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Supermaps between quantum channels (completely positive trace-preserving (CPTP) maps of matrix algebras) were introduced in [Chiribella et al., EPL 83(3) (2008)]. In this work we generalise to supermaps between channels of any type; by channels we mean CPTP maps of finite-dimensional C*-algebras. Channels include POVMs, quantum instruments, classically controlled families of quantum channels, classical channels, quantum multimeters, and more. We show that deterministic supermaps between channels of any type can be realised using simple circuits, recovering the previous realisation theorems of [Chiribella et al., EPL 83(3) (2008)] (for deterministic supermaps between quantum channels) and [Bluhm et al. (2024)] (for deterministic supermaps between quantum multimeters) as special cases. To prove this realisation theorem we use the graphical calculus of the 2-category of finite-dimensional 2-Hilbert spaces; the paper includes an accessible and elementary introduction to this graphical calculus, and no prior knowledge of category theory is expected of the reader., Comment: 46 pages, many figures

On 2022 March 10, a coronal mass ejection (CME) erupted from the Sun, resulting in Solar Orbiter observations at 0.45 au of both dispersive solar energetic particles arriving prior to the interplanetary CME (ICME) and locally accelerated particles near the ICME-associated shock structure as it passed the spacecraft on 2022 March 11. This shock was later detected on 2022 March 14 by the Advanced Composition Explorer (ACE), which was radially aligned with Solar Orbiter, at 1 au. Ion composition data from both spacecraft -- via the Solar Orbiter Energetic Particle Detector/ Suprathermal Ion Spectrograph (EPD/SIS) and the Ultra Low Energy Isotope Spectrometer (ULEIS) on ACE -- allows for in-depth analysis of the radial evolution of species-dependent ICME shock-associated acceleration processes for this event. We present a study of the ion spectra observed at 0.45 and 1 au during both the gradual solar energetic particle (SEP) and energetic storm particle (ESP) phases of the event. We find that the shapes of the spectra seen at each spacecraft have significant differences that were likely caused by varying shock geometry: Solar Orbiter spectra tend to lack spectral breaks, and the higher energy portions of the ACE spectra have comparable average flux to the Solar Orbiter spectra. Through an analysis of rigidity effects on the spectral breaks observed by ACE, we conclude that the 1 au observations were largely influenced by a suprathermal pool of $\mathrm{He}^{+}$ ions that were enhanced due to propagation along a stream interaction region (SIR) that was interacting with the ICME at times of observation., Comment: 15 pages, 7 figures, submitted to A&A

Robust delay induced oscillations, common in nature, are often modeled by delay-differential equations (DDEs). Motivated by the success of phase-amplitude reductions for ordinary differential equations with limit cycle oscillations, there is now a growing interest in the development of analogous approaches for DDEs to understand their response to external forcing. When combined with Floquet theory, the fundamental quantities for this reduction are phase and amplitude response functions. Here, we develop a framework for their construction that utilises the method of harmonic balance., Comment: 5 pages, 2 figures

We explore developing rich semantic models of systems. Specifically, we consider structured causal explanations about state changes in those systems. Essentially, we are developing process-based dynamic knowledge graphs. As an example, we construct a model of the causal threads for geological changes proposed by the Snowball Earth theory. Further, we describe an early prototype of a graphical interface to present the explanations. Unlike statistical approaches to summarization and explanation such as Large Language Models (LLMs), our approach of direct representation can be inspected and verified directly., Comment: 2023 ICADL

The problem of extending the insights and techniques of categorical quantum mechanics to infinite-dimensional systems was considered in (Coecke and Heunen, 2016). In that work the $\mathrm{CP}^{\infty}$-construction, which recovers the category of Hilbert spaces and quantum operations from the category of Hilbert spaces and bounded linear maps, was defined. Here we show that by a `horizontal categorification' of the $\mathrm{CP}^{\infty}$-construction, one can recover the category of all von Neumann algebras and channels (normal unital completely positive maps) from the 2-category $[W^*]$ of von Neumann algebras, bimodules and intertwiners. As an application, we extend Choi's characterisation of extremal channels between finite-dimensional matrix algebras to a characterisation of extremal channels between arbitrary von Neumann algebras., Comment: 25 pages, many figures. Rev 2: discusses relationship with arxiv:1603.04353

Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by the evolution of its phase and slowest decaying isostable coordinate have previously been shown to capture bifurcations and dynamics of the network which cannot be explained through standard phase reduction. An alternative framework using isostable coordinates to obtain higher-order phase reductions has also demonstrated a similar descriptive ability for two oscillators. In this work we consider the phase-isostable network equations for an arbitrary but finite number of identical coupled oscillators, obtaining conditions required for stability of phase-locked states including synchrony. For the mean-field complex Ginzburg-Landau equation where the solutions of the full system are known, we compare the accuracy of the phase-isostable network equations and higher-order phase reductions in capturing bifurcations of phase-locked states. We find the former to be the more accurate and therefore employ this to investigate the dynamics of globally linearly coupled networks of Morris-Lecar neuron models (both two and many nodes). We observe qualitative correspondence between results from numerical simulations of the full system and the phase-isostable description demonstrating that in both small and large networks the phase-isostable framework is able to capture dynamics that the first-order phase description cannot., Comment: 26 pages, 11 Figures

Coronal mass ejections (CMEs) are large eruptions from the Sun that propagate through the heliosphere after launch. Observational studies of these transient phenomena are usually based on 2D images of the Sun, corona, and heliosphere (remote-sensing data), as well as magnetic field, plasma, and particle samples along a 1D spacecraft trajectory (in-situ data). Given the large scales involved and the 3D nature of CMEs, such measurements are generally insufficient to build a comprehensive picture, especially in terms of local variations and overall geometry of the whole structure. This White Paper aims to address this issue by identifying the data sets and observational priorities that are needed to effectively advance our current understanding of the structure and evolution of CMEs, in both the remote-sensing and in-situ regimes. It also provides an outlook of possible missions and instruments that may yield significant improvements into the subject., Comment: White Paper submitted to the Heliophysics 2024-2033 Decadal Survey, 9 pages, 4 figures

Grothendieck-Verdier duality is a powerful and ubiquitous structure on monoidal categories, which generalises the notion of rigidity. Hopf algebroids are a generalisation of Hopf algebras, to a non-commutative base ring. Just as the category of finite-dimensional modules over a Hopf algebra inherits rigidity from the category of vector spaces, we show that the category of finite-dimensional modules over a Hopf algebroid with bijective antipode inherits a Grothendieck-Verdier structure from the category of bimodules over its base algebra. We investigate the algebraic and categorical structure of this duality., Comment: 12 pages, formerly 'The category of finite-dimensional modules over a Hopf algebroid with bijective antipode is Grothendieck-Verdier'

Diversity, equity and inclusion (DEI) programs can only be implemented successfully if proper work-life balance is possible in Heliophysics (and in STEM field in general). One of the core issues stems from the culture of "work-above-life" associated with mission concepts, development, and implementation but also the expectations that seem to originate from numerous announcements from NASA (and other agencies). The benefits of work-life balance are well documented; however, the entire system surrounding research in Heliophysics hinders or discourages proper work-life balance. For example, there does not seem to be attention paid by NASA Headquarters (HQ) on the timing of their announcements regarding how it will be perceived by researchers, and how the timing may promote a culture where work trumps personal life. The same is true for remarks by NASA HQ program officers during panels or informal discussions, where seemingly innocuous comments may give a perception that work is expected after "normal" work hours. In addition, we are calling for work-life balance plans and implementation to be one of the criteria used for down-selection and confirmation of missions (Key Decision Points: KDP-B, KDP-C)., Comment: White paper submitted to the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033; 6 pages

Particles measured in large gradual solar energetic particle (SEP) events are believed to be predominantly accelerated at shocks driven by coronal mass ejections (CMEs). Ion charge state and composition analyses suggest that the origin of the seed particle population for the mechanisms of particle acceleration at CME-driven shocks is not the bulk solar wind thermal material, but rather a suprathermal population present in the solar wind. This suprathermal population could result from remnant material accelerated in prior solar flares and/or preceding CME-driven shocks. In this work, we examine the distribution of this suprathermal particle population in the inner heliosphere by combining a magnetohydrodynamic (MHD) simulation of the solar wind and a Monte-Carlo simulation of particle acceleration and transport. Assuming that the seed particles are uniformly distributed near the Sun by solar flares of various magnitudes, we study the longitudinal distribution of the seed population at multiple heliocentric distances. We consider a non-uniform background solar wind, consisting of fast and slow streams that lead to compression and rarefaction regions within the solar wind. Our simulations show that the seed population at a particular location (e.g., 1 au) is strongly modulated by the underlying solar wind configuration. Corotating interaction regions (CIRs) and merged interactions regions (MIRs) can strongly alter the energy spectra of the seed particle populations. In addition, cross-field diffusion plays an important role in mitigating strong variations of the seed population in both space and energy., Comment: 20 pages, 7 figures

Drawing connections between heliospheric spacecraft and solar wind sources is a vital step in understanding the evolution of the solar corona into the solar wind and contextualizing \textit{in situ} timeseries. Furthermore, making advanced predictions of this linkage for ongoing heliospheric missions, such as Parker Solar Probe (PSP), is necessary for achieving useful coordinated remote observations and maximizing scientific return. The general procedure for estimating such connectivity is straightforward (i.e. magnetic field line tracing in a coronal model) but validating the resulting estimates difficult due to the lack of an independent ground truth and limited model constraints. In its most recent orbits, PSP has reached perihelia of 13.3$R_\odot$ and moreover travels extremely fast prograde relative to the solar surface, covering over 120 degrees longitude in three days. Here we present footpoint predictions and subsequent validation efforts for PSP Encounter 10, the first of the 13.3$R_\odot$ orbits, which occurred in November 2021. We show that the longitudinal dependence of \textit{in situ} plasma data from these novel orbits provides a powerful method of footpoint validation. With reference to other encounters, we also illustrate that the conditions under which source mapping is most accurate for near-ecliptic spacecraft (such as PSP) occur when solar activity is low, but also requires that the heliospheric current sheet is strongly warped by mid-latitude or equatorial coronal holes. Lastly, we comment on the large-scale coronal structure implied by the Encounter 10 mapping, highlighting an empirical equatorial cut of the Alfv\`{e}n surface consisting of localized protrusions above unipolar magnetic separatrices., Comment: 33 Pages, 7 Figures, JGR Space Physics, Published Online 2023/3/28, In Final Production

We examine the production of energetic neutral atoms (ENAs) in solar flares and CME-driven shocks and their subsequent propagation to 1 au. Time profiles and fluence spectra of solar ENAs at 1 au are computed for two scenarios: 1) ENAs are produced downstream at CME-driven shocks, and 2) ENAs are produced at large-scale post-flare loops in solar flares. Both the time profiles and fluence spectra for these two scenarios are vastly different. Our calculations indicate that we can use solar ENAs as a new probe to examine the underlying acceleration process of solar energetic particles (SEPs) and to differentiate the two accelertion sites: large loops in solar flares and downstream of CME-driven shocks, in large SEP events., Comment: 11 pages, updated figures and paper is accepted by ApJ

We investigate composition-differentiation operators acting on the space $S^2$, the space of analytic functions on the open unit disk whose first derivative is in $H^2$. Specifically, we determine characterizations for bounded and compact composition-differentiation operators acting on $S^p$. In addition, for particular classes of inducing maps, we compute the norm, and identify the spectrum. Finally, for particular linear fractional inducing maps, we determine the adjoint of the composition-differentiation operator acting on weighted Bergman spaces which include $S^2, H^2$, and the Dirichlet space., Comment: in submission

We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide computable estimates on the operator norm.

In this paper, we study the hypercyclic composition operators on weighted Banach spaces of functions defined on discrete metric spaces. We show that the only such composition operators act on the "little" spaces. We characterize the bounded composition operators on the little spaces, as well as provide various necessary conditions for hypercyclicity.

Let $\mathcal{L}$ be the space of complex-valued functions $f$ on the set of vertices $T$ of an rooted infinite tree rooted at $o$ such that the difference of the values of $f$ at neighboring vertices remains bounded throughout the tree, and let $\mathcal{L}_{\textbf{w}}$ be the set of functions $f\in \mathcal{L}$ such that $|f(v)-f(v^-)|=O(|v|^{-1})$, where $|v|$ is the distance between $o$ and $v$ and $v^-$ is the neighbor of $v$ closest to $o$. In this article, we characterize the bounded and the compact multiplication operators between $\mathcal{L}$ and $\mathcal{L}_{\textbf{w}}$, and provide operator norm and essential norm estimates. Furthermore, we characterize the bounded and compact multiplication operators between $\mathcal{L}_{\textbf{w}}$ and the space $L^\infty$ of bounded functions on $T$ and determine their operator norm and their essential norm. We establish that there are no isometries among the multiplication operators between these spaces.

Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces $\mathcal{D}_\alpha$. Specifically we study differences of composition operators on the Dirichlet space $\mathcal{D}$ and $S^2$, the space of analytic functions whose first derivative is in $H^2$, and then use Calder\'{o}n's complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.

We investigate the isometric composition operators on the analytic Besov spaces. For $12$, we extend previous work on the subject. Finally, we analyze this same problem for the Besov spaces with an equivalent norm.

We study the multiplication operators on the weighted Lipschitz space $\mathcal{L}_{\textbf{w}}$ consisting of the complex-valued functions $f$ on the set of vertices of an infinite tree $T$ rooted at $o$ such that $\sup_{v\neq o}|v||f(v)-f(v^-)|<\infty$, where $|v|$ denotes the distance between $o$ and $v$ and $v^-$ is the neighbor of $v$ closest to $o$. For the multiplication operator, we characterize boundedness, compactness, provide estimates on the operator norm and the essential norm, and determine the spectrum. We prove that there are no isometric multiplication operators or isometric zero divisors on $\mathcal{L}_{\textbf{w}}$., Comment: arXiv admin note: text overlap with arXiv:2207.12212

In this paper, we present the current results in the study of weighted composition operators on the Bloch space of bounded homogeneous domains in $\mathbb{C}^n$ with particular emphasis on the issues of boundedness and compactness. We also discuss the bounded and the compact weighted composition operators from the Bloch space to the Hardy space $H^\infty$.

In this article, we characterize the bounded and the compact multiplication operators between distinct iterated logarithmic Lipschitz spaces, and between the Lipschitz space and an iterated logarithmic Lipschitz space of an infinite tree. In addition, we provide operator norm estimates and show that there are no isometries among such operators. %We obtain a new characterization of the bounded multiplication operators acting on an iterated logarithmic Lipschitz space and the compact multiplication operators between the weighted Lipschitz space and the Lipschitz space.

In this paper, we study the multiplication operators on $S^2$, the space of analytic functions on the open unit disk $\mathbb D$ whose first derivative is in $H^2$. Specifically, we characterize the bounded and the compact multiplication operators, establish estimates on the operator norm, and determine the spectrum. Finally, we prove that the isometric multiplication operators are precisely those induced by a constant function of modulus one.

We introduce a class of iterated logarithmic Lipschitz spaces $\mathcal{L}^{(k)}$, $k\in\mathbb{N}$, on an infinite tree which arise naturally in the context of operator theory. We characterize boundedness and compactness of the multiplication operators on $\mathcal{L}^{(k)}$ and provide estimates on their operator norm and their essential norm. In addition, we determine the spectrum, characterize the multiplication operators that are bounded below, and prove that on such spaces there are no nontrivial isometric multiplication operators and no isometric zero divisors.

In this paper, we investigate the existence of stability-changing bifurcations in epidemiological models used to study the spread of zombiism through a human population. These bifurcations show that although linear instability of disease-free equilibria may exist in a model, perturbations of model parameters may result in stability. Thus, we show that humans can survive a zombie outbreak.

In this paper, we study the differentiation operator acting on discrete function spaces; that is spaces of functions defined on an infinite rooted tree. We discuss, through its connection with composition operators, the boundedness and compactness of this operator. In addition, we discuss the operator norm and spectrum, and consider when such an operator can be an isometry. We then apply these results to the operator acting on the discrete Lipschitz space and weighted Banach spaces, as well as the Hardy spaces defined on homogeneous trees.

We investigate composition-differentiation operators acting on the Dirichlet space of the unit disk. Specifically, we determine characterizations for bounded, compact, and Hilbert-Schmidt composition-differentiation operators. In addition, for particular classes of inducing maps, we derive an adjoint formula, compute the norm, and identify the spectrum.

We study properties of the topological space of composition operators on the Banach algebra of bounded functions on an unbounded, locally finite metric space in the operator norm topology and essential norm topology. Moreover, we characterize the compactness of differences of two such composition operators., Comment: in submission

We present the current results in the study of weighted composition operators on weighted Banach spaces of an unbounded, locally finite metric space. Specifically, we determine characterizations of bounded and compact weighted composition operators, including the operator and essential norms. In addition, we characterize the weighted composition operators that are injective, are bounded below, have closed range, and have bounded inverse. We characterize the isometries and surjective isometries among the weighted composition operators, as well as those that satisfy the Fredholm condition. Lastly, we provide numerous interesting examples of the richness of these operators acting on the discrete weighted Banach spaces., Comment: to appear, Acta Sci. Math. (Szeged)

We study composition operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm and the essential norm. In addition, we study the isometric composition operators.

We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological differences. We compute the basic reproduction number for each model, as well as analyze the sensitivity of $R_0$ to changes in sociological parameter values.

We give a complete characterization of the spectrum of composition operators, induced by an automorphism of the open unit disk, acting on a family of Banach spaces of analytic functions that includes the Bloch space and BMOA. We show that for parabolic and hyperbolic automorphisms, the spectrum is the unit circle. For the case of elliptic automorphisms, the spectrum is either the unit circle or a finite cyclic subgroup of the unit circle.

Let $D$ be a bounded homogeneous domain in $\mathbb{C}^n$. In this paper, we study the bounded and the compact weighted composition operators mapping the Hardy space $H^\infty(D)$ into the Bloch space of $D$. We characterize the bounded weighted composition operators, provide operator norm estimates, and give sufficient conditions for compactness. We prove that these conditions are necessary in the case of the unit ball and the polydisk. We then show that if $D$ is a bounded symmetric domain, the bounded multiplication operators from $H^\infty(D)$ to the Bloch space of $D$ are the operators whose symbol is bounded.