Recent Preprint Research Articles

On the existence of funneled orientations for classes of rooted phylogenetic networks

Recently, there has been a growing interest in the relationships between unrooted and rooted phylogenetic networks. In this context, a natural question to ask is if an unrooted phylogenetic network U can be oriented as a rooted phylogenetic network such that the latter satisfies certain structural properties. In a recent preprint, Bulteau et al. claim that it is NP-hard to decide if U has a funneled (resp. funneled tree-child) orientation, for when the internal vertices of U have degree at most 5. Unfortunately, the proof of their funneled tree-child result appears to be incorrect. In this paper, we show that, despite their incorrect proof, it is NP-hard to decide if U has a funneled tree-child orientation even if each internal vertex has degree 5 and that NP-hardness remains for other popular classes of rooted phylogenetic networks such as funneled normal and funneled reticulation-visible. Additionally, our results hold regardless of whether U is rooted at an existing vertex or by subdividing an edge with the root.

Re-analysis of whole genome sequencing ends a diagnostic odyssey: Case report of an RNU4-2 related neurodevelopmental disorder.

Despite increasing knowledge of disease-causing genes in human genetics, approximately half of the individuals affected by neurodevelopmental disorders remain genetically undiagnosed. Part of this missing heritability might be caused by genetic variants outside of protein-coding genes, which are not routinely diagnostically investigated. A recent preprint identified de novo variants in the non-coding spliceosomal snRNA gene RNU4-2 as a cause of a frequent novel syndromic neurodevelopmental disorder. Here we mined 164 whole genome sequencing (WGS) trios from individuals with neurodevelopmental or multiple congenital anomaly disorders that received diagnostic genomic investigations at our clinic. We identify a recurrent de novo RNU4-2 variant (NR_003137.2(RNU4-2):n.64_65insT) in a 5-year-old girl with severe global developmental delay, hypotonia, microcephaly, and seizures that likely explains her phenotype, given that extensive previous genetic investigations failed to identify an alternative cause. We present detailed phenotyping of the individual obtained during a 5-year follow-up. This includes photographs showing recognizable facial features for this novel disorder, which might allow prioritizing other currently unexplained affected individuals sharing similar facial features for targeted investigations of RNU4-2. This case illustrates the power of re-analysis to solve previously unexplained cases even when a diagnostic genome remains negative.

A note on the 𝑉-invariant

Let R R be a finitely generated N \mathbb N -graded algebra domain over a Noetherian ring and let I I be a homogeneous ideal of R R . Given P ∈ A s s ( R / I ) P\in Ass(R/I) one defines the v v -invariant v P ( I ) v_P(I) of I I at P P as the least c ∈ N c\in \mathbb N such that P = I : f P=I:f for some f ∈ R c f\in R_c . A classical result of Brodmann [Proc. Amer. Math. Soc. 74 (1979), pp. 16–18] asserts that A s s ( R / I n ) Ass(R/I^n) is constant for large n n . So it makes sense to consider a prime ideal P ∈ A s s ( R / I n ) P\in Ass(R/I^n) for all the large n n and investigate how v P ( I n ) v_P(I^n) depends on n n . We prove that v P ( I n ) v_P(I^n) is eventually a linear function of n n . When R R is the polynomial ring over a field this statement has been proved independently also by Ficarra and Sgroi in their recent preprint [Asymptotic behaviour of the v \text {v} -number of homogeneous ideals, https://arxiv.org/abs/2306.14243, 2023].

A Predictor-Corrector Algorithm for Semidefinite Programming that Uses the Factor Width Cone

AbstractWe propose an interior point method (IPM) for solving semidefinite programming problems (SDPs). The standard interior point algorithms used to solve SDPs work in the space of positive semidefinite matrices. Contrary to that the proposed algorithm works in the cone of matrices of constant factor width. We prove global convergence and provide a complexity analysis. Our work is inspired by a series of papers by Ahmadi, Dash, Majumdar and Hall, and builds upon a recent preprint by Roig-Solvas and Sznaier [arXiv:2202.12374, 2022].

Bijective proof of a conjecture on unit interval posets

In a recent preprint, Matherne, Morales and Selover conjectured that two different representations of unit interval posets are related by the famous zeta map in $q,t$-Catalan combinatorics. This conjecture was proved recently by G\'elinas, Segovia and Thomas using induction. In this short note, we provide a bijective proof of the same conjecture with a reformulation of the zeta map using left-aligned colored trees, first proposed in the study of parabolic Tamari lattices.

Gaussian kernels on nonsimply connected closed Riemannian manifolds are never positive definite

AbstractWe show that the Gaussian kernel on any nonsimply connected closed Riemannian manifold , where is the geodesic distance, is not positive definite for any , combining analyses in the recent preprint by Da Costa–Mostajeran–Ortega and classical comparison theorems in Riemannian geometry.

Comment on the Feasibility of Carbon Burning in Betelgeuse

The recent pre-print (version published to arxiv on 2023 June 3rd) by Saio et al. argues that the supergiant Betelgeuse is already undergoing carbon burning, based the assumption that all of its light variations are caused by radial pulsations. However, the angular diameter measurements of the star are in conflict with the stellar radius required by their models, as we show in this note. We discuss the feasibility that the Great Dimming was caused by constructive mode interference using long-term brightness measurements and comment on differences in modeling frameworks adopted in Saio et al. versus Joyce et al.

Why trust nuclear data evaluations with Bayesian networks

Bayesian networks were recently suggested as a framework for nuclear data evaluation. Their theory was to some extent described in a recent preprint and some example evaluations were presented. However, due to their newness in the context of nuclear data evaluation and consequently the lack of experience with them within the community makes it dicult to develop trust in the underlying methodology and consequently also the results produced by it. In this contribution, we aim to make a case why evaluators can trust this methodology in principle but will also elaborate on the fact that Bayesian networks are not a silver bullet for evaluation work. On the contrary, evaluators must assess and quantify essential assumptions about nuclear models and experiments with the same dilligence that is already necessary for the application of the wellestablished Generalized Least Squares (GLS) method. We also explain that the increased ease and flexibility to introduce assumptions regarding nuclear models, experiments and their relationships can help an evaluator to rigorously account for assumptions that are very often neglected in evaluations with the GLS method, such as the non-negativity of cross sections, relative experimental normalization uncertainties and the non-linearity in ratios of cross sections. We believe that adopting the Bayesian network paradigm can help both humans to produce evaluations with clearly traceable assumptions and machines to deal with nuclear data more eciently in terms of execution speed and storage size requirements.

An elementary alternative to ECH capacities

The embedded contact homology (ECH) capacities are a sequence of numerical invariants of symplectic four-manifolds that give (sometimes sharp) obstructions to symplectic embeddings. These capacities are defined using embedded contact homology, and establishing their basic properties currently requires Seiberg-Witten theory. In this paper we define a sequence of symplectic capacities in four dimensions using only basic notions of holomorphic curves. The capacities satisfy the same basic properties as ECH capacities and agree with the ECH capacities for the main examples for which the latter have been computed, namely convex and concave toric domains. The capacities are also useful for obstructing symplectic embeddings into closed symplectic four-manifolds. This work is inspired by a recent preprint of McDuff and Siegel [D. McDuff, K. Siegel, arXiv [Preprint] (2021)], giving a similar elementary alternative to symplectic capacities from rational symplectic field theory (SFT).

A note on the concurrent normal conjecture

It is conjectured since long that for any convex body \(K \in \mathbb{R}^n\) there exists a point in the interior of K which belongs to at least 2n normals from different points on the boundary of K. The conjecture is known to be true for n = 2, 3, 4.Motivated by a recent preprint of Y. Martinez-Maure [4], we give a short proof of his result: for dimension \(n\geq 3\), under mild conditions, almost every normal through a boundary point to a smooth convex body \(K \in \mathbb{R}^n\) contains an intersection point of at least 6 normals from different points on the boundary of K.

In preprints: morphogens in motion.

In preprints: morphogens in motion.

Proposal for the search for new spin interactions at the micrometer scale using diamond quantum sensors

For decades, searches for exotic spin interactions have used increasingly-precise laboratory measurements to test various theoretical models of particle physics. However, most searches have focused on interaction length scales greater than 1 mm, corresponding to hypothetical boson masses less than 0.2 meV. Recently, quantum sensors based on Nitrogen-Vacancy (NV) centers in diamond have emerged as a promising platform to probe spin interactions at the micrometer scale, opening the door to explore new physics at this length scale. Here, we propose experiments to search for several hypothetical interactions between NV electron spins and moving masses. We focus on potential interactions involving the coupling of NV spin ensembles to both spin-polarized and unpolarized masses attached to vibrating mechanical oscillators. For each interaction, we estimate the sensitivity, identify optimal experimental conditions, and analyze potential systematic errors. Using multi-pulse quantum sensing protocols with NV spin ensembles to improve sensitivity, we project new constraints that are ~5 orders-of-magnitude improvement over previous constraints at the micrometer scale. We also identify a spin-polarized test mass, based on hyperpolarized 13C nuclear spins in a thin diamond membrane, which offers a favorable combination of high spin density and low stray magnetic fields. Our analysis is timely in light of a recent preprint (arXiv:2010.15667) reporting a surprising non-zero result of micrometer-scale spin-velocity interactions.

Note on Fundamental Physics Tests from Black Hole Imaging: Comment on “Hunting for Extra Dimensions in the Shadow of Sagittarius A*”

Several recent works have tested fundamental physics with horizon-scale black hole (BH) images, using the size r sh and deviation from circularity of the BH shadow. For the Event Horizon Telescope image of Sgr A*, limits on are not available due to the sparse interferometric coverage of the 2017 observations, alongside the short variability timescale of Sgr A* compared to M87*. We comment on the results of a recent preprint which purports to have derived new limits on extra dimensions using the deviation from circularity of Sgr A*'s shadow. The latter is quoted to be ≲10% as with M87*, based on the “similarity” of the two shadows, which however is an incorrect assumption. In the immediate future, the simplest tests of fundamental physics from Sgr A*'s image will mostly have to rely on r sh.

On generalised Petersen graphs of girth 7 that have cop number 4

We show that if n = 7k/i with i ∈ {1, 2, 3} then the cop number of the generalised Petersen graph GP(n,k) is 4, with some small previously-known exceptions. It was previously proved by Ball et al. (2015) that the cop number of any generalised Petersen graph is at most 4. The results in this paper explain all of the known generalised Petersen graphs that actually have cop number 4 but were not previously explained by Morris et al. in a recent preprint, and places them in the context of infinite families. (More precisely, the preprint by Morris et al. explains all known generalised Petersen graphs with cop number 4 and girth 8, while this paper explains those that have girth 7.)

In preprints: the problem of producing precise patterns.

In preprints: the problem of producing precise patterns.

Weyl’s Laws and Connes’ Integration Formulas for Matrix-Valued $$L\!\log \!L$$-Orlicz Potentials

Thanks to the Birman-Schwinger principle, Weyl's laws for Birman-Schwinger operators yields semiclassical Weyl's laws for the corresponding Schr\"odinger operators. In a recent preprint Rozenblum established quite general Weyl's laws for Birman-Schwinger operators associated with pseudodifferential operators of critical order and potentials that are product of $L\log L$-Orlicz functions and Alfhors-regular measures supported on a submanifold. In this paper, for matrix-valued $L\log L$-Orlicz potentials supported on the whole manifold, Rozenblum's results are direct consequences of the Cwikel-type estimates on tori recently established by Sukochev-Zanin. As applications we obtain CLR-type inequalities and semiclassical Weyl's laws for critical Schr\"odinger operators associated with matrix-valued$L\log L$-Orlicz potentials. Finally, we explain how the Weyl's laws of this paper imply a strong version of Connes' integration formula for matrix-valued $L\log L$-Orlicz potentials.

Quantum induced broadening: A challenge for cosmic neutrino background discovery

A recent preprint by Cheipesh et al. pointed out that the zero-point motion of tritium atoms bound to graphene may blur the measured energies of $\ensuremath{\beta}$ electrons. Smearing due to zero point motion is well known. Such an effect features in studies of the $\ensuremath{\beta}$ spectrum expected in experiments like KATRIN using diatomic tritium. The recent preprint may, however, challenge new planned experiments seeking to discover the cosmic neutrino background (CNB) neutrinos (and/or other neutrinos of masses smaller than 0.1 eV), which plan to use tritium adsorbed onto graphene or other materials. Our paper clarifies these issues and examines the more general problem of smearing induced by quantum uncertainty. We find that the effect of Cheipesh et al. is reduced considerably. The importance of the chemical evolution of the $^{3}\mathrm{H}$ atom hosting the tritium nucleus into a tightly bound neutral $^{3}\mathrm{He}$ atom is emphasized. We estimate the excess blurring caused by the dense spectrum near the lowest state of the graphene or other hosts of the tritium atom, generated by the electronic response to the ``sudden'' escape of the $\ensuremath{\beta}$ electron. Our analysis suggests yet larger effects and difficulties facing many experiments searching for small mass neutrinos. We speculate on a possible experimental setup, which could minimize quantum broadening.

Geometric Optimization for Structure-Preserving Model Reduction of Hamiltonian Systems

Classical model reduction methods disregard the special symplectic structure associated with Hamiltonian systems. A key challenge in projection-based approaches is to construct a sym-plectic basis that captures the essential system information. This necessitates the computation of a so-called proper symplectic decomposition (PSD) of a given sample data set. The PSD problem allows for a canonical formulation as an optimization problem on the symplectic Stiefel manifold. However, as with their Euclidean counterparts, symplectic projectors only depend on the underlying symplectic subspaces and not on the selected symplectic bases. This motivates to tackle the PSD problem as a Riemannian optimization problem on the symplectic Grassmann manifold, i.e., the matrix manifold of symplectic projectors. Initial investigations on this manifold feature in a recent preprint of the authors. In this work, we investigate the feasibility and performance of this approach on two academic numerical examples. More precisely, we calculate an optimized PSD for snapshot matrices that stem from solving the one-dimensional linear wave equation and the one-dimensional nonlinear Schrödinger equation.

Study of the non-Hermitian PT -symmetric gϕ2(iϕ)ε theory: Analysis of all orders in ε and resummations

In a recent work the Green's functions of the $\mathcal{PT}$-symmetric scalar theory $g \phi^{2}(i\phi)^\epsilon$ were calculated at the first order of the logarithmic expansion, i.e. at first order in $\epsilon$, and it was proposed to use this expansion in powers of $\epsilon$ to implement a systematic renormalization of the theory. Using techniques that we recently developed for the analysis of an ordinary (hermitian) scalar theory, in the present work we calculate the Green's functions at $O(\epsilon^2)$, pushing also the analysis to higher orders. We find that, at each finite order in $\epsilon$, the theory is non-interacting for any dimension $d \geq 2$. We then conclude that by no means this expansion can be used for a systematic renormalization of the theory. We are then lead to consider resummations, and we start with the leading contributions. Unfortunately, the results are quite poor. Specifying to the physically relevant $i g \phi^3$ model, we show that this resummation simply gives the trivial lowest order results of the weak-coupling expansion. We successively resum subleading diagrams, but again the results are rather poor. All this casts serious doubts on the possibility of studying the theory $g \phi^{2}(i\phi)^\epsilon$ with the help of such an expansion. We finally add that the findings presented in this work were obtained by us some time ago (December 2019), and we are delighted to see that these results, that we communicated to C.M. Bender in December 2019, are confirmed in a recent preprint (e-Print:2103.07577) of C.M. Bender and collaborators.

Correction to: Rel leaves of the Arnoux–Yoccoz surfaces

Our arguments in §6 of the paper [3] contain an error. In this note we explain the error and how to fix it. We are grateful to Florent Ygouf for both pointing out the mistake, and for indicating the correct argument included below. All of the results stated in the introduction of the paper remain valid, as a consequence of the amended argument which will be given below. In the recent preprint [4], Ygouf proves related results about existence of dense rel leaves in other loci.