TY - JOUR
AB - Hill's Conjecture states that the crossing number cr(πΎπ) of the complete graph πΎπ in the plane (equivalently, the sphere) is 14βπ2ββπβ12ββπβ22ββπβ32β=π4/64+π(π3) . Moon proved that the expected number of crossings in a spherical drawing in which the points are randomly distributed and joined by geodesics is precisely π4/64+π(π3) , thus matching asymptotically the conjectured value of cr(πΎπ) . Let crπ(πΊ) denote the crossing number of a graph πΊ in the projective plane. Recently, Elkies proved that the expected number of crossings in a naturally defined random projective plane drawing of πΎπ is (π4/8π2)+π(π3) . In analogy with the relation of Moon's result to Hill's conjecture, Elkies asked if limπβββcrπ(πΎπ)/π4=1/8π2 . We construct drawings of πΎπ in the projective plane that disprove this.
AU - Arroyo Guevara, Alan M
AU - Mcquillan, Dan
AU - Richter, R. Bruce
AU - Salazar, Gelasio
AU - Sullivan, Matthew
ID - 9295
JF - Journal of Graph Theory
SN - 0364-9024
TI - Drawings of complete graphs in the projective plane
ER -
TY - JOUR
AB - We establish finite time extinction with probability one for weak solutions of the CauchyβDirichlet problem for the 1D stochastic porous medium equation with Stratonovich transport noise and compactly supported smooth initial datum. Heuristically, this is expected to hold because Brownian motion has average spread rate O(t12) whereas the support of solutions to the deterministic PME grows only with rate O(t1m+1). The rigorous proof relies on a contraction principle up to time-dependent shift for WongβZakai type approximations, the transformation to a deterministic PME with two copies of a Brownian path as the lateral boundary, and techniques from the theory of viscosity solutions.
AU - Hensel, Sebastian
ID - 9307
JF - Stochastics and Partial Differential Equations: Analysis and Computations
SN - 21940401
TI - Finite time extinction for the 1D stochastic porous medium equation with transport noise
ER -
TY - JOUR
AB - Several Ising-type magnetic van der Waals (vdW) materials exhibit stable magnetic ground states. Despite these clear experimental demonstrations, a complete theoretical and microscopic understanding of their magnetic anisotropy is still lacking. In particular, the validity limit of identifying their one-dimensional (1-D) Ising nature has remained uninvestigated in a quantitative way. Here we performed the complete mapping of magnetic anisotropy for a prototypical Ising vdW magnet FePS3 for the first time. Combining torque magnetometry measurements with their magnetostatic model analysis and the relativistic density functional total energy calculations, we successfully constructed the three-dimensional (3-D) mappings of the magnetic anisotropy in terms of magnetic torque and energy. The results not only quantitatively confirm that the easy axis is perpendicular to the ab plane, but also reveal the anisotropies within the ab, ac, and bc planes. Our approach can be applied to the detailed quantitative study of magnetism in vdW materials.
AU - Nauman, Muhammad
AU - Kiem, Do Hoon
AU - Lee, Sungmin
AU - Son, Suhan
AU - Park, J-G
AU - Kang, Woun
AU - Han, Myung Joon
AU - Jo, Youn Jung
ID - 9282
JF - 2D Materials
KW - Mechanical Engineering
KW - General Materials Science
KW - Mechanics of Materials
KW - General Chemistry
KW - Condensed Matter Physics
SN - 2053-1583
TI - Complete mapping of magnetic anisotropy for prototype Ising van der Waals FePS3
ER -
TY - JOUR
AB - Assemblies of actin and its regulators underlie the dynamic morphology of all eukaryotic cells. To understand how actin regulatory proteins work together to generate actin-rich structures such as filopodia, we analyzed the localization of diverse actin regulators within filopodia in Drosophila embryos and in a complementary in vitro system of filopodia-like structures (FLSs). We found that the composition of the regulatory protein complex where actin is incorporated (the filopodial tip complex) is remarkably heterogeneous both in vivo and in vitro. Our data reveal that different pairs of proteins correlate with each other and with actin bundle length, suggesting the presence of functional subcomplexes. This is consistent with a theoretical framework where three or more redundant subcomplexes join the tip complex stochastically, with any two being sufficient to drive filopodia formation. We provide an explanation for the observed heterogeneity and suggest that a mechanism based on multiple components allows stereotypical filopodial dynamics to arise from diverse upstream signaling pathways.
AU - Dobramysl, Ulrich
AU - Jarsch, Iris Katharina
AU - Inoue, Yoshiko
AU - Shimo, Hanae
AU - Richier, Benjamin
AU - Gadsby, Jonathan R.
AU - Mason, Julia
AU - SzaΕapak, Alicja
AU - Ioannou, Pantelis Savvas
AU - Correia, Guilherme Pereira
AU - Walrant, Astrid
AU - Butler, Richard
AU - Hannezo, Edouard B
AU - Simons, Benjamin D.
AU - Gallop, Jennifer L.
ID - 9306
IS - 4
JF - The Journal of Cell Biology
TI - Stochastic combinations of actin regulatory proteins are sufficient to drive filopodia formation
VL - 220
ER -
TY - JOUR
AB - Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run average objective, the decision maker has approximately optimal strategies with finite memory. This implies notably that approximating the long-run value is recursively enumerable, as well as a weak continuity property of the value with respect to the transition function.
AU - Chatterjee, Krishnendu
AU - Saona Urmeneta, Raimundo J
AU - Ziliotto, Bruno
ID - 9311
JF - Mathematics of Operations Research
KW - Management Science and Operations Research
KW - General Mathematics
KW - Computer Science Applications
SN - 0364-765X
TI - Finite-memory strategies in POMDPs with long-run average objectives
ER -