, while its continuous version is an integrable PDE, whose physical meaning was obscure. Here we show that this continuous Toda flow can be naturally regarded as a special IPM equation, while the key double-bracket property of Toda is shared by all equations of the IPM type, thus manifesting their gradient and non-autonomous Hamiltonian origin. Finally, we comment on Toda and IPM modifications of the QR diagonalization algorithm, as well as describe double-bracket flows in an invariant setting of general Lie groups with arbitrary inertia operators.
description: 18 pages, 6 figures
Simplicial volume of manifolds with amenable fundamental group at infinity
Creators: name: Bargagnati, Giuseppe
Publisher: name: arXiv
Year: 2022
Subjects: subject: Geometric Topology (math.GT)
subject: FOS: Mathematics
subject: 57N16, 55N10 (Primary), 53C23, 57N65 (Secondary)

description: We show that for $n \neq 1,4$ the simplicial volume of an inward tame triangulable open $n$-manifold $M$ with amenable fundamental group at infinity at each end is finite; moreover, we show that if also $π_1(M)$ is amenable, then the simplicial volume of $M$ vanishes. We show that the same result holds for finitely-many-ended triangulable manifolds which are simply connected at infinity.
description: 11 pages
2-positive contractive projections on noncommutative $\mathrm{L}^p$-spaces
Creators: name: Arhancet, Cédric
name: Raynaud, Yves
Publisher: name: arXiv
Year: 2019
Subjects: subject: Operator Algebras (math.OA)
subject: Functional Analysis (math.FA)
subject: FOS: Mathematics

description: We prove the first theorem on projections on general noncommutative $\mathrm{L}^p$-spaces associated with non-type I von Neumann algebras where $1 \leqslant p < \infty$. This is the first progress on this topic since the seminal work of Arazy and Friedman [Memoirs AMS 1992] where the problem of the description of contractively complemented subspaces of noncommutative $\mathrm{L}^p$-spaces is explicitly raised. We show that the range of a 2-positive contractive projection on an arbitrary noncommutative $\mathrm{L}^p$-space is completely order isometrically isomorphic to some noncommutative $\mathrm{L}^p$-space. This result is sharp and is even new for Schatten spaces $S^p$. Our approach relies on non-tracial Haagerup's noncommutative $\mathrm{L}^p$-spaces in an essential way, even in the case of a projection acting on a Schatten space and is unrelated to the methods of Arazy and Friedman.
description: 28 pages, final version, minor typos corrected. arXiv admin note: text overlap with arXiv:1909.00391
On the structure of repeated-root polycyclic codes over local rings
Creators: name: Bajalan, Maryam
name: Martinez-Moro, Edgar
name: Sobhani, Reza
name: Szabo, Steve
name: Yilmazguc, Gulsum Gozde
Publisher: name: arXiv
Year: 2022
Subjects: subject: Information Theory (cs.IT)
subject: Rings and Algebras (math.RA)
subject: FOS: Computer and information sciences
subject: FOS: Mathematics

description: This paper provides the Generalized Mattson Solomon polynomial for repeated-root polycyclic codes over local rings that gives an explicit decomposition of them in terms of idempotents that completes the single root study. It also states some structural properties of repeated-root polycyclic codes over finite fields in terms of matrix product codes. Both approaches provide a description of the $\perp_0$-dual code of a given polycyclic code.
Generation, manipulation and detection of snake state trajectories of a neutral atom in a ring-cavity
Creators: name: Shakya, Poornima
name: Dogra, Nishant
name: Ghosh, Sankalpa
Publisher: name: arXiv
Year: 2020
Subjects: subject: Quantum Gases (cond-mat.quant-gas)
subject: Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
subject: Optics (physics.optics)
subject: FOS: Physical sciences

description: We propose a set-up to create and detect the atomic counterpart of snake state trajectories which occur at the interface where the magnetic field reverses direction. Such a magnetic field is generated by coupling two counter-propagating modes of a ring cavity to a two-level atom. The spatial distribution and the strength of the induced magnetic field are controlled by the transverse mode profile of the cavity modes and the number of photons in the two modes, respectively. By analysing the atomic motion in such a magnetic field while including the cavity back-action, we find that the atom follows snake state trajectories which can be non-destructively detected and reconstructed from the phase and the intensity of the light field leaking from the cavity. We finally show that the system parameters can be tuned to modify the transport properties of the snake states and even amplify the effect of cavity feedback which can completely alter their topology.
description: Latex file with thirteen figures ( including appendices). Accepted for publication in Physical Review A
Product manifolds and the curvature operator of the second kind
Creators: name: Li, Xiaolong
Publisher: name: arXiv
Year: 2022
Subjects: subject: Differential Geometry (math.DG)
subject: FOS: Mathematics
subject: 53C20, 53C21, 53C24

description: We investigate the curvature operator of the second kind on product Riemannian manifolds and obtain some optimal rigidity results. For instance, we prove that the universal cover of an $n$-dimensional non-flat complete locally reducible Riemannian manifold with $(n+\frac{n-2}{n})$-nonnegative (respectively, $(n+\frac{n-2}{n})$-nonpositive) curvature operator of the second kind must be isometric to $\mathbb{S}^{n-1}\times \mathbb{R}$ (respectively, $\mathbb{H}^{n-1}\times \mathbb{R}$) up to scaling. We also prove analogous optimal rigidity results for $\mathbb{S}^{n_1}\times \mathbb{S}^{n_2}$ and $\mathbb{H}^{n_1}\times \mathbb{H}^{n_2}$, $n_1,n_2 \geq 2$, among product Riemannian manifolds, as well as for $\mathbb{CP}^{m_1}\times \mathbb{CP}^{m_2}$ and $\mathbb{CH}^{m_1}\times \mathbb{CH}^{m_2}$, $m_1,m_2\geq 1$, among product Kähler manifolds. Our approach is pointwise and algebraic.
description: 23 pages, comments are welcome. arXiv admin note: text overlap with arXiv:2208.14505
Supplementary Figures and Tables from Chimpanzees (Pan troglodytes) recognise that their guesses could be wrong and can pass a 2-cup disjunctive syllogism task.
Creators: name: Jones, Benjamin
name: Call, Josep
Publisher: name: The Royal Society
Year: 2024
Subjects: classificationCode: 310901
subject: Animal behaviour

description: Subject details, individual rates and model coefficients.
Upper bound on the number of resonances for even asymptotically hyperbolic manifolds with real-analytic ends
Creators: name: Jézéquel, Malo
Publisher: name: arXiv
Year: 2022
Subjects: subject: Analysis of PDEs (math.AP)
subject: Spectral Theory (math.SP)
subject: FOS: Mathematics
subject: 58J50

description: We prove a polynomial upper bound on the number of resonances in a disc whose radius tends to infinity for even asymptotically hyperbolic manifolds with real-analytic ends. Our analysis also gives a similar upper bound on the number of quasinormal frequencies for Schwarzschild-de Sitter spacetimes.
description: v2: Revision according to referees comments
On Horizontal Immersions of Discs in Fat Distributions of Type $(4,6)$
Creators: name: Bhowmick, Aritra
Publisher: name: arXiv
Year: 2020
Subjects: subject: Differential Geometry (math.DG)
subject: FOS: Mathematics
subject: 58A30, 58J05, 58A15, 35J60, 53C23

description: In this article we discuss horizontal immersions of discs in certain corank-$2$ fat distributions on $6$-dimensional manifolds. The underlying real distribution of a holomorphic contact distribution on a complex $3$ manifold belongs to this class. The main result presented here says that the associated nonlinear PDE is locally invertible. Using this we prove the existence of germs of embedded horizontal discs.
description: Reorganized and added existence result. To appear in the Journal of Topology and Analysis
Closed cap condition under the cap construction algorithm
Creators: name: Sandu, Mercedes
name: Weng, Shuyi
name: Zhang, Jade
Publisher: name: arXiv
Year: 2022
Subjects: subject: Computational Geometry (cs.CG)
subject: FOS: Computer and information sciences

description: Every polygon $P$ can be companioned by a cap polygon $\hat P$ such that $P$ and $\hat P$ serve as two parts of the boundary surface of a polyhedron $V$. Pairs of vertices on $P$ and $\hat P$ are identified successively to become vertices of $V$. In this paper, we study the cap construction that asserts equal angular defects at these pairings. We exhibit a linear relation that arises from the cap construction algorithm, which in turn demonstrates an abundance of polygons that satisfy the closed cap condition, that is, those that can successfully undergo the cap construction process.
description: 13 pages, 8 figures, accepted by Involve
The ELBO of Variational Autoencoders Converges to a Sum of Three Entropies
Creators: name: Damm, Simon
name: Forster, Dennis
name: Velychko, Dmytro
name: Dai, Zhenwen
name: Fischer, Asja
name: Lücke, Jörg
Publisher: name: arXiv
Year: 2020
Subjects: subject: Machine Learning (stat.ML)
subject: Machine Learning (cs.LG)
subject: FOS: Computer and information sciences

description: The central objective function of a variational autoencoder (VAE) is its variational lower bound (the ELBO). Here we show that for standard (i.e., Gaussian) VAEs the ELBO converges to a value given by the sum of three entropies: the (negative) entropy of the prior distribution, the expected (negative) entropy of the observable distribution, and the average entropy of the variational distributions (the latter is already part of the ELBO). Our derived analytical results are exact and apply for small as well as for intricate deep networks for encoder and decoder. Furthermore, they apply for finitely and infinitely many data points and at any stationary point (including local maxima and saddle points). The result implies that the ELBO can for standard VAEs often be computed in closed-form at stationary points while the original ELBO requires numerical approximations of integrals. As a main contribution, we provide the proof that the ELBO for VAEs is at stationary points equal to entropy sums. Numerical experiments then show that the obtained analytical results are sufficiently precise also in those vicinities of stationary points that are reached in practice. Furthermore, we discuss how the novel entropy form of the ELBO can be used to analyze and understand learning behavior. More generally, we believe that our contributions can be useful for future theoretical and practical studies on VAE learning as they provide novel information on those points in parameters space that optimization of VAEs converges to.
Interplay of Pauli blockade with electron-photon coupling in quantum dots
Creators: name: Ginzel, Florian
name: Burkard, Guido
Publisher: name: arXiv
Year: 2022
Subjects: subject: Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
subject: FOS: Physical sciences

description: Both quantum transport measurements in the Pauli blockade regime and microwave cavity transmission measurements are important tools for spin-qubit readout and characterization. Based on a generalized input-output theory we derive a theoretical framework to investigate how a double quantum dot (DQD) in a transport setup interacts with a coupled microwave resonator while the current through the DQD is rectified by Pauli blockade. We show that the output field of the resonator can be used to infer the leakage current and thus obtain insight into the blockade mechanisms. In the case of a silicon DQD, we show how the valley quasi-degeneracy can impose limitations on this scheme. We also demonstrate that a large number of unknown DQD parameters including (but not limited to) the valley splitting can be estimated from the resonator response simultaneous to a transport experiment, providing more detailed knowledge about the microscopic environment of the DQD. Furthermore, we describe and quantify a back-action of the resonator photons on the steady state leakage current.
Polynomial progressions in topological fields
Creators: name: Krause, Ben
name: Mirek, Mariusz
name: Peluse, Sarah
name: Wright, James
Publisher: name: arXiv
Year: 2022
Subjects: subject: Number Theory (math.NT)
subject: Classical Analysis and ODEs (math.CA)
subject: Combinatorics (math.CO)
subject: FOS: Mathematics

description: Let $P_1, \ldots, P_m \in K[y]$ be polynomials with distinct degrees, no constant terms and coefficients in a general locally compact topological field $K$. We give a quantitative count of the number of polynomial progressions $x, x+P_1(y), \ldots, x + P_m(y)$ lying in a set $S\subseteq K$ of positive density. The proof relies on a general $L^{\infty}$ inverse theorem which is of independent interest. This inverse theorem implies a Sobolev improving estimate for multilinear polynomial averaging operators which in turn implies our quantitative estimate for polynomial progressions. This general Sobolev inequality has the potential to be applied in a number of problems in real, complex and $p$-adic analysis.
description: 51 pages, no figures, suggestions from the referees reports incorporated. Accepted for publication in the Forum of Mathematics, Sigma
title: Respiratory virus coinfection and superinfection exclusion
Creators: name: Sims, Anna
Publisher: name: University of Glasgow
Year: 2024

description: Influenza A virus (IAV) and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are responsible for two of the deadliest pandemics in modern history, and the emergence of pandemic respiratory viruses remains constant threat to human life. The emergence of novel pandemic viruses is driven by genetic exchange between existing viruses during coinfection of cells. Coinfection of cells can be controlled by superinfection exclusion (SIE), a mechanism by which a previously infected cell becomes resistant to secondary viral infection after a period of time. SIE is known to be induced following IAV infection but its mechanism is unknown, while SIE has not yet been observed for any coronavirus, including SARS-CoV-2. In this thesis, I use isogenic reporter viruses to study SIE, defining the kinetics of onset for IAV and presenting the first evidence for SIE for SARS-CoV-2. I demonstrate that in both cases SIE onset does not occur immediately, but that infected cells shift from a permissive to exclusionary state within 6 hours of primary infection. I used this system to investigate the mechanism for IAV SIE, showing that it is unlikely to be driven by direct competition between the viruses, or by the cellular interferon response. I then modelled the foci of infection observed within infected hosts in vitro using plaque assays. For both viruses, I also show how SIE at the level of individual cells affects the ability of virus populations to coinfect cells during localised viral spread. I found that viruses within one plaque could coinfect freely, as all new infections were of cells that had not yet established SIE. In contrast, viruses spreading towards each other from separate plaques could only establish minimal regions of overlap before SIE blocked further coinfection. For IAV, these interactions were then also observed in the lungs of infected mice. The results suggests that the kinetics of SIE onset separate a spreading infection into discrete regions, within which interactions between virus populations can occur freely, and between which they are blocked. These findings are likely to apply other viruses that induce SIE. Finally, I investigated the potential for coinfection between IAV and SARS-CoV-2. I found no evidence of SIE, but instead found evidence of viral interference mediated by type-1 interferon. Understanding the mechanisms and dynamics of SIE could help us understand coinfection and the generation of novel pandemic viruses, and potentially aid in predicting when new pandemics will arise.
Experimental method to determine specific heat and transition enthalpy at a first order phase transition: fundamentals and application to a NiMnIn Heusler alloy
Creators: name: Romero, F. J.
name: Gallardo, M. C.
name: Martín-Olalla, J. -M.
name: del Cerro, J.
Publisher: name: arXiv
Year: 2021
Subjects: subject: Materials Science (cond-mat.mtrl-sci)
subject: Applied Physics (physics.app-ph)
subject: Chemical Physics (physics.chem-ph)
subject: Instrumentation and Detectors (physics.ins-det)
subject: FOS: Physical sciences

description: A new method that characterizes thermal properties during a first-order phase transition is described. The technique consists in exciting the sample by a series of constant frequency thermal pulses which one in every N pulses (N is a small number like four) being exceedingly large in amplitude. This pulse induces phase transformation which is inhibited during the following smaller pulses due to thermal hysteresis. That way the specific heat for a given mixture of phases can be determined. The results obtained are independent of experimental parameters like the rate and the amplitude of the pulses, unlike what happens in other calorimetric techniques. The method also provides the enthalpy excess by analyzing the energy balance between the dissipated heat and the heat flowing during each pulse of measurement.
 The protocol is tested to analyze the phase transitions of a Heusler alloy Ni 50.54 Mn 33.65 In 15.82 . The paramagnetic-ferromagnetic transition for the austenite phase is continuous and the specific heat shows a lambda anomaly. The martensitic phase transition shows a first-order character and the specific heat follows a step-like behaviour in contrast with previously reported large-peak anomalies.
description: 15 pages, 5 figures
Discrete approximations to Dirichlet and Neumann Laplacians on a half-space and norm resolvent convergence
Creators: name: Cornean, Horia
name: Garde, Henrik
name: Jensen, Arne
Publisher: name: arXiv
Year: 2022
Subjects: subject: Functional Analysis (math.FA)
subject: Numerical Analysis (math.NA)
subject: Mathematical Physics (math-ph)
subject: Spectral Theory (math.SP)
subject: FOS: Mathematics
subject: FOS: Physical sciences
subject: 47A10, 47A58, 47B39

description: We extend recent results on discrete approximations of the Laplacian in $\mathbf{R}^d$ with norm resolvent convergence to the corresponding results for Dirichlet and Neumann Laplacians on a half-space. The resolvents of the discrete Dirichlet/Neumann Laplacians are embedded into the continuum using natural discretization and embedding operators. Norm resolvent convergence to their continuous counterparts is proven with a quadratic rate in the mesh size. These results generalize with a limited rate to also include operators with a real, bounded, and Hölder continuous potential, as well as certain functions of the Dirichlet/Neumann Laplacians, including any positive real power.
 Note (Nov 27, 2024): A corrigendum has been added to the end of the PDF.
description: 11 pages (original paper) + 3 pages (corrigendum, submitted for publication)
Semidistributive nearrings with identity
Creators: name: Raievska, Iryna
name: Raievska, Maryna
name: Sysak, Yaroslav
Publisher: name: arXiv
Year: 2022
Subjects: subject: Rings and Algebras (math.RA)
subject: FOS: Mathematics
subject: 16Y30, 20D15

description: It is proved that the additive group of every semidistributive nearring $R$ with an identity is abelian and if R has no elements of order $2$, then the nearring $R$ actually is an associative ring.
Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches
Creators: name: Petersen, Pip
name: Akrami, Yashar
name: Copi, Craig J.
name: Jaffe, Andrew H.
name: Kosowsky, Arthur
name: Mihaylov, Deyan P.
name: Starkman, Glenn D.
name: Tamosiunas, Andrius
name: Eskilt, Johannes R.
name: Güngör, Özenç
name: Saha, Samanta
name: Taylor, Quinn
Publisher: name: arXiv
Year: 2022
Subjects: subject: Cosmology and Nongalactic Astrophysics (astro-ph.CO)
subject: General Relativity and Quantum Cosmology (gr-qc)
subject: High Energy Physics - Phenomenology (hep-ph)
subject: High Energy Physics - Theory (hep-th)
subject: FOS: Physical sciences

description: The Einstein field equations of general relativity constrain the local curvature at every point in spacetime, but say nothing about the global topology of the Universe. Cosmic microwave background anisotropies have proven to be the most powerful probe of non-trivial topology since, within $Λ$CDM, these anisotropies have well-characterized statistical properties, the signal is principally from a thin spherical shell centered on the observer (the last scattering surface), and space-based observations nearly cover the full sky. The most generic signature of cosmic topology in the microwave background is pairs of circles with matching temperature and polarization patterns. No such circle pairs have been seen above noise in the WMAP or Planck temperature data, implying that the shortest non-contractible loop around the Universe through our location is longer than 98.5% of the comoving diameter of the last scattering surface. We translate this generic constraint into limits on the parameters that characterize manifolds with each of the nine possible non-trivial orientable Euclidean topologies, and provide a code which computes these constraints. In all but the simplest cases, the shortest non-contractible loop in the space can avoid us, and be shorter than the diameter of the last scattering surface by a factor ranging from 2 to at least 6. This result implies that a broader range of manifolds is observationally allowed than widely appreciated. Probing these manifolds will require more subtle statistical signatures than matched circles, such as off-diagonal correlations of harmonic coefficients.
description: 22 pages, 7 figures. v3: Corrected Figs. 3, 4, and 5 as published in Erratum. v4: Corrected omission of late-contributing author to author list
Adolescents with Rett syndrome at critical care pathway junctures: Examining clinicians’ decision to initiate invasive long-term ventilation
Creators: name: Bridget Quirke, Mary
name: Alexander, Denise
name: Cassidy, Lorna
name: WALSH, CATHAL
name: Masterson, Kate
name: Hill, Katie
name: Brenner, Maria
Publisher: name: University of Limerick
Year: 2024
Subjects: classificationCode: 42
subject: Health sciences
subject: FOS: Health sciences
classificationCode: 49
subject: Mathematical sciences

description: Background: The initiation of invasive long-term ventilation (I-LTV) for an adolescent with Rett Syndrome (RTT) involves many serious bioethical considerations. In moving towards a more inclusive model of patient participation, transparency surrounding the main influencing factors around this decision is important. Objective: We aimed to identify the main drivers influencing a clinician’s decision to support initiation of I-LTV for an adolescent with RTT. Method: We used an anonymous online vignette-based factorial survey. The survey was distributed internationally through eight professional multi-disciplinary organisations to reach clinicians working in paediatrics. Results: We analysed 504 RTT vignettes completed by 246 clinicians using mixed effect regression modelling. The main three significant influencing factors identified were: parental agreement with the decision to support initiation, the family’s support network, and proximity to a tertiary care centre. Additional comments from participants focused on family support, and the importance of on-going communication with the family. Conclusion: As the rights of those with disabilities improve and participation of adolescents in decision-making becomes more established, effective communications with the family around goals of care and particular sensitivity and reflective practice around methods of consensus building will likely contribute to a positive decision-making process at this difficult time.
The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher $\ell$-Modes of Linear Waves on a Schwarzschild Background
Creators: name: Kehrberger, Leonhard M. A.
Publisher: name: arXiv
Year: 2021
Subjects: subject: General Relativity and Quantum Cosmology (gr-qc)
subject: High Energy Physics - Theory (hep-th)
subject: Mathematical Physics (math-ph)
subject: Analysis of PDEs (math.AP)
subject: FOS: Physical sciences
subject: FOS: Mathematics

description: In this paper, we derive the early-time asymptotics for fixed-frequency solutions $ϕ_\ell$ to the wave equation $\Box_g ϕ_\ell=0$ on a fixed Schwarzschild background ($M>0$) arising from the no incoming radiation condition on $\mathcal I^-$ and polynomially decaying data, $rϕ_\ell\sim t^{-1}$ as $t\to-\infty$, on either a timelike boundary of constant area radius (I) or an ingoing null hypersurface (II). In case (I), we show that the asymptotic expansion of $\partial_v(rϕ_\ell)$ along outgoing null hypersurfaces near spacelike infinity $i^0$ contains logarithmic terms at order $r^{-3-\ell}\log r$. In contrast, in case (II), we obtain that the asymptotic expansion of $\partial_v(rϕ_\ell)$ near spacelike infinity $i^0$ contains logarithmic terms already at order $r^{-3}\log r$ (unless $\ell=1$).
 These results suggest an alternative approach to the study of late-time asymptotics near future timelike infinity $i^+$ that does not assume conformally smooth or compactly supported Cauchy data: In case (I), our results indicate logarithmic modifications to Price's law for each $\ell$-mode. On the other hand, the data of case (II) lead to much stronger deviations from Price's law. In particular, we conjecture that compactly supported scattering data on $\mathcal H^-$ and $\mathcal I^-$ lead to solutions that exhibit the same late-time asymptotics on $\mathcal I^+$ for each $\ell$: $rϕ_\ell|_{\mathcal I^+}\sim u^{-2}$ as $u\to\infty$.
description: 100 pages, 6 figures. v3: Comments by reviewer worked in. v4: correction to Figure 6, v5: Fixed typesetting error added in v4
Temporal patterns in insulin needs for Type 1 diabetes
Creators: name: Degen, Isabella
name: Abdallah, Zahraa S.
Publisher: name: arXiv
Year: 2022
Subjects: subject: Machine Learning (cs.LG)
subject: Quantitative Methods (q-bio.QM)
subject: Machine Learning (stat.ML)
subject: FOS: Computer and information sciences
subject: FOS: Biological sciences

description: Type 1 Diabetes (T1D) is a chronic condition where the body produces little or no insulin, a hormone required for the cells to use blood glucose (BG) for energy and to regulate BG levels in the body. Finding the right insulin dose and time remains a complex, challenging and as yet unsolved control task. In this study, we use the OpenAPS Data Commons dataset, which is an extensive dataset collected in real-life conditions, to discover temporal patterns in insulin need driven by well-known factors such as carbohydrates as well as potentially novel factors. We utilised various time series techniques to spot such patterns using matrix profile and multi-variate clustering. The better we understand T1D and the factors impacting insulin needs, the more we can contribute to building data-driven technology for T1D treatments.
description: Submitted and accepted for presentation as a poster at the NeurIPS22 Time series for Health workshop, https://timeseriesforhealth.github.io/
Development of a new quantum trajectory molecular dynamics framework
Creators: name: Svensson, Pontus
name: Campbell, Thomas
name: Graziani, Frank
name: Moldabekov, Zhandos
name: Lyu, Ningyi
name: Batista, Victor S.
name: Richardson, Scott
name: Vinko, Sam M.
name: Gregori, Gianluca
Publisher: name: arXiv
Year: 2022
Subjects: subject: Plasma Physics (physics.plasm-ph)
subject: FOS: Physical sciences

description: An extension to the wave packet description of quantum plasmas is presented, where the wave packet can be elongated in arbitrary directions. A generalised Ewald summation is constructed for the wave packet models accounting for long-range Coulomb interactions and fermionic effects are approximated by purpose-built Pauli potentials, self-consistent with the wave packets used. We demonstrate its numerical implementation with good parallel support and close to linear scaling in particle number, used for comparisons with the more common wave packet employing isotropic states. Ground state and thermal properties are compared between the models with differences occurring primarily in the electronic subsystem. Especially, the electrical conductivity of dense hydrogen is investigated where a 15% increase in DC conductivity can be seen in our wave packet model compared to other models.
description: 20 pages, 6 figures
Supplementary material from Is SARS-CoV-2 elimination or mitigation best? Regional and disease characteristics determine the recommended strategy
Creators: name: Martignoni, Maria M.
name: Arino, Julien
name: Hurford, Amy
Publisher: name: The Royal Society
Year: 2024
Subjects: classificationCode: 420299
subject: Epidemiology not elsewhere classified
classificationCode: 499999
subject: Other mathematical sciences not elsewhere classified

description: sections A and B, uploaded as files
Variations in Vocalizations of Fin Whales, Balaenoptera physalus, in the St. Lawrence River
Creators: name: Edds, Peggy Louise
Publisher: name: Digital Repository at the University of Maryland
Year: 1980

description: Recordings were made of vocalizations from fin whales, Balaenoptera physalus from a fixed hydrophone in the St. Lawrence River between 28 June and 27 September 1979. Land-based observers monitored activity from a hillside hut while recordings were being made from a shoreline site. Photographs of dorsal fin variations were used to identify distinctive individuals. The 1522 sounds recorded were classified into 11 categories based on frequency and temporal characteristics. The predominant call was a descending sweep of frequencies. Parameters measured for this downsweep exhibited a dichotomy of characteristics which indicates calls with initial frequencies below 40 Hz have less variability than calls with initial frequencies above 40 Hz. In general, solitary animals produced primarily the lower frequency downsweeps. Higher frequency downsweeps were recorded from pairs or trios of fin whales. Solitary individuals did not exhibit unique variations in downsweep parameters. No clusters of values which might indicate uniquely individual ranges were consistently present in multiple animal recordings. The data suggest that the variability of fin whale vocalizations is primarily contextual rather than individual.
Supplementary material from Is SARS-CoV-2 elimination or mitigation best? Regional and disease characteristics determine the recommended strategy
Creators: name: Martignoni, Maria M.
name: Arino, Julien
name: Hurford, Amy
Publisher: name: The Royal Society
Year: 2024
Subjects: classificationCode: 420299
subject: Epidemiology not elsewhere classified

description: sections A and B, uploaded as files
Data-driven enhancement of coherent structure-based models for predicting instantaneous wall turbulence
Creators: name: Deshpande, Rahul
name: de Silva, Charitha M.
name: Lee, Myoungkyu
name: Monty, Jason P.
name: Marusic, Ivan
Publisher: name: arXiv
Year: 2021
Subjects: subject: Fluid Dynamics (physics.flu-dyn)
subject: FOS: Physical sciences

description: Predictions of the spatial representation of instantaneous wall-bounded flows, via coherent structure-based models, are highly sensitive to the geometry of the representative structures employed by them. In this study, we propose a methodology to extract the three-dimensional (3-D) geometry of the statistically significant eddies from multi-point wall-turbulence datasets, for direct implementation into these models to improve their predictions. The methodology is employed here for reconstructing a 3-D statistical picture of the inertial wall coherent turbulence for all canonical wall-bounded flows, across a decade of friction Reynolds number ($Re_τ$). These structures are responsible for the $Re_τ$-dependence of the skin-friction drag and also facilitate the inner-outer interactions, making them key targets of structure-based models. The empirical analysis brings out the geometric self-similarity of the large-scale wall-coherent motions and also suggests the hairpin packet as the representative flow structure for all wall-bounded flows, thereby aligning with the framework on which the attached eddy model (AEM) is based. The same framework is extended here to also model the very-large-scaled motions, with a consideration of their differences in internal versus external flows. Implementation of the empirically-obtained geometric scalings for these large structures into the AEM is shown to enhance the instantaneous flow predictions for all three velocity components. Finally, an active flow control system driven by the same geometric scalings is conceptualized, towards favourably altering the influence of the wall coherent motions on the skin-friction drag.
description: 16 pages, 11 figures, accepted for publication in the International Journal of Heat and Fluid Flow
Reconnectads
Creators: name: Dotsenko, Vladimir
name: Keilthy, Adam
name: Lyskov, Denis
Publisher: name: arXiv
Year: 2022
Subjects: subject: Category Theory (math.CT)
subject: Combinatorics (math.CO)
subject: K-Theory and Homology (math.KT)
subject: FOS: Mathematics

description: We introduce a new operad-like structure that we call a reconnectad; the ``input'' of an element of a reconnectad is a finite simple graph, rather than a finite set, and ``compositions'' of elements are performed according to the notion of the reconnected complement of a subgraph. The prototypical example of a reconnectad is given by the collection of toric varieties of graph associahedra of Carr and Devadoss, with the structure operations given by inclusions of orbits closures. We develop the general theory of reconnectads, and use it to study the ``wonderful reconnectad'' assembled from homology groups of complex toric varieties of graph associahedra.
description: 44 pages, submitted version
Philosophical Specification of Empathetic Ethical Artificial Intelligence
Creators: name: Bennett, Michael Timothy
name: Maruyama, Yoshihiro
Publisher: name: arXiv
Year: 2021
Subjects: subject: Artificial Intelligence (cs.AI)
subject: FOS: Computer and information sciences

description: In order to construct an ethical artificial intelligence (AI) two complex problems must be overcome. Firstly, humans do not consistently agree on what is or is not ethical. Second, contemporary AI and machine learning methods tend to be blunt instruments which either search for solutions within the bounds of predefined rules, or mimic behaviour. An ethical AI must be capable of inferring unspoken rules, interpreting nuance and context, possess and be able to infer intent, and explain not just its actions but its intent. Using enactivism, semiotics, perceptual symbol systems and symbol emergence, we specify an agent that learns not just arbitrary relations between signs but their meaning in terms of the perceptual states of its sensorimotor system. Subsequently it can learn what is meant by a sentence and infer the intent of others in terms of its own experiences. It has malleable intent because the meaning of symbols changes as it learns, and its intent is represented symbolically as a goal. As such it may learn a concept of what is most likely to be considered ethical by the majority within a population of humans, which may then be used as a goal. The meaning of abstract symbols is expressed using perceptual symbols of raw sensorimotor stimuli as the weakest (consistent with Ockham's Razor) necessary and sufficient concept, an intensional definition learned from an ostensive definition, from which the extensional definition or category of all ethical decisions may be obtained. Because these abstract symbols are the same for both situation and response, the same symbol is used when either performing or observing an action. This is akin to mirror neurons in the human brain. Mirror symbols may allow the agent to empathise, because its own experiences are associated with the symbol, which is also associated with the observation of another agent experiencing something that symbol represents.
description: To appear in IEEE Transactions in Cognitive and Developmental Systems
The quermassintegral preserving mean curvature flow in the sphere
Creators: name: Cabezas-Rivas, Esther
name: Scheuer, Julian
Publisher: name: arXiv
Year: 2022
Subjects: subject: Differential Geometry (math.DG)
subject: Analysis of PDEs (math.AP)
subject: FOS: Mathematics
subject: 53E10, 53C21

description: We introduce a mean curvature flow with global term of convex hypersurfaces in the sphere, for which the global term can be chosen to keep any quermassintegral fixed. Then, starting from a strictly convex initial hypersurface, we prove that the flow exists for all times and converges smoothly to a geodesic sphere. This provides a workaround to an issue present in the volume preserving mean curvature flow in the sphere introduced by Huisken in 1987. We also classify solutions for some constant curvature type equations in space forms, as well as solitons in the sphere and in the upper branch of the De Sitter space.
description: 35 pages
Hyperbolic domains in real Euclidean spaces
Creators: name: Drnovsek, Barbara Drinovec
name: Forstneric, Franc
Publisher: name: arXiv
Year: 2021
Subjects: subject: Complex Variables (math.CV)
subject: Differential Geometry (math.DG)
subject: FOS: Mathematics
subject: Primary 53A10. Secondary 32Q45, 30C80, 31A05

description: The second named author and David Kalaj introduced a pseudometric on any domain in the real Euclidean space $\mathbb R^n$, $n\ge 3$, defined in terms of conformal harmonic discs, by analogy with Kobayashi's pseudometric on complex manifolds, which is defined in terms of holomorphic discs. They showed that on the unit ball of $\mathbb R^n$, the minimal metric coincides with the classical Beltrami-Cayley-Klein metric, one of the models of hyperbolic geometry. In the present paper we investigate properties of the minimal pseudometric and give sufficient conditions for a domain to be (complete) hyperbolic, meaning that the minimal pseudometric is a (complete) metric. We show in particular that a convex domain is complete hyperbolic if and only if it does not contain any affine 2-planes. One of our main results is that a domain with a negative minimal plurisubharmonic exhaustion function is hyperbolic, and a bounded strongly minimally convex domain is complete hyperbolic. We also prove a localization theorem for the minimal pseudometric.
description: Dedicated to H. Blaine Lawson in honour of his 80th birthday. Pure Appl. Math. Q., to appear
Dominance for Containment Problems
Creators: name: Akram, Waseem
name: Saxena, Sanjeev
Publisher: name: arXiv
Year: 2022
Subjects: subject: Data Structures and Algorithms (cs.DS)
subject: Computational Geometry (cs.CG)
subject: FOS: Computer and information sciences

description: In a containment problem, the goal is to preprocess a set of geometric objects so that, given a geometric query object, we can report all the objects containing the query object. We consider the containment problem where input objects are homothetic triangles and the query objects considered are line segments, circles, and trapezoids with bases parallel to either axis. We show that this problem can be solved using the 3-d query dominance problem. The solutions presented can also be extended for higher dimensions.
Which images to label for few-shot medical landmark detection?
Creators: name: Quan, Quan
name: Yao, Qingsong
name: Li, Jun
name: Zhou, S. Kevin
Publisher: name: arXiv
Year: 2021
Subjects: subject: Image and Video Processing (eess.IV)
subject: Computer Vision and Pattern Recognition (cs.CV)
subject: Machine Learning (cs.LG)
subject: FOS: Electrical engineering, electronic engineering, information engineering
subject: FOS: Computer and information sciences

description: The success of deep learning methods relies on the availability of well-labeled large-scale datasets. However, for medical images, annotating such abundant training data often requires experienced radiologists and consumes their limited time. Few-shot learning is developed to alleviate this burden, which achieves competitive performances with only several labeled data. However, a crucial yet previously overlooked problem in few-shot learning is about the selection of template images for annotation before learning, which affects the final performance. We herein propose a novel Sample Choosing Policy (SCP) to select "the most worthy" images for annotation, in the context of few-shot medical landmark detection. SCP consists of three parts: 1) Self-supervised training for building a pre-trained deep model to extract features from radiological images, 2) Key Point Proposal for localizing informative patches, and 3) Representative Score Estimation for searching the most representative samples or templates. The advantage of SCP is demonstrated by various experiments on three widely-used public datasets. For one-shot medical landmark detection, its use reduces the mean radial errors on Cephalometric and HandXray datasets by 14.2% (from 3.595mm to 3.083mm) and 35.5% (4.114mm to 2.653mm), respectively.
Differential embeddings into algebras of topological stable rank 1
Creators: name: Kania, Tomasz
name: Maślany, Natalia
Publisher: name: arXiv
Year: 2023
Subjects: subject: Operator Algebras (math.OA)
subject: Functional Analysis (math.FA)
subject: FOS: Mathematics
subject: 46A30 (primary), and 46J10 (secondary)

description: We identify a class of smooth Banach *-algebras that are differential subalgebras of commutative C*-algebras whose openness of multiplication is completely determined by the topological stable rank of the target C*-algebra. We then show that group algebras of Abelian groups of unbounded exponent fail to have uniformly open convolution. Finally, we completely characterise in the complex case (uniform) openness of multiplication in algebras of continuous functions in terms of the covering dimension.
description: 23 pp; to appear in Proceedings of the Royal Society of Edinburgh Section A: Mathematics
НЕКОТОРЫЕ НЕДОСТАТКИ РЕГУЛИРОВАНИЯ ЦИФРОВЫХ АКТИВОВ В РЕСПУБЛИКИ УЗБЕКИСТАН
Creators: name: Абдусатаров, Джалолиддин
Publisher: name: Zenodo
Year: 2024

description: Регулирование цифровых активов в Республике Узбекистан стало одной из актуальных тем в современном экономическом контексте. Несмотря на усилия правительства по созданию законодательной базы и инфраструктуры для развития цифровых активов, наблюдаются определенные недостатки в этой области. Одним из основных недостатков является отсутствие четкой системы регулирования и контроля за использованием цифровых активов, что может привести к возникновению финансовых мошенничеств и других негативных последствий. Также отмечается нехватка механизмов защиты прав потребителей при использовании цифровых активов, что ограничивает доверие к этим инструментам. Для эффективного развития рынка цифровых активов в Узбекистане необходимо устранить указанные недостатки и создать прозрачные и надежные условия для участников этого рынка.
Differential forms on universal K3 surfaces
Creators: name: Ma, Shouhei
Publisher: name: arXiv
Year: 2023
Subjects: subject: Algebraic Geometry (math.AG)
subject: FOS: Mathematics
subject: 14J28, 14J15, 11F55

description: We give a vanishing and classification result for holomorphic differential forms on smooth projective models of the moduli spaces of pointed K3 surfaces. We prove that there is no nonzero holomorphic k-form for 019. In the remaining cases, we give an isomorphism between the space of holomorphic k-forms with that of vector-valued modular forms (918) for the modular group. These results are in fact proved in the generality of lattice-polarization.
On disjoint stationary sequences
Creators: name: Levine, Maxwell
Publisher: name: arXiv
Year: 2023
Subjects: subject: Logic (math.LO)
subject: FOS: Mathematics
subject: 03E35, 03E55

description: We answer a question of Krueger by obtaining disjoint stationary sequences on successive cardinals. The main idea is an alternative presentation of a mixed support iteration, using it even more explicitly as a variant of Mitchell forcing. We also use a Mahlo cardinal to obtain a model in which $\aleph_2 \notin I[\aleph_2]$ and there is no disjoint stationary sequence on $\aleph_2$, answering a question of Gilton.
description: Substantial changes to the proof of Theorem 3, which is now only stated for $\aleph_2$. Amendments to the proof of Theorem 2. Other small changes throughout
Omnisolver: an extensible interface to Ising spin glass solvers
Creators: name: Jałowiecki, Konrad
name: Pawela, Łukasz
Publisher: name: arXiv
Year: 2021
Subjects: subject: Software Engineering (cs.SE)
subject: Quantum Physics (quant-ph)
subject: FOS: Computer and information sciences
subject: FOS: Physical sciences

description: We introduce a new framework for implementing Binary Quadratic Model (BQM) solvers called Omnisolver. The framework provides an out-of-the-box dynamically built command-line interface as well as an input/output system, thus heavily reducing the effort required for implementing new algorithms for solving BQMs. The proposed software should be of benefit for researchers focusing on quantum annealers or discrete optimization algorithms as well as groups utilizing discrete optimization as a part of their daily work. We demonstrate the ease of use of the proposed software by presenting a step-by-step, concise implementation of an example plugin.