433 research outputs found
Aggregation of Votes with Multiple Positions on Each Issue
We consider the problem of aggregating votes cast by a society on a fixed set
of issues, where each member of the society may vote for one of several
positions on each issue, but the combination of votes on the various issues is
restricted to a set of feasible voting patterns. We require the aggregation to
be supportive, i.e. for every issue the corresponding component of
every aggregator on every issue should satisfy . We prove that, in such a set-up, non-dictatorial
aggregation of votes in a society of some size is possible if and only if
either non-dictatorial aggregation is possible in a society of only two members
or a ternary aggregator exists that either on every issue is a majority
operation, i.e. the corresponding component satisfies , or on every issue is a minority operation, i.e.
the corresponding component satisfies We then introduce a notion of uniformly non-dictatorial
aggregator, which is defined to be an aggregator that on every issue, and when
restricted to an arbitrary two-element subset of the votes for that issue,
differs from all projection functions. We first give a characterization of sets
of feasible voting patterns that admit a uniformly non-dictatorial aggregator.
Then making use of Bulatov's dichotomy theorem for conservative constraint
satisfaction problems, we connect social choice theory with combinatorial
complexity by proving that if a set of feasible voting patterns has a
uniformly non-dictatorial aggregator of some arity then the multi-sorted
conservative constraint satisfaction problem on , in the sense introduced by
Bulatov and Jeavons, with each issue representing a sort, is tractable;
otherwise it is NP-complete
On the Computational Complexity of Non-dictatorial Aggregation
We investigate when non-dictatorial aggregation is possible from an
algorithmic perspective, where non-dictatorial aggregation means that the votes
cast by the members of a society can be aggregated in such a way that the
collective outcome is not simply the choices made by a single member of the
society. We consider the setting in which the members of a society take a
position on a fixed collection of issues, where for each issue several
different alternatives are possible, but the combination of choices must belong
to a given set of allowable voting patterns. Such a set is called a
possibility domain if there is an aggregator that is non-dictatorial, operates
separately on each issue, and returns values among those cast by the society on
each issue. We design a polynomial-time algorithm that decides, given a set
of voting patterns, whether or not is a possibility domain. Furthermore, if
is a possibility domain, then the algorithm constructs in polynomial time
such a non-dictatorial aggregator for . We then show that the question of
whether a Boolean domain is a possibility domain is in NLOGSPACE. We also
design a polynomial-time algorithm that decides whether is a uniform
possibility domain, that is, whether admits an aggregator that is
non-dictatorial even when restricted to any two positions for each issue. As in
the case of possibility domains, the algorithm also constructs in polynomial
time a uniform non-dictatorial aggregator, if one exists. Then, we turn our
attention to the case where is given implicitly, either as the set of
assignments satisfying a propositional formula, or as a set of consistent
evaluations of an sequence of propositional formulas. In both cases, we provide
bounds to the complexity of deciding if is a (uniform) possibility domain.Comment: 21 page
Anomalous tunneling of bound pairs in crystal lattices
A novel method of solving scattering problems for bound pairs on a lattice is
developed. Two different break ups of the hamiltonian are employed to calculate
the full Green operator and the wave function of the scattered pair. The
calculation converges exponentially in the number of basis states used to
represent the non-translation invariant part of the Green operator. The method
is general and applicable to a variety of scattering and tunneling problems. As
the first application, the problem of pair tunneling through a weak link on a
one-dimensional lattice is solved. It is found that at momenta close to \pi the
pair tunnels much easier than one particle, with the transmission coefficient
approaching unity. This anomalously high transmission is a consequence of the
existence of a two-body resonant state localized at the weak link.Comment: REVTeX, 5 pages, 4 eps figure
Hyperspherical theory of anisotropic exciton
A new approach to the theory of anisotropic exciton based on Fock
transformation, i.e., on a stereographic projection of the momentum to the unit
4-dimensional (4D) sphere, is developed. Hyperspherical functions are used as a
basis of the perturbation theory. The binding energies, wave functions and
oscillator strengths of elongated as well as flattened excitons are obtained
numerically. It is shown that with an increase of the anisotropy degree the
oscillator strengths are markedly redistributed between optically active and
formerly inactive states, making the latter optically active. An approximate
analytical solution of the anisotropic exciton problem taking into account the
angular momentum conserving terms is obtained. This solution gives the binding
energies of moderately anisotropic exciton with a good accuracy and provides a
useful qualitative description of the energy level evolution.Comment: 23 pages, 8 figure
Shear band dynamics from a mesoscopic modeling of plasticity
The ubiquitous appearance of regions of localized deformation (shear bands)
in different kinds of disordered materials under shear is studied in the
context of a mesoscopic model of plasticity. The model may or may not include
relaxational (aging) effects. In the absence of relaxational effects the model
displays a monotonously increasing dependence of stress on strain-rate, and
stationary shear bands do not occur. However, in start up experiments transient
(although long lived) shear bands occur, that widen without bound in time. I
investigate this transient effect in detail, reproducing and explaining a t^1/2
law for the thickness increase of the shear band that has been obtained in
atomistic numerical simulations. Relaxation produces a negative sloped region
in the stress vs. strain-rate curve that stabilizes the formation of shear
bands of a well defined width, which is a function of strain-rate. Simulations
at very low strain-rates reveal a non-trivial stick-slip dynamics of very thin
shear bands that has relevance in the study of seismic phenomena. In addition,
other non-stationary processes, such as stop-and-go, or strain-rate inversion
situations display a phenomenology that matches very well the results of recent
experimental studies.Comment: 10 pages, 10 figure
Microstructural Shear Localization in Plastic Deformation of Amorphous Solids
The shear-transformation-zone (STZ) theory of plastic deformation predicts
that sufficiently soft, non-crystalline solids are linearly unstable against
forming periodic arrays of microstructural shear bands. A limited nonlinear
analysis indicates that this instability may be the mechanism responsible for
strain softening in both constant-stress and constant-strain-rate experiments.
The analysis presented here pertains only to one-dimensional banding patterns
in two-dimensional systems, and only to very low temperatures. It uses the
rudimentary form of the STZ theory in which there is only a single kind of zone
rather than a distribution of them with a range of transformation rates.
Nevertheless, the results are in qualitative agreement with essential features
of the available experimental data. The nonlinear theory also implies that
harder materials, which do not undergo a microstructural instability, may form
isolated shear bands in weak regions or, perhaps, at points of concentrated
stress.Comment: 32 pages, 6 figure
Bose-Einstein Condensation of Excitons: Reply to Tikhodeev's Criticism
The extended version of our reply to Comment on ``Critical Velocities in
Exciton Superfluidity'' by S. G. Tikhodeev (Phys. Rev. Lett., 84 (2000), 3502
or from http://prl.aps.org/) is presented here. The principal question is
discussed: does the moving exciton-phonon packet contain the coherent
`nucleus', or the exciton-phonon condensate?Comment: 3 pages in LaTe
On Critical Velocities in Exciton Superfluidity
The presence of exciton phonon interactions is shown to play a key role in
the exciton superfluidity. We apply the Landau criterion for an exciton-phonon
condensate moving uniformly at zero temperature. It turns out that there are
essentially two critical velocities in the theory. Within the range of these
velocities the condensate can exist only as a bright soliton. The excitation
spectrum and differential equations for the wave function of this condensate
are derived.Comment: 7 pages, Latex; to be published in Phys.Rev.Lett (1997
Targeting Cullin-RING E3 ubiquitin ligases for drug discovery: Structure, assembly and small-molecule modulation
© The Authors Journal compilation © 2015 Biochemical Society. In the last decade, the ubiquitin-proteasome system has emerged as a valid target for the development of novel therapeutics. E3 ubiquitin ligases are particularly attractive targets because they confer substrate specificity on the ubiquitin system. CRLs [Cullin-RING (really interesting new gene) E3 ubiquitin ligases] draw particular attention, being the largest family of E3s. The CRLs assemble into functional multisubunit complexes using a repertoire of substrate receptors, adaptors, Cullin scaffolds and RING-box proteins. Drug discovery targeting CRLs is growing in importance due to mounting evidence pointing to significant roles of these enzymes in diverse biological processes and human diseases, including cancer, where CRLs and their substrates often function as tumour suppressors or oncogenes. In the present review, we provide an account of the assembly and structure of CRL complexes, and outline the current state of the field in terms of available knowledge of small-molecule inhibitors and modulators of CRL activity. A comprehensive overview of the reported crystal structures of CRL subunits, components and full-size complexes, alone or with bound small molecules and substrate peptides, is included. This information is providing increasing opportunities to aid the rational structure-based design of chemical probes and potential small-molecule therapeutics targeting CRLs
Strain localization in a shear transformation zone model for amorphous solids
We model a sheared disordered solid using the theory of Shear Transformation
Zones (STZs). In this mean-field continuum model the density of zones is
governed by an effective temperature that approaches a steady state value as
energy is dissipated. We compare the STZ model to simulations by Shi, et
al.(Phys. Rev. Lett. 98 185505 2007), finding that the model generates
solutions that fit the data,exhibit strain localization, and capture important
features of the localization process. We show that perturbations to the
effective temperature grow due to an instability in the transient dynamics, but
unstable systems do not always develop shear bands. Nonlinear energy
dissipation processes interact with perturbation growth to determine whether a
material exhibits strain localization. By estimating the effects of these
interactions, we derive a criterion that determines which materials exhibit
shear bands based on the initial conditions alone. We also show that the shear
band width is not set by an inherent diffusion length scale but instead by a
dynamical scale that depends on the imposed strain rate.Comment: 8 figures, references added, typos correcte
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