54,980 research outputs found
On the Usefulness of Predicates
Motivated by the pervasiveness of strong inapproximability results for
Max-CSPs, we introduce a relaxed notion of an approximate solution of a
Max-CSP. In this relaxed version, loosely speaking, the algorithm is allowed to
replace the constraints of an instance by some other (possibly real-valued)
constraints, and then only needs to satisfy as many of the new constraints as
possible.
To be more precise, we introduce the following notion of a predicate
being \emph{useful} for a (real-valued) objective : given an almost
satisfiable Max- instance, there is an algorithm that beats a random
assignment on the corresponding Max- instance applied to the same sets of
literals. The standard notion of a nontrivial approximation algorithm for a
Max-CSP with predicate is exactly the same as saying that is useful for
itself.
We say that is useless if it is not useful for any . This turns out to
be equivalent to the following pseudo-randomness property: given an almost
satisfiable instance of Max- it is hard to find an assignment such that the
induced distribution on -bit strings defined by the instance is not
essentially uniform.
Under the Unique Games Conjecture, we give a complete and simple
characterization of useful Max-CSPs defined by a predicate: such a Max-CSP is
useless if and only if there is a pairwise independent distribution supported
on the satisfying assignments of the predicate. It is natural to also consider
the case when no negations are allowed in the CSP instance, and we derive a
similar complete characterization (under the UGC) there as well.
Finally, we also include some results and examples shedding additional light
on the approximability of certain Max-CSPs
Recommended from our members
Using cellular fitness to map the structure and function of a major facilitator superfamily effluxer.
The major facilitator superfamily (MFS) effluxers are prominent mediators of antimicrobial resistance. The biochemical characterization of MFS proteins is hindered by their complex membrane environment that makes in vitro biochemical analysis challenging. Since the physicochemical properties of proteins drive the fitness of an organism, we posed the question of whether we could reverse that relationship and derive meaningful biochemical parameters for a single protein simply from fitness changes it confers under varying strengths of selection. Here, we present a physiological model that uses cellular fitness as a proxy to predict the biochemical properties of the MFS tetracycline efflux pump, TetB, and a family of single amino acid variants. We determined two lumped biochemical parameters roughly describing Km and Vmax for TetB and variants. Including in vivo protein levels into our model allowed for more specified prediction of pump parameters relating to substrate binding affinity and pumping efficiency for TetB and variants. We further demonstrated the general utility of our model by solely using fitness to assay a library of tet(B) variants and estimate their biochemical properties
Impact of sidewalls on electrical characterization
In this article the impact of sidewalls, formed during reactive ion etching, on the electrical behavior of thin film structures is presented. The presence of sidewalls was experimentally characterized by sheet resistance measurements on Van der Pauw structures. The effect of these sidewalls on the extraction of specific contact resistance from Cross Bridge Kelvin Resistance (CBKR) structures is discussed
Tuning phase-stability and short-range order through Al-doping in (CoCrFeMn)100-xAlx high entropy alloys
For (CoCrFeMn)Al high-entropy alloys, we investigate the
phase evolution with increasing Al-content (0 x 20 at.%). From
first-principles theory, the Al-doping drives the alloy structurally from FCC
to BCC separated by a narrow two-phase region (FCC+BCC), which is well
supported by our experiments. We highlight the effect of Al-doping on the
formation enthalpy and electronic structure of (CoCrFeMn)Al
alloys. As chemical short-range order (SRO) in multicomponent alloys indicates
the nascent local order (and entropy changes), as well as expected
low-temperature ordering behavior, we use thermodynamic linear-response within
density-functional theory to predict SRO and ordering transformation and
temperatures inherent in (CoCrFeMn)Al. The predictions agree
with our present experimental findings, and other reported ones.Comment: 27 pages, 9 figures, 1 tabl
- …