@article{9651, abstract = {We introduce a hierachy of equivalence relations on the set of separated nets of a given Euclidean space, indexed by concave increasing functions ϕ:(0,∞)→(0,∞). Two separated nets are called ϕ-displacement equivalent if, roughly speaking, there is a bijection between them which, for large radii R, displaces points of norm at most R by something of order at most ϕ(R). We show that the spectrum of ϕ-displacement equivalence spans from the established notion of bounded displacement equivalence, which corresponds to bounded ϕ, to the indiscrete equivalence relation, coresponding to ϕ(R)∈Ω(R), in which all separated nets are equivalent. In between the two ends of this spectrum, the notions of ϕ-displacement equivalence are shown to be pairwise distinct with respect to the asymptotic classes of ϕ(R) for R→∞. We further undertake a comparison of our notion of ϕ-displacement equivalence with previously studied relations on separated nets. Particular attention is given to the interaction of the notions of ϕ-displacement equivalence with that of bilipschitz equivalence.}, author = {Dymond, Michael and Kaluza, Vojtech}, issn = {1572-9168}, journal = {Geometriae Dedicata}, publisher = {Springer Nature}, title = {{Divergence of separated nets with respect to displacement equivalence}}, doi = {10.1007/s10711-023-00862-3}, volume = {218}, year = {2024}, } @article{14660, abstract = {The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull of a set 𝑆⊂ℝ𝑑, then there are at most 2𝑑 points of 𝑆 whose convex hull contains the origin in the interior. Bárány, Katchalski,and Pach proved the following quantitative version of Steinitz’s theorem. Let 𝑄 be a convex polytope in ℝ𝑑 containing the standard Euclidean unit ball 𝐁𝑑. Then there exist at most 2𝑑 vertices of 𝑄 whose convex hull 𝑄′ satisfies 𝑟𝐁𝑑⊂𝑄′ with 𝑟⩾𝑑−2𝑑. They conjectured that 𝑟⩾𝑐𝑑−1∕2 holds with a universal constant 𝑐>0. We prove 𝑟⩾15𝑑2, the first polynomial lower bound on 𝑟. Furthermore, we show that 𝑟 is not greater than 2/√𝑑.}, author = {Ivanov, Grigory and Naszódi, Márton}, issn = {1469-2120}, journal = {Bulletin of the London Mathematical Society}, number = {2}, pages = {796--802}, publisher = {London Mathematical Society}, title = {{Quantitative Steinitz theorem: A polynomial bound}}, doi = {10.1112/blms.12965}, volume = {56}, year = {2024}, } @article{18617, abstract = {Any complex-valued polynomial on (Rn)k decomposes into an algebraic combination of O(n)-invariant polynomials and harmonic polynomials. This decomposition, separation of variables, is granted to be unique if n≥2k−1. We prove that the condition n≥2k−1 is not only sufficient, but also necessary for uniqueness of the separation. Moreover, we describe the structure of non-uniqueness of the separation in the boundary cases when n=2k−2 and n=2k−3. Formally, we study the kernel of a multiplication map ϕ carrying out separation of variables. We devise a general algorithmic procedure for describing Ker ϕ in the restricted non-stable range k≤n<2k−1. In the full non-stable range n<2k−1, we give formulas for highest weights of generators of the kernel as well as formulas for its Hilbert series. Using the developed methods, we obtain a list of highest weight vectors generating Ker ϕ.}, author = {Beďatš, Daniel}, issn = {0021-8693}, journal = {Journal of Algebra}, pages = {281--304}, publisher = {Elsevier}, title = {{Separation of variables for scalar-valued polynomials in the non-stable range}}, doi = {10.1016/j.jalgebra.2024.04.013}, volume = {651}, year = {2024}, } @article{13974, abstract = {The Tverberg theorem is one of the cornerstones of discrete geometry. It states that, given a set X of at least (d+1)(r−1)+1 points in Rd, one can find a partition X=X1∪⋯∪Xr of X, such that the convex hulls of the Xi, i=1,…,r, all share a common point. In this paper, we prove a trengthening of this theorem that guarantees a partition which, in addition to the above, has the property that the boundaries of full-dimensional convex hulls have pairwise nonempty intersections. Possible generalizations and algorithmic aspects are also discussed. As a concrete application, we show that any n points in the plane in general position span ⌊n/3⌋ vertex-disjoint triangles that are pairwise crossing, meaning that their boundaries have pairwise nonempty intersections; this number is clearly best possible. A previous result of Álvarez-Rebollar et al. guarantees ⌊n/6⌋pairwise crossing triangles. Our result generalizes to a result about simplices in Rd, d≥2.}, author = {Fulek, Radoslav and Gärtner, Bernd and Kupavskii, Andrey and Valtr, Pavel and Wagner, Uli}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {831--848}, publisher = {Springer Nature}, title = {{The crossing Tverberg theorem}}, doi = {10.1007/s00454-023-00532-x}, volume = {72}, year = {2024}, } @inproceedings{15296, abstract = {In this paper we build a constructive algorithm that returns a rectifiable curve that connects two points in a weakly convex set in a Hilbert space. We have proven that this algorithm converges and obtained an estimate on the curve’s length and compare the length of the curve obtained to known results.}, author = {Lopushanski, Mariana and Ivanov, Grigory}, booktitle = {AIP Conference Proceedings}, issn = {1551-7616}, location = {Virtual}, number = {1}, publisher = {AIP Publishing}, title = {{A constructive algorithm for building rectifiable curves in weakly convex sets}}, doi = {10.1063/5.0195908}, volume = {3030}, year = {2024}, } @inproceedings{18917, abstract = {An eight-partition of a finite set of points (respectively, of a continuous mass distribution) in ℝ³ consists of three planes that divide the space into 8 octants, such that each open octant contains at most 1/8 of the points (respectively, of the mass). In 1966, Hadwiger showed that any mass distribution in ℝ³ admits an eight-partition; moreover, one can prescribe the normal direction of one of the three planes. The analogous result for finite point sets follows by a standard limit argument. We prove the following variant of this result: Any mass distribution (or point set) in ℝ³ admits an eight-partition for which the intersection of two of the planes is a line with a prescribed direction. Moreover, we present an efficient algorithm for calculating an eight-partition of a set of n points in ℝ³ (with prescribed normal direction of one of the planes) in time O^*(n^{5/2}).}, author = {Aronov, Boris and Basit, Abdul and Ramesh, Indu and Tasinato, Gianluca and Wagner, Uli}, booktitle = {40th International Symposium on Computational Geometry}, isbn = {9783959773164}, location = {Athens, Greece}, pages = {8:1--8:15}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Eight-partitioning points in 3D, and efficiently too}}, doi = {10.4230/LIPIcs.SoCG.2024.8}, volume = {293}, year = {2024}, } @article{18483, abstract = {In this paper we prove a perturbative version of a remarkable Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) result. They prove non perturbative Birkhoff conjecture for centrally-symmetric convex domains, namely, a centrally-symmetric convex domain with integrable billiard is ellipse. We combine techniques from Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) with a local result by Kaloshin–Sorrentino (Ann. Math. 188(1):315–380, 2018) and show that a domain close enough to a centrally symmetric one with integrable billiard is ellipse. To combine these results we derive a slight extension of Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) by proving that a notion of rational integrability is equivalent to the C0-integrability condition used in their paper.}, author = {Kaloshin, Vadim and Koudjinan, Edmond and Zhang, Ke}, issn = {1420-8970}, journal = {Geometric and Functional Analysis}, pages = {1973--2007}, publisher = {Springer Nature}, title = {{Birkhoff conjecture for nearly centrally symmetric domains}}, doi = {10.1007/s00039-024-00695-6}, volume = {34}, year = {2024}, } @article{18065, abstract = {We establish a close connection between acceleration and dynamical degree for one-frequency quasi-periodic compact cocycles, by showing that two vectors derived separately from each coincide. Based on this, we provide a dynamical classification of one-frequency quasi-periodic SO(3, R)-cocycles.}, author = {Hou, Xuanji and Pan, Yi and Zhou, Qi}, issn = {1090-2082}, journal = {Advances in Mathematics}, publisher = {Elsevier}, title = {{Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles}}, doi = {10.1016/j.aim.2024.109943}, volume = {457}, year = {2024}, } @article{18604, abstract = {A face in a curve arrangement is called popular if it is bounded by the same curve multiple times. Motivated by the automatic generation of curved nonogram puzzles, we investigate possibilities to eliminate the popular faces in an arrangement by inserting a single additional curve. This turns out to be NP-hard; however, it becomes tractable when the number of popular faces is small: We present a randomized FPT-time algorithm where the parameter is the number of popular faces.}, author = {De Nooijer, Phoebe and Terziadis, Soeren and Weinberger, Alexandra and Masárová, Zuzana and Mchedlidze, Tamara and Löffler, Maarten and Rote, Günter}, issn = {1526-1719}, journal = {Journal of Graph Algorithms and Applications}, number = {2}, pages = {47--82}, publisher = {Brown University}, title = {{Removing popular faces in curve arrangements}}, doi = {10.7155/jgaa.v28i2.2988}, volume = {28}, year = {2024}, } @inproceedings{14888, abstract = {A face in a curve arrangement is called popular if it is bounded by the same curve multiple times. Motivated by the automatic generation of curved nonogram puzzles, we investigate possibilities to eliminate the popular faces in an arrangement by inserting a single additional curve. This turns out to be NP-hard; however, it becomes tractable when the number of popular faces is small: We present a probabilistic FPT-approach in the number of popular faces.}, author = {De Nooijer, Phoebe and Terziadis, Soeren and Weinberger, Alexandra and Masárová, Zuzana and Mchedlidze, Tamara and Löffler, Maarten and Rote, Günter}, booktitle = {31st International Symposium on Graph Drawing and Network Visualization}, isbn = {9783031492747}, issn = {1611-3349}, location = {Isola delle Femmine, Palermo, Italy}, pages = {18--33}, publisher = {Springer Nature}, title = {{Removing popular faces in curve arrangements}}, doi = {10.1007/978-3-031-49275-4_2}, volume = {14466}, year = {2024}, } @article{18586, abstract = {We prove the Central Limit Theorem and superpolynomial mixing for environment viewed from the particle process in quasi periodic Diophantine random environment. The main ingredients are smoothness estimates for the solution of the Poisson equation and local limit asymptotics for certain accelerated walks.}, author = {Czudek, Klaudiusz S and Dolgopyat, Dmitry}, issn = {1980-0436}, journal = {Alea}, number = {2}, pages = {1853--1865}, publisher = {Instituto Nacional de Matematica Pura e Aplicada}, title = {{The central limit theorem and rate of mixing for simple random walks on the circle}}, doi = {10.30757/ALEA.V21-70}, volume = {21}, year = {2024}, } @article{17231, abstract = {In the class of projective billiards, which contains the usual billiards, we exhibit counter-examples to Ivrii's conjecture, which states that in any planar billiard with smooth boundary the set of periodic orbits has zero measure. The counter-examples are polygons admitting a 2-parameters family of n-periodic orbits, with n being either 3 or any even integer greater than 4.}, author = {Fiorebe, Corentin}, issn = {1553-5231}, journal = {Discrete and Continuous Dynamical Systems- Series A}, number = {11}, pages = {3287--3301}, publisher = {AIMS}, title = {{Examples of projective billiards with open sets of periodic orbits}}, doi = {10.3934/dcds.2024059}, volume = {44}, year = {2024}, } @article{18524, abstract = {Recent works have constrained the binary fraction of evolved populations of massive stars in local galaxies such as red supergiants and Wolf–Rayet stars, but the binary fraction of yellow supergiants (YSGs) in the Hertzsprung gap remains unconstrained. Binary evolution theory predicts that the Hertzsprung gap is home to multiple populations of binary systems with varied evolutionary histories. In this paper, we develop a method to distinguish single YSGs from YSG plus O- or B-type main-sequence binaries using optical and ultraviolet photometry, and then apply this method to identify candidate YSG binaries in the Magellanic Clouds. After constructing a set of combined stellar atmosphere models, we find that optical photometry is, given typical measurement and reddening uncertainties, sufficient to discern single YSGs from YSG+OB binaries if the OB-star is at least ∼5M⊙ for Teff,YSG ∼ 4000 K, but requires a ∼20M⊙ OB star for YSGs up to Teff,YSG ∼ 9000 K. For these hotter YSG temperatures, ultraviolet photometry allows binaries with OB companions as small as ∼7M⊙ to be identified. We use color–color spaces developed from these models to search for evidence of excess blue or ultraviolet light in a set of ∼1000 YSG candidates in the Magellanic Clouds. We identify hundreds of candidate YSG binary systems and report a preliminary fraction of YSGs that show a blue/UV color excess of 20%–60%. Spectroscopic follow-up is now required to confirm the true nature of this population.}, author = {O’Grady, Anna J.G. and Drout, Maria R. and Neugent, Kathryn F. and Ludwig, Bethany and Götberg, Ylva Louise Linsdotter and Gaensler, B. M.}, issn = {1538-4357}, journal = {Astrophysical Journal}, publisher = {IOP Publishing}, title = {{Binary yellow supergiants in the Magellanic Clouds. I. Photometric candidate identification}}, doi = {10.3847/1538-4357/ad778a}, volume = {975}, year = {2024}, } @article{15375, abstract = {In the eukaryotic nucleus, heterochromatin forms highly condensed, visible foci known as heterochromatin foci (HF). These HF are enriched with linker histone H1, a key player in heterochromatin condensation and silencing. However, it is unknown how H1 aggregates HF and condenses heterochromatin. In this study, we established that H1 facilitates heterochromatin condensation by enhancing inter- and intrachromosomal interactions between and within heterochromatic regions of the Arabidopsis (Arabidopsis thaliana) genome. We demonstrated that H1 drives HF formation via phase separation, which requires its C-terminal intrinsically disordered region (C-IDR). A truncated H1 lacking the C-IDR fails to form foci or recover HF in the h1 mutant background, whereas C-IDR with a short stretch of the globular domain (18 out of 71 amino acids) is sufficient to rescue both defects. In addition, C-IDR is essential for H1's roles in regulating nucleosome repeat length and DNA methylation in Arabidopsis, indicating that phase separation capability is required for chromatin functions of H1. Our data suggest that bacterial H1-like proteins, which have been shown to condense DNA, are intrinsically disordered and capable of mediating phase separation. Therefore, we propose that phase separation mediated by H1 or H1-like proteins may represent an ancient mechanism for condensing chromatin and DNA.}, author = {He, Shengbo and Yu, Yiming and Wang, Liang and Zhang, Jingyi and Bai, Zhengyong and Li, Guohong and Li, Pilong and Feng, Xiaoqi}, issn = {1532-298X}, journal = {The Plant Cell}, number = {5}, pages = {1829--1843}, publisher = {Oxford University Press}, title = {{Linker histone H1 drives heterochromatin condensation via phase separation in Arabidopsis}}, doi = {10.1093/plcell/koae034}, volume = {36}, year = {2024}, } @inproceedings{17236, abstract = {Currently, the best known tradeoff between approximation ratio and complexity for the Sparsest Cut problem is achieved by the algorithm in [Sherman, FOCS 2009]: it computes O(√(log n)/ε)-approximation using O(nε logO(1) n) maxflows for any ε∈[Θ(1/log n),Θ(1)]. It works by solving the SDP relaxation of [Arora-Rao-Vazirani, STOC 2004] using the Multiplicative Weights Update algorithm (MW) of [Arora-Kale, JACM 2016]. To implement one MW step, Sherman approximately solves a multicommodity flow problem using another application of MW. Nested MW steps are solved via a certain "chaining" algorithm that combines results of multiple calls to the maxflow algorithm. We present an alternative approach that avoids solving the multicommodity flow problem and instead computes "violating paths". This simplifies Sherman's algorithm by removing a need for a nested application of MW, and also allows parallelization: we show how to compute O(√(log n)/ε)-approximation via O(logO(1) n) maxflows using O(nε) processors. We also revisit Sherman's chaining algorithm, and present a simpler version together with a new analysis.}, author = {Kolmogorov, Vladimir}, booktitle = {Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures}, isbn = {9798400704161}, issn = {1548-6109}, location = {Nantes, France}, pages = {403--414}, publisher = {Association for Computing Machinery}, title = {{A simpler and parallelizable O(√log n)-approximation algorithm for sparsest cut}}, doi = {10.1145/3626183.3659969}, year = {2024}, } @article{17408, abstract = {Background: The remarkable regenerative abilities observed in planarians and cnidarians are closely linked to the active proliferation of adult stem cells and the precise differentiation of their progeny, both of which typically deteriorate during aging in low regenerative animals. While regeneration-specific genes conserved in highly regenerative organisms may confer regenerative abilities and long-term maintenance of tissue homeostasis, it remains unclear whether introducing these regenerative genes into low regenerative animals can improve their regeneration and aging processes. Results: Here, we ectopically express highly regenerative species-specific JmjC domain-encoding genes (HRJDs) in Drosophila, a widely used low regenerative model organism. Surprisingly, HRJD expression impedes tissue regeneration in the developing wing disc but extends organismal lifespan when expressed in the intestinal stem cell lineages of the adult midgut under non-regenerative conditions. Notably, HRJDs enhance the proliferative activity of intestinal stem cells while maintaining their differentiation fidelity, ameliorating age-related decline in gut barrier functions. Conclusions: These findings together suggest that the introduction of highly regenerative species-specific genes can improve stem cell functions and promote a healthy lifespan when expressed in aging animals.}, author = {Nagai, Hiroki and Adachi, Yuya and Nakasugi, Tenki and Takigawa, Ema and Ui, Junichiro and Makino, Takashi and Miura, Masayuki and Nakajima, Yu Ichiro}, issn = {1741-7007}, journal = {BMC Biology}, publisher = {Springer Nature}, title = {{Highly regenerative species-specific genes improve age-associated features in the adult Drosophila midgut}}, doi = {10.1186/s12915-024-01956-4}, volume = {22}, year = {2024}, } @article{18111, abstract = {Observations of tidal disruption events (TDEs) show signs of nitrogen enrichment reminiscent of other astrophysical sources such as active galactic nuclei and star-forming galaxies. Given that TDEs probe the gas from a single star, it is possible to test whether the observed enrichment is consistent with expectations from the CNO cycle by looking at the observed nitrogen/carbon (N/C) abundance ratios. Given that ≈20% of solar-mass stars (and an even larger fraction of more massive stars) live in close binaries, it is worthwhile to also consider what TDEs from stars influenced by binary evolution would look like. We show here that TDEs from stars stripped of their hydrogen-rich (and nitrogen-poor) envelopes through previous binary-induced mass loss can produce much higher observable N/C enhancements than even TDEs from massive stars. Additionally, we predict that the time dependence of the N/C abundance ratio in the mass fallback rate of stripped stars will follow the inverse behavior of main-sequence stars, enabling a more accurate characterization of the disrupted star.}, author = {Mockler, Brenna and Gallegos-Garcia, Monica and Götberg, Ylva Louise Linsdotter and Miller, Jon M. and Ramirez-Ruiz, Enrico}, issn = {2041-8213}, journal = {Astrophysical Journal Letters}, number = {1}, publisher = {IOP Publishing}, title = {{Tidal disruption events from stripped stars}}, doi = {10.3847/2041-8213/ad6c34}, volume = {973}, year = {2024}, } @article{14886, abstract = {It is a basic principle that an effect cannot come before the cause. Dispersive relations that follow from this fundamental fact have proven to be an indispensable tool in physics and engineering. They are most powerful in the domain of linear response where they are known as Kramers-Kronig relations. However, when it comes to nonlinear phenomena the implications of causality are much less explored, apart from several notable exceptions. Here in this paper we demonstrate how to apply the dispersive formalism to analyze the ultrafast nonlinear response in the context of the paradigmatic nonlinear Kerr effect. We find that the requirement of causality introduces a noticeable effect even under assumption that Kerr effect is mediated by quasi-instantaneous off-resonant electronic hyperpolarizability. We confirm this by experimentally measuring the time-resolved Kerr dynamics in GaAs by means of a hybrid pump-probe Mach-Zehnder interferometer and demonstrate the presence of an intrinsic lagging between amplitude and phase responses as predicted by dispersive analysis. Our results describe a general property of the time-resolved nonlinear processes thereby highlighting the importance of accounting for dispersive effects in the nonlinear optical processes involving ultrashort pulses.}, author = {Lorenc, Dusan and Alpichshev, Zhanybek}, issn = {2643-1564}, journal = {Physical Review Research}, number = {1}, publisher = {American Physical Society}, title = {{Dispersive effects in ultrafast nonlinear phenomena: The case of optical Kerr effect}}, doi = {10.1103/PhysRevResearch.6.013042}, volume = {6}, year = {2024}, } @article{17285, abstract = {Winter plants rely on vernalization, a crucial process for adapting to cold conditions and ensuring successful reproduction. However, understanding the role of histone modifications in guiding the vernalization process in winter wheat remains limited. In this study, we investigated the transcriptome and chromatin dynamics in the shoot apex throughout the life cycle of winter wheat in the field. Two core histone modifications, H3K27me3 and H3K36me3, exhibited opposite patterns on the key vernalization gene VERNALIZATION1 (VRN1), correlating with its induction during cold exposure. Moreover, the H3K36me3 level remained high at VRN1 after cold exposure, which may maintain its active state. Mutations in FERTILIZATION-INDEPENDENT ENDOSPERM (TaFIE) and SET DOMAIN GROUP 8/EARLY FLOWERING IN SHORT DAYS (TaSDG8/TaEFS), components of the writer complex for H3K27me3 and H3K36me3, respectively, affected flowering time. Intriguingly, VRN1 lost its high expression after the cold exposure memory in the absence of H3K36me3. During embryo development, VRN1 was silenced with the removal of active histone modifications in both winter and spring wheat, with selective restoration of H3K27me3 in winter wheat. The mutant of Tafie-cr-87, a component of H3K27me3 “writer” complex, did not influence the silence of VRN1 during embryo development, but rather attenuated the cold exposure requirement of winter wheat. Integrating gene expression with H3K27me3 and H3K36me3 patterns identified potential regulators of flowering. This study unveils distinct roles of H3K27me3 and H3K36me3 in controlling vernalization response, maintenance, and resetting in winter wheat.}, author = {Liu, Xuemei and Deng, Min and Shi, Bingxin and Zhu, Kehui and Chen, Jinchao and Xu, Shujuan and Bie, Xiaomin and Zhang, Xiansheng and Lin, Xuelei and Xiao, Jun}, issn = {1869-1889}, journal = {Science China Life Sciences}, pages = {2251--2266}, publisher = {Springer Nature}, title = {{Distinct roles of H3K27me3 and H3K36me3 in vernalization response, maintenance, and resetting in winter wheat}}, doi = {10.1007/s11427-024-2664-0}, volume = {67}, year = {2024}, } @article{17476, abstract = {Lead halide perovskites have recently been reported to demonstrate an exceptionally high nonlinear (Kerr) refractive index n2 of up to 10−8cm2/W in CH3⁢NH3⁢PbBr3. Other researchers, however, observe different, substantially more conservative numbers. In order to resolve this disagreement, the nonlinear Kerr index of a bulk sample of lead halide perovskite was measured directly by means of an interferometer. This approach has many advantages as compared to the more standard z-scan technique. In particular, this method allows studying the induced changes to the refractive index in a time-resolved manner, thus enabling to separate the different contributions to 𝑛2. The extracted 𝑛2 values for CsPbBr3 and MAPbBr3 at 𝜆≈1µ⁢m are 𝑛2=+2.1×10−14cm2/W and 𝑛2=+6×10−15cm2/W, respectively. Hence, these values are substantially lower than what has been indicated in most of the previous reports, implying the latter one should be regarded with great care.}, author = {Lorenc, Dusan and Zhumekenov, Ayan and Bakr, Osman M. and Alpichshev, Zhanybek}, issn = {2475-9953}, journal = {Physical Review Materials}, number = {8}, publisher = {American Physical Society}, title = {{No extraordinary χ(3) in lead-halide perovskites: Placing an upper bound on Kerr nonlinearity by means of time-resolved interferometry}}, doi = {10.1103/PhysRevMaterials.8.085403}, volume = {8}, year = {2024}, }