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We report the results of a comprehensive study of the spectroscopic binary (SB2) system HD 34736 hosting two chemically peculiar (CP) late B-type stars. Using new and archival observational data, we characterise the system and its components, including their rotation and magnetic fields. Fitting of the radial velocities yields $P_\mathrm{orb}=83.\!^\mathrm{d}219(3)$ and $e=0.8103(3)$. The primary component is a CP He-wk star with $T_{\mathrm{eff}A}=13000\pm500$ K and $\upsilon_\mathrm{e}\sin i\;=75\pm3$ km/s, while the secondary exhibits variability of Mg and Si lines, and has $T_{\mathrm{eff}B}=11500\pm1000$ K and $\upsilon_\mathrm{e}\sin i=110$-180 km/s. TESS and KELT photometry reveal clear variability of the primary component with a rotational period $P_{\mathrm{rot}A}=1.\!^\mathrm{d}279\,988\,5(11)$, which is lengthening at a rate of $1.26(6)$ s/yr. For the secondary, $P_{\mathrm{rot}B}=0.\!^\mathrm{d}522\,693\,8(5)$, reducing at a rate of $-0.14(3)$ s/yr. The longitudinal component $\langle B_\mathrm{z}\rangle$ of the primary's strongly asymmetric global magnetic field varies from $-6$ to +5 kG. Weak spectropolarimetric evidence of a magnetic field is found for the secondary star. The observed X-ray and radio emission of HD 34736 may equally be linked to a suspected T Tau-like companion or magnetospheric emission from the principal components. Given the presence of a possible third magnetically active body, one can propose that the magnetic characteristics of the protostellar environment may be connected to the formation of such systems., Comment: This preprint has 28 pages, 23 figures, and includes the complete version of Table 1. Published in MNRAS

We revisit the computation of the beta function in the two-dimensional $\mathbb{CP}(1)$ sigma model. We show that in different schemes, different diagrams are responsible for the running, such as momentum-independent tadpoles or even UV-finite bubble diagrams. We also comment on the relation between the beta functions and the energy dependence of scattering amplitudes.

The tree-structured varying coefficient model (TSVC) is a flexible regression approach that allows the effects of covariates to vary with the values of the effect modifiers. Relevant effect modifiers are identified inherently using recursive partitioning techniques. To quantify uncertainty in TSVC models, we propose a procedure to construct confidence intervals of the estimated partition-specific coefficients. This task constitutes a selective inference problem as the coefficients of a TSVC model result from data-driven model building. To account for this issue, we introduce a parametric bootstrap approach, which is tailored to the complex structure of TSVC. Finite sample properties, particularly coverage proportions, of the proposed confidence intervals are evaluated in a simulation study. For illustration, we consider applications to data from COVID-19 patients and from patients suffering from acute odontogenic infection. The proposed approach may also be adapted for constructing confidence intervals for other tree-based methods.

We develop a new regularization method for the stress-energy tensor and the two-point function of free quantum scalar fields propagating in cosmological spacetimes. We proceed by extending the adiabatic regularization scheme with the introduction of two additional mass scales. By setting them to the order of the physical scale of the studied scenario, we obtain ultraviolet-regularized quantities that do not distort the power spectra amplitude at the infrared scales amplified by the expansion of the universe. This is not ensured by the standard adiabatic approach. We also show how our proposed subtraction terms can be interpreted as a renormalization of coupling constants in the Einstein equations. We finally illustrate our proposed regularization method in two scenarios of cosmological interest: de Sitter inflation and geometric reheating., Comment: It matches published version in PRD. 22 pages + references, 5 figures

A toric variety is called fibered if it can be represented as a total space of fibre bundle over toric base and with toric fiber. Fibered toric varieties form a special case of toric variety bundles. In this note we first give an introduction to the class of fibered toric varieties. Then we use them to illustrate some known and conjectural results on topology and intersection theory of general toric variety bundles. Finally, using the language of fibered toric varieties, we compute the equivariant cohomology rings of smooth complete toric varieties., Comment: 9 pages, 1 figure, comments are welcome!

We consider correlators for the flux of energy and charge in the background of operators with large global $U(1)$ charge in conformal field theory (CFT). It has recently been shown that the corresponding Euclidean correlators generically admit a semiclassical description in terms of the effective field theory (EFT) for a conformal superfluid. We adapt the semiclassical description to Lorentzian observables and compute the leading large charge behavior of the flux correlators in general $U(1)$ symmetric CFTs. We discuss the regime of validity of the large charge EFT for these Lorentzian observables and the subtleties in extending the EFT approach to subleading corrections. We also consider the Wilson-Fisher fixed point in $d=4-\epsilon$ dimensions, which offers a specific weakly coupled realization of the general setup, where the subleading corrections can be systematically computed without relying on an EFT., Comment: 33 pages, 8 figures

We study a broad class of polynomial optimization problems whose constraints and objective functions exhibit sparsity patterns. We give two characterizations of the number of critical points to these problems, one as a mixed volume and one as an intersection product on a toric variety. As a corollary, we obtain a convex geometric interpretation of polar degrees, a classical invariant of algebraic varieties, as well as Euclidean distance degrees. Furthermore, we prove the BKK generality of Lagrange systems in many instances., Comment: 29 pages

We discuss various differences in the instanton-based calculations of the $\beta$ functions in theories such as Yang-Mills and $\mathbb{CP}(N\!-\!1)$ on one hand, and $\lambda\phi^4$ theory with Symanzik's sign-reversed prescription for the coupling constant $\lambda$ on the other hand. Although the aforementioned theories are asymptotically free, in the first two theories, instantons are topological, whereas the Fubini-Lipatov instanton in the third theory is topologically trivial. The spectral structure in the background of the Fubini-Lipatov instanton can be continuously deformed into that in the flat background, establishing a one-to-one correspondence between the two spectra. However, when considering topologically nontrivial backgrounds for Yang-Mills and $\mathbb{CP}(N\!-\!1)$ theories, the spectrum undergoes restructuring. In these cases, a mismatch between the spectra around the instanton and the trivial vacuum occurs., Comment: 22 pages

Recent works have shown that depth information can be obtained from Dual-Pixel (DP) sensors. A DP arrangement provides two views in a single shot, thus resembling a stereo image pair with a tiny baseline. However, the different point spread function (PSF) per view, as well as the small disparity range, makes the use of typical stereo matching algorithms problematic. To address the above shortcomings, we propose a Continuous Cost Aggregation (CCA) scheme within a semi-global matching framework that is able to provide accurate continuous disparities from DP images. The proposed algorithm fits parabolas to matching costs and aggregates parabola coefficients along image paths. The aggregation step is performed subject to a quadratic constraint that not only enforces the disparity smoothness but also maintains the quadratic form of the total costs. This gives rise to an inherently efficient disparity propagation scheme with a pixel-wise minimization in closed-form. Furthermore, the continuous form allows for a robust multi-scale aggregation that better compensates for the varying PSF. Experiments on DP data from both DSLR and phone cameras show that the proposed scheme attains state-of-the-art performance in DP disparity estimation.

In this paper we propose a method that uses Lagrange multipliers and numerical algebraic geometry to find all critical points, and therefore globally solve, polynomial optimization problems. We design a polyhedral homotopy algorithm that explicitly constructs an optimal start system, circumventing the typical bottleneck associated with polyhedral homotopy algorithms. The correctness of our algorithm follows from intersection theoretic computations of the algebraic degree of polynomial optimization programs and relies on explicitly solving the tropicalization of a corresponding Lagrange system. We present experiments that demonstrate the superiority of our algorithm over traditional homotopy continuation algorithms., Comment: 17 pages, 2 figures

A cosmological polytope is a lattice polytope introduced by Arkani-Hamed, Benincasa, and Postnikov in their study of the wavefunction of the universe in a class of cosmological models. More concretely, they construct a cosmological polytope for any Feynman diagram, i.e. an undirected graph. In this paper, we initiate a combinatorial study of these polytopes. We give a complete description of their faces, identify minimal faces that are not simplices and compute the number of faces in specific instances. In particular, we give a recursive description of the $f$-vector of cosmological polytopes of trees., Comment: Revised exposition

Approximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic complexity of this approximation problem. Using the theory of Khovanskii bases, we show that this number is given by the volume of a certain polytope. We also show how to compute all solutions using numerical nonlinear algebra.

The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around a superfluid background. In this work, focussing on $U(1)$ invariant Wilson-Fisher fixed points, we study the spectrum of spinning large charge operators. For sufficiently low spin these correspond to the phonon excitations of the superfluid state. We discuss the organization of these states into conformal multiplets and the form of the corresponding composite operators in the free field theory limit. The latter entails a mapping, built order-by-order in the inverse charge $n^{-1}$, between the Fock space of vacuum fluctuations and the Fock space of fluctuations around the superfluid state. We discuss the limitations of the semiclassical method, and find that the phonon description breaks down for spins of order $n^{1/2}$ while the computation of observables is valid up to spins of order $n$. Finally, we apply the semiclassical method to compute some conformal 3-point and 4-point functions, and analyze the conformal block decomposition of the latter with our knowledge of the operator spectrum., Comment: 45 pages + appendices, 5 figures

This work focuses on a quasi-linear-in-complexity strategy for a hybrid surface-wire integral equation solver for the electroencephalography forward problem. The scheme exploits a block diagonally dominant structure of the wire self block -- that models the neuronal fibers self interactions -- and of the surface self block -- modeling interface potentials. This structure leads to two Neumann iteration schemes further accelerated with adaptive integral methods. The resulting algorithm is linear up to logarithmic factors. Numerical results confirm the performance of the method in biomedically relevant scenarios.

There exist two notions of typicality in computability theory, namely, genericity and randomness. In this article, we introduce a new notion of genericity, called partition genericity, which is at the intersection of these two notions of typicality, and show that many basis theorems apply to partition genericity. More precisely, we prove that every co-hyperimmune set and every Kurtz random is partition generic, and that every partition generic set admits weak infinite subsets. In particular, we answer a question of Kjos-Hanssen and Liu by showing that every Kurtz random admits an infinite subset which does not compute any set of positive Hausdorff dimension. Partition genericty is a partition regular notion, so these results imply many existing pigeonhole basis theorems., Comment: 23 pages

In this paper we develop a theory of volume polynomials of generalized virtual polytopes based on the study of topology of affine subspace arrangements in a real Euclidean space. We apply this theory to obtain a topological version of the BKK Theorem, the Stanley-Reisner and Pukhlikov-Khovanskii type descriptions for cohomology rings of generalized quasitoric manifolds., Comment: 18 pages

CANVAS caused by RFC1 biallelic expansions is a major cause of inherited sensory neuronopathy. Detection of RFC1 expansion is challenging and CANVAS can be associated with atypical features. We clinically and genetically characterized 50 patients, selected based on the presence of sensory neuronopathy confirmed by EMG. We screened RFC1 expansion by PCR, repeat-primed PCR, and Southern blotting of long-range PCR products, a newly developed method. Neuropathological characterization was performed on the brain and spinal cord of one patient. Most patients (88%) carried a biallelic (AAGGG)n expansion in RFC1. In addition to the core CANVAS phenotype (sensory neuronopathy, cerebellar syndrome, and vestibular impairment), we observed chronic cough (97%), oculomotor signs (85%), motor neuron involvement (55%), dysautonomia (50%), and parkinsonism (10%). Motor neuron involvement was found for 24 of 38 patients (63.1%). First motor neuron signs, such as brisk reflexes, extensor plantar responses, and/or spasticity, were present in 29% of patients, second motor neuron signs, such as fasciculations, wasting, weakness, or a neurogenic pattern on EMG in 18%, and both in 16%. Mixed motor and sensory neuronopathy was observed in 19% of patients. Among six non-RFC1 patients, one carried a heterozygous AAGGG expansion and a pathogenic variant in GRM1. Neuropathological examination of one RFC1 patient with an enriched phenotype, including parkinsonism, dysautonomia, and cognitive decline, showed posterior column and lumbar posterior root atrophy. Degeneration of the vestibulospinal and spinocerebellar tracts was mild. We observed marked astrocytic gliosis and axonal swelling of the synapse between first and second motor neurons in the anterior horn at the lumbar level. The cerebellum showed mild depletion of Purkinje cells, with empty baskets, torpedoes, and astrogliosis characterized by a disorganization of the Bergmann's radial glia. We found neuronal loss in the vagal nucleus. The pars compacta of the substantia nigra was depleted, with widespread Lewy bodies in the locus coeruleus, substantia nigra, hippocampus, entorhinal cortex, and amygdala. We propose new guidelines for the screening of RFC1 expansion, considering different expansion motifs. Here, we developed a new method to more easily detect pathogenic RFC1 expansions. We report frequent motor neuron involvement and different neuronopathy subtypes. Parkinsonism was more prevalent in this cohort than in the general population, 10% versus the expected 1% (p < .001). We describe, for the first time, the spinal cord pathology in CANVAS, showing the alteration of posterior columns and roots, astrocytic gliosis and axonal swelling, suggesting motor neuron synaptic dysfunction.

Numerous magnetic hot stars exhibit gyrosynchrotron radio emission. The source electrons were previously thought to be accelerated to relativistic velocities in the current sheet formed in the middle magnetosphere by the wind opening magnetic field lines. However, a lack of dependence of radio luminosity on the wind power, and a strong dependence on rotation, has recently challenged this paradigm. We have collected all radio measurements of magnetic early-type stars available in the literature. When constraints on the magnetic field and/or the rotational period are not available, we have determined these using previously unpublished spectropolarimetric and photometric data. The result is the largest sample of magnetic stars with radio observations that has yet been analyzed: 131 stars with rotational and magnetic constraints, of which 50 are radio-bright. We confirm an obvious dependence of gyrosynchrotron radiation on rotation, and furthermore find that accounting for rotation neatly separates stars with and without detected radio emission. There is a close correlation between H$\alpha$ emission strength and radio luminosity. These factors suggest that radio emission may be explained by the same mechanism responsible for H$\alpha$ emission from centrifugal magnetospheres, i.e. centrifugal breakout (CBO), however, whereas the H$\alpha$-emitting magnetosphere probes the cool plasma before breakout, radio emission is a consequence of electrons accelerated in centrifugally-driven magnetic reconnection., Comment: 47 pages (16 pages plus appendices), 43 figures, 9 tables, accepted for publication in MNRAS

The classical BKK theorem computes the intersection number of divisors on toric variety in terms of volumes of corresponding polytopes. It was observed by Pukhlikov and the first author that the BKK theorem leads to a presentation of the cohomology ring of toric variety as a quotient of the ring of differential operators with constant coefficients by the annihilator of an explicit polynomial. In this paper we generalize this construction to the case of quasitoric bundles. These are fiber bundles with generalized quasitoric manifolds as fibers. First we obtain a generalization of the BKK theorem to this case. Then we use recently obtained descriptions of the graded-commutative algebras which satisfy Poincar\'e duality to give a description of cohomology rings of quasitoric bundles., Comment: 16 pages, comments are welcome! arXiv admin note: substantial text overlap with arXiv:2006.12043

We propose an algebraic construction of the operator-state correspondence in non-relativistic conformal field theories by explicitly constructing an automorphism of the Schr\"odinger algebra relating generators in different frames. It is shown that the construction follows closely that of relativistic conformal field theories., Comment: Journal version---a few minor changes

We study commutative algebras with Gorenstein duality, i.e. algebras $A$ equipped with a non-degenerate bilinear pairing such that $\langle ac,b\rangle=\langle a,bc\rangle$ for any $a,b,c\in A$. If an algebra $A$ is Artinian, such pairing exists if and only if $A$ is Gorenstein. We give a description of algebras with Gorenstein duality as a quotients of the ring of differential operators by the annihilator of an explicit polynomial (or more generally formal polynomial series). This provides a calculation of Macaulay's inverse systems for (not necessarily Artinian) algebras with Gorenstein duality. Our description generalizes previously know description of graded algebras with Gorenstein duality generated in degree 1. Our main motivation comes from the study of even degree cohomology rings. In particular, we apply our main result to compute the ring of cohomology classes of even degree of toric bundles and the ring of conditions of horospherical homogeneous spaces., Comment: 14 pages, comments are welcome!

Given a pair of translation surfaces it is very difficult to determine whether they are supported on the same algebraic curve. In fact, there are very few examples of such pairs. In this note we present infinitely many examples of finite collections of translation surfaces supported on the same algebraic curve. The underlying curves are hyperelliptic curves with many automorphisms. For each curve, the automorphism of maximal order acts on the space of holomorphic 1-forms. We present a translation surface corresponding to each of the eigenforms of this action., Comment: 13 pages, comments are welcome!

This paper is devoted to the study of multigraded algebras and multigraded linear series. For an $\mathbb{N}^s$-graded algebra $A$, we define and study its volume function $F_A:\mathbb{N}_+^s\to \mathbb{R}$, which computes the asymptotics of the Hilbert function of $A$. We relate the volume function $F_A$ to the volume of the fibers of the global Newton-Okounkov body $\Delta(A)$ of $A$. Unlike the classical case of standard multigraded algebras, the volume function $F_A$ is not a polynomial in general. However, in the case when the algebra $A$ has a decomposable grading, we show that the volume function $F_A$ is a polynomial with non-negative coefficients. We then define mixed multiplicities in this case and provide a full characterization for their positivity. Furthermore, we apply our results on multigraded algebras to multigraded linear series. Our work recovers and unifies recent developments on mixed multiplicities. In particular, we recover results on the existence of mixed multiplicities for (not necessarily Noetherian) graded families of ideals and on the positivity of the multidegrees of multiprojective varieties., Comment: to appear in Journal of the London Mathematical Society