2,784 research outputs found
Minimal Envy and Popular Matchings
We study ex-post fairness in the object allocation problem where objects are
valuable and commonly owned. A matching is fair from individual perspective if
it has only inevitable envy towards agents who received most preferred objects
-- minimal envy matching. A matching is fair from social perspective if it is
supported by majority against any other matching -- popular matching.
Surprisingly, the two perspectives give the same outcome: when a popular
matching exists it is equivalent to a minimal envy matching.
We show the equivalence between global and local popularity: a matching is
popular if and only if there does not exist a group of size up to 3 agents that
decides to exchange their objects by majority, keeping the remaining matching
fixed. We algorithmically show that an arbitrary matching is path-connected to
a popular matching where along the path groups of up to 3 agents exchange their
objects by majority. A market where random groups exchange objects by majority
converges to a popular matching given such matching exists.
When popular matching might not exist we define most popular matching as a
matching that is popular among the largest subset of agents. We show that each
minimal envy matching is a most popular matching and propose a polynomial-time
algorithm to find them
Spin crossover: the quantum phase transition induced by high pressure
The relationship is established between the Berry phase and spin crossover in
condensed matter physics induced by high pressure. It is shown that the
geometric phase has topological origin and can be considered as the order
parameter for such transition.Comment: 4 pages, 3 figure
3,5-Bis(4-chlorobenzylidene)-1-methylpiperidin-4-one
In the title molecule, C20H17Cl2NO, the central heterocyclic ring adopts a flattened boat conformation. The dihedral angles between the planar part of this central heterocyclic ring [maximum deviation = 0.004 (1) Å] and the two almost planar side-chain fragments [maximum deviations = 0.015 (1) and 0.019 (1) Å], that include the aromatic ring and bridging atoms, are 18.1 (1) and 18.0 (1)°. In the crystal, pairs of weak intermolecular C—H⋯O hydrogen bonds link molecules into inversion dimers that form stacks along the a axis. The structure is further stabilized by weak intermolecular C—H⋯π interactions involving the benzene rings
Anomalous Josephson effect in semiconducting nanowires as a signature of the topologically nontrivial phase
We study Josephson junctions made of semiconducting nanowires with Rashba
spin-orbit coupling, where superconducting correlations are induced by the
proximity effect. In the presence of a suitably directed magnetic field, the
system displays the anomalous Josephson effect: a nonzero supercurrent in the
absence of a phase bias between two superconductors. We show that this
anomalous current can be increased significantly by tuning the nanowire into
the helical regime. In particular, in a short junction, a large anomalous
current is a signature for topologically nontrivial superconductivity in the
nanowire.Comment: 10 pages, 9 figures; published versio
1-Benzyl-3,5-bis(4-chlorobenzylidene)piperidin-4-one
The title compound, C26H21Cl2NO, crystallizes with two symmetry-independent molecules (A and B) in the asymmetric unit. In both molecules, the central heterocyclic ring adopts a sofa conformation. The dihedral angles between the planar part of this central heterocyclic ring [maximum deviations of 0.011 (1) and 0.036 (1) Å in molecules A and B, respectively] and the two almost planar [maximum deviations of 0.020 (1) and 0.008 (1) Å in A and 0.007 (1) and 0.011 (1) in B] side-chain fragments that include the aromatic ring and bridging atoms are 20.1 (1) and 31.2 (1)° in molecule A, and 26.4 (1) and 19.6 (1)° in molecule B. The dihedral angles between the planar part of the heterocyclic ring and the benzyl substituent are 79.7 (1) and 53.2 (1)° in molecules A and B, respectively. In the crystal, weak intermolecular C—H⋯O hydrogen bonds link the two independent molecules into dimers
The coexistence of superconductivity and ferromagnetism in nano-scale metallic grains
A nano-scale metallic grain in which the single-particle dynamics are chaotic
is described by the so-called universal Hamiltonian. This Hamiltonian includes
a superconducting pairing term and a ferromagnetic exchange term that compete
with each other: pairing correlations favor minimal ground-state spin, while
the exchange interaction favors maximal spin polarization. Of particular
interest is the fluctuation-dominated regime where the bulk pairing gap is
comparable to or smaller than the single-particle mean level spacing and the
Bardeen-Cooper-Schrieffer theory of superconductivity breaks down.
Superconductivity and ferromagnetism can coexist in this regime. We identify
signatures of the competition between superconductivity and ferromagnetism in a
number of quantities: ground-state spin, conductance fluctuations when the
grain is weakly coupled to external leads and the thermodynamic properties of
the grain, such as heat capacity and spin susceptibility.Comment: 13 pages, 13 figures, Proceedings of the Conference on the Frontiers
of Quantum and Mesoscopic Thermodynamics (FQMT11
Mirror Descent and Convex Optimization Problems With Non-Smooth Inequality Constraints
We consider the problem of minimization of a convex function on a simple set
with convex non-smooth inequality constraint and describe first-order methods
to solve such problems in different situations: smooth or non-smooth objective
function; convex or strongly convex objective and constraint; deterministic or
randomized information about the objective and constraint. We hope that it is
convenient for a reader to have all the methods for different settings in one
place. Described methods are based on Mirror Descent algorithm and switching
subgradient scheme. One of our focus is to propose, for the listed different
settings, a Mirror Descent with adaptive stepsizes and adaptive stopping rule.
This means that neither stepsize nor stopping rule require to know the
Lipschitz constant of the objective or constraint. We also construct Mirror
Descent for problems with objective function, which is not Lipschitz
continuous, e.g. is a quadratic function. Besides that, we address the problem
of recovering the solution of the dual problem
Study of High Energy Gamma-Quanta Beyond the Atmosphere
Measurements of primary cosmic radiation gamma quanta from Proton I and II satellite
Many-to-Many Graph Matching: a Continuous Relaxation Approach
Graphs provide an efficient tool for object representation in various
computer vision applications. Once graph-based representations are constructed,
an important question is how to compare graphs. This problem is often
formulated as a graph matching problem where one seeks a mapping between
vertices of two graphs which optimally aligns their structure. In the classical
formulation of graph matching, only one-to-one correspondences between vertices
are considered. However, in many applications, graphs cannot be matched
perfectly and it is more interesting to consider many-to-many correspondences
where clusters of vertices in one graph are matched to clusters of vertices in
the other graph. In this paper, we formulate the many-to-many graph matching
problem as a discrete optimization problem and propose an approximate algorithm
based on a continuous relaxation of the combinatorial problem. We compare our
method with other existing methods on several benchmark computer vision
datasets.Comment: 1
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