121 research outputs found
On Complexity of 1-Center in Various Metrics
We consider the classic 1-center problem: Given a set P of n points in a
metric space find the point in P that minimizes the maximum distance to the
other points of P. We study the complexity of this problem in d-dimensional
-metrics and in edit and Ulam metrics over strings of length d. Our
results for the 1-center problem may be classified based on d as follows.
Small d: We provide the first linear-time algorithm for 1-center
problem in fixed-dimensional metrics. On the other hand, assuming the
hitting set conjecture (HSC), we show that when , no
subquadratic algorithm can solve 1-center problem in any of the
-metrics, or in edit or Ulam metrics.
Large d. When , we extend our conditional lower bound
to rule out sub quartic algorithms for 1-center problem in edit metric
(assuming Quantified SETH). On the other hand, we give a
-approximation for 1-center in Ulam metric with running time
.
We also strengthen some of the above lower bounds by allowing approximations
or by reducing the dimension d, but only against a weaker class of algorithms
which list all requisite solutions. Moreover, we extend one of our hardness
results to rule out subquartic algorithms for the well-studied 1-median problem
in the edit metric, where given a set of n strings each of length n, the goal
is to find a string in the set that minimizes the sum of the edit distances to
the rest of the strings in the set
The Power of Uniform Sampling for Coresets
Motivated by practical generalizations of the classic -median and
-means objectives, such as clustering with size constraints, fair
clustering, and Wasserstein barycenter, we introduce a meta-theorem for
designing coresets for constrained-clustering problems. The meta-theorem
reduces the task of coreset construction to one on a bounded number of ring
instances with a much-relaxed additive error. This reduction enables us to
construct coresets using uniform sampling, in contrast to the widely-used
importance sampling, and consequently we can easily handle constrained
objectives. Notably and perhaps surprisingly, this simpler sampling scheme can
yield coresets whose size is independent of , the number of input points.
Our technique yields smaller coresets, and sometimes the first coresets, for
a large number of constrained clustering problems, including capacitated
clustering, fair clustering, Euclidean Wasserstein barycenter, clustering in
minor-excluded graph, and polygon clustering under Fr\'{e}chet and Hausdorff
distance. Finally, our technique yields also smaller coresets for -median in
low-dimensional Euclidean spaces, specifically of size
in and
in
An elasto-visco-plastic model for immortal foams or emulsions
A variety of complex fluids consist in soft, round objects (foams, emulsions,
assemblies of copolymer micelles or of multilamellar vesicles -- also known as
onions). Their dense packing induces a slight deviation from their prefered
circular or spherical shape. As a frustrated assembly of interacting bodies,
such a material evolves from one conformation to another through a succession
of discrete, topological events driven by finite external forces. As a result,
the material exhibits a finite yield threshold. The individual objects usually
evolve spontaneously (colloidal diffusion, object coalescence, molecular
diffusion), and the material properties under low or vanishing stress may alter
with time, a phenomenon known as aging. We neglect such effects to address the
simpler behaviour of (uncommon) immortal fluids: we construct a minimal, fully
tensorial, rheological model, equivalent to the (scalar) Bingham model.
Importantly, the model consistently describes the ability of such soft
materials to deform substantially in the elastic regime (be it compressible or
not) before they undergo (incompressible) plastic creep -- or viscous flow
under even higher stresses.Comment: 69 pages, 29 figure
Characterization of elastomer sliding behavior across silica and polydimethylsiloxane grafted surfaces
Soft Dynamics simulation: 2. Elastic spheres undergoing a T1 process in a viscous fluid
Robust empirical constitutive laws for granular materials in air or in a
viscous fluid have been expressed in terms of timescales based on the dynamics
of a single particle. However, some behaviours such as viscosity bifurcation or
shear localization, observed also in foams, emulsions, and block copolymer
cubic phases, seem to involve other micro-timescales which may be related to
the dynamics of local particle reorganizations. In the present work, we
consider a T1 process as an example of a rearrangement. Using the Soft dynamics
simulation method introduced in the first paper of this series, we describe
theoretically and numerically the motion of four elastic spheres in a viscous
fluid. Hydrodynamic interactions are described at the level of lubrication
(Poiseuille squeezing and Couette shear flow) and the elastic deflection of the
particle surface is modeled as Hertzian. The duration of the simulated T1
process can vary substantially as a consequence of minute changes in the
initial separations, consistently with predictions. For the first time, a
collective behaviour is thus found to depend on another parameter than the
typical volume fraction in particles.Comment: 11 pages - 5 figure
Younger age, higher body mass index and lower adiponectin concentration predict higher serum thromboxane B2 level in aspirin-treated patients with type 2 diabetes: an observational study
CARACTÉRISATION DE L'INTERACTION MANGANÈSE-TRYPSINE PAR SPECTROSCOPIES RMN ET RPE
L'interaction manganèse-trypsine est étudiée par la relaxation magnétique des protons de l'eau liée à l'ion manganèse et par la spectroscopie RPE de cet ion.The manganese-trypsine interaction is studied by observing the magnetic relaxation of protons of water molecules bound to the manganese ion and by using EPR spectroscopy of this ion
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