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We present TESS photometry of the asynchronous polar BY Cam, which undergoes a beat-cycle between the 199.384-min white dwarf (WD) spin period and the 201.244-min orbital period. This results in changes in the flow of matter onto the WD. The TESS light curve covers 92% of the beat cycle once and 71% of the beat cycle twice. The strongest photometric signal, at 197.560-min, is ascribed to a side-band period. During times of light-curve stability, the photometry modulates at the spin frequency, supporting our WD spin-period identification. Both one-pole and two-pole accretion configurations repeat from one beat cycle to the next with clear and repeatable beat-phase dependent intensity variations. To explain these, we propose the operation of a magnetic valve at L1. The magnetic valve modulates the mass-transfer rate, as evidenced by a factor of 5 variation in orbital-averaged intensity, over the course of the beat cycle in a repeatable manner. The accretion stream threading distance from the WD is also modulated at the beat-period, because of the variation of the WD magnetic field with respect to the stream and because of changes in the mass transfer rate due to the operation of the magnetic valve. Changes in the threading distance result in significant shifts in the position of accreting spots around the beat cycle. As a consequence, only the faintest photometric minima allow for an accurate ephemeris determination. Three regions on the white dwarf appear to receive most of the accretion flow, suggestive of a complex WD magnetic field.

In this paper, first we introduce a new approach to the notion of $F$-algebroids, which is a generalization of $F$-manifold algebras and $F$-manifolds, and show that $F$-algebroids are the corresponding semi-classical limits of pre-Lie formal deformations of commutative associative algebroids. Then we use the deformation cohomology of pre-Lie algebroids to study pre-Lie infinitesimal deformations and extension of pre-Lie $n$-deformations to pre-Lie $(n+1)$-deformations of a commutative associative algebroid. Next we develop the theory of Dubrovin's dualities of $F$-algebroids with eventual identities and use Nijenhuis operators on $F$-algebroids to construct new $F$-algebroids. Finally we introduce the notion of pre-$F$-algebroids, which is a generalization of $F$-manifolds with compatible flat connections. Dubrovin's dualities of pre-$F$-algebroids with eventual identities, Nijenhuis operators on pre-$F$-algebroids and their applications to integral systems are discussed.

In this essay we give a general picture about the evolution of Grohendieck's ideas regarding the notion of space. Starting with his fundamental work in algebraic geometry, where he introduces schemes and toposes as generalizations of classical notions of spaces, passing through tame topology and ending with the formulation of a geometry of forms, we show how the ideas of Grothendieck evolved from pure mathematical considerations to physical and philosophical questions about the nature and structure of space and its mathematical models., Comment: Published in Handbook of the History and Philosophy of Mathematical Practice

We introduce Jo, a mobile application that attempts to improve user's well-being. Jo is a journaling application--users log their important moments via short texts and optionally an attached photo. Unlike a static journal, Jo analyzes these moments and helps users take action towards increased well-being. For example, Jo annotates each moment with a set of values (e.g., family, socialization, mindfulness), thereby giving the user insights about the balance in their lives. In addition, Jo helps the user create reminders that enable them to create additional happy moments. We describe the results of fielding Jo in a study of 39 participants. The results illustrate the promise of a journaling application that provides personalized feedback, and points at further research., Comment: 7 pages, 3 figures

We define F-algebra--Rinehart pairs and super F-algebroids and study the connection between them., Comment: 14 pages. Version 2, the main result has not been changed; a discussion about tensor product and direct product of F-algebras has been added and the theorem about monoidal structure of the category of F-algebras has been removed

We describe Voyageur, which is an application of experiential search to the domain of travel. Unlike traditional search engines for online services, experiential search focuses on the experiential aspects of the service under consideration. In particular, Voyageur needs to handle queries for subjective aspects of the service (e.g., quiet hotel, friendly staff) and combine these with objective attributes, such as price and location. Voyageur also highlights interesting facts and tips about the services the user is considering to provide them with further insights into their choices., Comment: Demo paper accepted to the Web Conference

Generalizing previous work of Hora (1998) on the asymptotic spectral analysis for the Hamming graph $H(n,q)$ which is the $n^{\mathrm{th}}$ Cartesian power $K_q^{\square n}$ of the complete graph $K_q$ on $q$ vertices, we describe the possible limits of the joint spectral distribution of the pair $(G^{\square n},\overline{G}\vphantom{G}^{\square n})$ of the $n^{\mathrm{th}}$ Cartesian powers of a strongly regular graph $G$ and its complement $\overline{G}$, where we let $n\rightarrow\infty$, and $G$ may vary with $n$. This result is an analogue of the bivariate central limit theorem, and we obtain in this way the bivariate Poisson distributions and the standard bivariate Gaussian distribution, together with the product measures of univariate Poisson and Gaussian distributions. We also report a family of bivariate hypergeometric orthogonal polynomials with respect to the last distributions, which we call the bivariate Charlier-Hermite polynomials, and prove basic formulas for them. This family of orthogonal polynomials seems previously unnoticed, possibly because of its peculiarity., Comment: 19 pages

In this note we introduce the concept of F-algebroid, and give its elementary properties and some examples. We provide a description of the almost duality for Frobenius manifolds, introduced by Dubrovin, in terms of a composition of two anchor maps of a unique cotangent F-algebroid., Comment: 13 pages; v2 has small changes, it has improved exposition. Revised version to appear in: "Archivum Mathematicum"

In this article we present and describe a notion of "logical perfection". We extract the notion of "perfection" from the contemporary logical concept of categoricity. Categoricity (in power) has become in the past half century a main driver of ideas in model theory, both mathematically (stability theory may be regarded as a way of approximating categoricity) and philosophically. In the past two decades, categoricity notions have started to overlap with more classical notions of robustness and smoothness. These have been crucial in various parts of mathematics since the nineteenth century. We postulate and present the category of logical perfection. We draw on various notions of perfection from mathematics of the 19th and 20th centuries and then trace the relation to the concept of categoricity in power as a logical notion of what a "mathematically perfect" structure is., Comment: Title has changed.Exposition has been improved and some explanations are added. The second author is added

We study thermal properties of a large-N massless pion gas using a low-energy QCD approach given by an $O(N +1)/O(N)$ Nonlinear Sigma Model. We build diagrammatically the associated finite free energy to $O(TM^{3})$ in the pion mass expansion through an effective vertex that considers all the contributions coming from closed diagrams. Subsequently, we calculate finite order parameters such as the quark condensate and its respective derivative, i.e., the scalar susceptibility, in the chiral limit, along with their associated critical exponents. These results are compared with our previous unitarized scattering analyses for the chiral transition universality class, thus showing a reasonable agreement both with lattice simulations and these resonant studies., Comment: 4 pages, 3 figures, conference paper

Many distinct problems give birth to Darboux-Halphen system of differential equations and here we review some of them. The first is the classical problem presented by Darboux and later solved by Halphen concerning finding infinite number of double orthogonal surfaces in $\mathbb{R}^3$. The second is a problem in general relativity about gravitational instanton in Bianchi IX metric space. The third problem stems from the new take on the moduli of enhanced elliptic curves called Gauss-Manin connection in disguise developed by one of the authors and finally in the last problem Darboux-Halphen system emerges from the associative algebra on the tangent space of a Frobenius manifold.

We compute the magnetic dipole moment (MDM) for massive flavor neutrinos using the neutrino self-energy in a magnetized media. The framework to incorporate neutrino masses is one minimal extension of the Standard Model in which neutrinos are Dirac particles and their masses coming from tiny Yukawa couplings from a second Higgs doublet with a small vacuum expectation value. The computations are carried out by using proper time formalism in the weak field approximation $eB<

The subject of this paper is the big quantum cohomology rings of symplectic isotropic Grassmannians $\text{IG}(2, 2n)$. We show that these rings are regular. In particular, by "generic smoothness", we obtain a conceptual proof of generic semisimplicity of the big quantum cohomology for $\text{IG}(2, 2n)$. Further, by a general result of Claus Hertling, the regularity of these rings implies that they have a description in terms of isolated hypersurface singularities, which we show in this case to be of type $A_{n-1}$. By the homological mirror symmetry conjecture, these results suggest the existence of a very special full exceptional collection in the derived category of coherent sheaves on $\text{IG}(2, 2n)$. Such a collection is constructed in the appendix by Alexander Kuznetsov., Comment: Appendix by Alexander Kuznetsov. The paper incorporates the results of the earlier preprint arXiv:1510.07903. Comments are welcome

We discuss recent advances on QCD chiral symmetry restoration at finite temperature, within the theoretical framework of Effective Theories. $U(3)$ Ward Identities are derived between pseudoscalar susceptibilities and quark condensates, allowing to explain the behaviour of lattice meson screening masses. Unitarized interactions and the generated $f_0(500)$ thermal state are showed to play an essential role in the description of the transition through the scalar susceptibility, Comment: 10 pages, 9 figures. Proceedings of "XII Quark Confinement and the Hadron Spectrum"

We prove an Assmus-Mattson-type theorem for block codes where the alphabet is the vertex set of a commutative association scheme (say, with $s$ classes). This in particular generalizes the Assmus-Mattson-type theorems for $\mathbb{Z}_4$-linear codes due to Tanabe (2003) and Shin, Kumar, and Helleseth (2004), as well as the original theorem by Assmus and Mattson (1969). The weights of a code are $s$-tuples of non-negative integers in this case, and the conditions in our theorem for obtaining $t$-designs from the code involve concepts from polynomial interpolation in $s$ variables. The Terwilliger algebra is the main tool to establish our results., Comment: 24 pages

We analyze chiral restoration within the $O(N+1)/O(N)$ Non-Linear Sigma Model for large $N$ as an effective theory for low-energy QCD at finite temperature $T$. The free energy is constructed diagramatically to ${\cal O}(TM^3)$ in the pion mass expansion, which allows to derive the quark condensate and the scalar susceptibility in the chiral limit. At this order, we do not have to deal with renormalization, neither from divergences from mass tadpoles nor from those of higher order loop contributions. Our results for the critical behaviour are consistent with expectations from lattice analysis and with previous works where the susceptibility is saturated by the thermal $f_0(500)$ pole., Comment: 13 pages, 5 figures. Version accepted in Phys.Rev.D

We study the vacuum behavior of an extended Higgs sector with two doublets in a scenario with a softly broken \texorpdfstring{$U(1)$}{lg} global symmetry. The soft-violation term is introduced to avoid massless-axion particles arising when the global symmetry becomes spontaneously broken. This model has metastable states through the possible presence of multiple non-degenerate minima, which is unwanted from the phenomenological point of view if the metastable state is not long-lived enough. The analysis of this fact leads to find possible exclusion limits over parameter space of quartic couplings. Results improve the individual behavior of initial conditions for renormalization group equations; also determining unstable zones for the effective Higgs potential at one loop level. Besides vacuum stability analyses, the influence of absence of charge violation minima is considered as a limiting case excluding zones in the parameter space. Extremal cases for the model as well as criticality phenomena are discussed with the aid of relation among Higgs masses or splittings among them. From vacuum behavior and LHC results, phenomenological aspects in the searching of charged and heavier Higgs bosons are considered to evaluate the scalar alignment regimen of the two Higgs doublet model., Comment: 22 pages, 37 Figures

In this work, we review how the mass and the width of the $f_{0}(500)$ pole behave in a regime where temperature is below the critical chiral transition value. This is attained by considering a large-$N$ $O(N + 1)/O(N)$ invariant Non-Linear Sigma Model (NLSM) such that we can study the dynamical generation of a $f_{0}(500)$ resonance. Introducing thermal effects via the imaginary time formalism allows us to study the behavior of the pole and relate it to chiral restoration., Comment: 6 pages, 3 figures, conference paper. To be published in Acta Physica Polonica B: Proceeding Suplements. Acknowledgments added

In several frameworks for leptons-sectors of two Higgs doublet models, we calculate the magnetic dipole moment for the different flavor types of neutrino. Computations are carried out by assuming a normal hierarchy for neutrino masses, and analyzing the process $\nu \rightarrow \nu \gamma $ with a charged Higgs boson into the loop. The analysis was performed by sweeping the charged Higgs mass and taking into account the experimental constraints for relevant parameters in Two Higgs Doublet Models with and without flavor changing neutral currents; obtaining magnetic dipole moments close to the experimental thresholds for tau neutrinos in type II and Lepton-specific cases. In the neutrino-specific scenario, the contribution of new physics could be sizeable to the current measurement for flavor magnetic dipole moment. This fact leads to excluding possible zones in the parameter space of charged Higgs mass and vacuum expectation value of the second doublet., Comment: 16 pages, 6 figures. Some parts of the formulations have been treated formerly in our article arXiv:1506.00735 and arXiv:1512.07722

We consider the $O(N+1)/O(N)$ Non-Linear Sigma Model for large $N$ as an effective theory for low-energy QCD at finite temperature $T$, in the chiral limit. At $T=0$ this formulation provides a good description of scattering data in the scalar channel and generates dynamically the $f_0(500)$ pole, the pole position lying within experimental determinations. Previous $T=0$ results with this model are updated using newer analysis of pion scattering data. We calculate the pion scattering amplitude at finite $T$ and show that it satisfies exactly thermal unitarity, which had been assumed but not formally proven in previous works. We discuss the main differences with the $T=0$ result and we show that one can define a proper renormalization scheme with $T=0$ counterterms such that the renormalized amplitude can be chosen to depend only on a few parameters. Next, we analyze the behaviour of the $f_0(500)$ pole at finite $T$, which is consistent with chiral symmetry restoration when the scalar susceptibility is saturated by the $f_0(500)$ state, in a second-order transition scenario and in accordance with lattice and theoretical analysis., Comment: 24 pages, 12 figures. Funding agency added in the Acknowledgments

We study the vacuum behavior at one loop level in extended Higgs sectors with two doublets (2HDM), where $U(1)$ and $Z_{2}$ symmetries are considered to protect the $CP$ symmetry in the Higgs potential and to avoid Flavor Changing Neutral Currents at tree level in the Yukawa sector. In the Inert Higgs Model case, a detailed comparison is made between both models by using the energy evolution of couplings, which should satisfy energy scale dependent relations deduced for minima and stationary points of the Higgs potential at tree level. Besides, perturbative unitarity constraints at tree level are considered to generate the allowed parameter space compatible with perturbativity (absence of Landau poles). Our studies illustrate exclusion regions for Higgs masses and other combinations of couplings in the scalar sector, in particular for splittings of mass square for neutral scalars $A^{0}$ and $H^{0}$, as well as the difference between the sum of these and the charged Higgs mass square. From the vacuum stability for inert-2HDM at the tree and one loop levels, analyses lead us to find out new hierarchical structures for scalar masses. To complete vacuum studies on the Inert model, and based on reparameterization invariance of the Higgs potential, we compute original discriminants that allow ensuring the presence of a global electroweak minimum at tree level. Moreover, the behavior in high energy scales drives out analyzing criticality phenomena for the additional parameters of extended Higgs sectors. Finally, and using the consistency with the electroweak precision analyses of oblique parameters, we describe several implications from different regimes of the inert model on charged and pseudoscalar Higgs searches., Comment: 23 Pages, 18 Figures. New references were added. Section 4-6 reformulated, Main results keep unchanged

In the framework of a two Higgs doublet model type I and type II, we calculate limits on neutrino masses for the different types of neutrinos, by using the experimental bounds on their magnetic dipole moments. This is carried out by analyzing diagrams of Cherenkov neutrino decays with a charged Higgs into the loop, coming from the two Higgs doublet model (2HDM). Such constraints are translated into allowed regions in the free parameters of the models, for each neutrino flavor. The analysis was performed by sweeping the charged Higgs mass between (100-900)GeV and taking into account the experimental constraints for $\tan\beta $ in the 2HDM type I and II, obtaining contributions close to the experimental thresholds for muon and tau neutrinos, while for electron neutrino the relevant contribution comes from standard model and keeps out of the reach of forthcoming experiments., Comment: 19 pages, 12 figures, 5 tables. LaTeX2e

In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.

Unitarity constraints for Yukawa couplings are considered in the Two Higgs Doublet Model type III, by using a general expansion in partial waves for fermionic scattering processes. Constraints over general Flavor Changing Neutral Currents are found from that systematic, such bounds compete with those coming from Lagrangian perturbativity requirement but are weaker than those imposed from phenomenological processes and precision tests. Nevertheless, for bounds based on unitarity the number of assumptions is the lowest among phenomenological and theoretical limits. Indeed, these new theoretical constraints are independent of scalar masses or mixing angles for this extended Higgs sector, making them less model dependent., Comment: 14 pages, 2 figures, LaTeX2e