TY - JOUR
AB - This paper presents two algorithms. The first decides the existence of a pointed homotopy between given simplicial maps 𝑓,𝑔:𝑋→𝑌, and the second computes the group [𝛴𝑋,𝑌]∗ of pointed homotopy classes of maps from a suspension; in both cases, the target Y is assumed simply connected. More generally, these algorithms work relative to 𝐴⊆𝑋.
AU - Filakovský, Marek
AU - Vokřínek, Lukas
ID - 6563
JF - Foundations of Computational Mathematics
SN - 16153375
TI - Are two given maps homotopic? An algorithmic viewpoint
VL - 20
ER -
TY - JOUR
AB - We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The method generates a strongly convergent iteration sequence; (b) The method requires, at each iteration, only one projection onto the feasible set and two evaluations of the operator; (c) The method is designed for variational inequality for which the underline operator is monotone and uniformly continuous; (d) The method includes an inertial term. The latter is also shown to speed up the convergence in our numerical results. A comparison with some related methods is given and indicates that the new method is promising.
AU - Shehu, Yekini
AU - Li, Xiao-Huan
AU - Dong, Qiao-Li
ID - 6593
JF - Numerical Algorithms
SN - 1017-1398
TI - An efficient projection-type method for monotone variational inequalities in Hilbert spaces
VL - 84
ER -
TY - JOUR
AB - While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.
AU - Benedikter, Niels P
AU - Nam, Phan Thành
AU - Porta, Marcello
AU - Schlein, Benjamin
AU - Seiringer, Robert
ID - 6649
JF - Communications in Mathematical Physics
SN - 0010-3616
TI - Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime
VL - 374
ER -
TY - JOUR
AB - Nearby grid cells have been observed to express a remarkable degree of long-rangeorder, which is often idealized as extending potentially to infinity. Yet their strict peri-odic firing and ensemble coherence are theoretically possible only in flat environments, much unlike the burrows which rodents usually live in. Are the symmetrical, coherent grid maps inferred in the lab relevant to chart their way in their natural habitat? We consider spheres as simple models of curved environments and waiting for the appropriate experiments to be performed, we use our adaptation model to predict what grid maps would emerge in a network with the same type of recurrent connections, which on the plane produce coherence among the units. We find that on the sphere such connections distort the maps that single grid units would express on their own, and aggregate them into clusters. When remapping to a different spherical environment, units in each cluster maintain only partial coherence, similar to what is observed in disordered materials, such as spin glasses.
AU - Stella, Federico
AU - Urdapilleta, Eugenio
AU - Luo, Yifan
AU - Treves, Alessandro
ID - 6796
IS - 4
JF - Hippocampus
SN - 10509631
TI - Partial coherence and frustration in self-organizing spherical grids
VL - 30
ER -
TY - JOUR
AB - Super-resolution fluorescence microscopy has become an important catalyst for discovery in the life sciences. In STimulated Emission Depletion (STED) microscopy, a pattern of light drives fluorophores from a signal-emitting on-state to a non-signalling off-state. Only emitters residing in a sub-diffraction volume around an intensity minimum are allowed to fluoresce, rendering them distinguishable from the nearby, but dark fluorophores. STED routinely achieves resolution in the few tens of nanometers range in biological samples and is suitable for live imaging. Here, we review the working principle of STED and provide general guidelines for successful STED imaging. The strive for ever higher resolution comes at the cost of increased light burden. We discuss techniques to reduce light exposure and mitigate its detrimental effects on the specimen. These include specialized illumination strategies as well as protecting fluorophores from photobleaching mediated by high-intensity STED light. This opens up the prospect of volumetric imaging in living cells and tissues with diffraction-unlimited resolution in all three spatial dimensions.
AU - Jahr, Wiebke
AU - Velicky, Philipp
AU - Danzl, Johann G
ID - 6808
IS - 3
JF - Methods
SN - 1046-2023
TI - Strategies to maximize performance in STimulated Emission Depletion (STED) nanoscopy of biological specimens
VL - 174
ER -