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 $P$ being \emph{useful} for a (real-valued) objective $Q$: given an almost satisfiable Max-$P$ instance, there is an algorithm that beats a random assignment on the corresponding Max-$Q$ instance applied to the same sets of literals. The standard notion of a nontrivial approximation algorithm for a Max-CSP with predicate $P$ is exactly the same as saying that $P$ is useful for $P$ itself. We say that $P$ is useless if it is not useful for any $Q$. This turns out to be equivalent to the following pseudo-randomness property: given an almost satisfiable instance of Max-$P$ it is hard to find an assignment such that the induced distribution on $k$-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

Prospects and Challenges of Compressed Stabilized Laterite Bricks in Enhancing Sustainable Housing Development in Nigeria

Sustaining housing development especially to the medium/low-income group of the society has become a huge challenge particularly because of the huge capital outlay required to do so. Thus, acquisition of indigenous building materials by way of Compressed Stabilized Laterite Bricks (CSLBs) has been suggested as a way out. This paper evaluated CSLBs as a building material for sustainable housing construction. The study focused primarily on evaluating its physical properties as a building material as well as a measure of its level of acceptability for housing construction among the populace. The study was carried out in four local governments namely; Ogbomoso North, Ibadan Southwest, (in Oyo State) Ado-Odo Ota, (Ogun State) and Agege Local Govenment in Lagos State, Nigeria. The methodology adopted was survey method which involved the administration of 600 questionnaires on randomly selected household heads out of which 551 responded. The data obtained was analyzed using various statistical tools. The result showed that there is apathy towards acceptability and use of CSLBs for housing construction due to lack of knowledge about its physical properties. It was also found out that non-availability of CSLBs in the open market was a major determinant of the apathy.The paper concluded that to ensure sustainable housing development via CSLBs, there must be continuous sensitization of the populace by stakeholders through construction of model houses with CSLBs. More researches on fabrication and production of the CSLBs making machines so as to make it more readily accessible should also be funded

Conformations of Randomly Linked Polymers

We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N; its mean squared end to end distance growing as r^2 ~ M/N. A possible collapse transition (to a region of order unity) is related to percolation in a one dimensional model with long--ranged connections. A directed version of the model is also solved exactly. Based on these results, we conjecture that the typical size of a self-avoiding polymer is reduced by the links to R > (N/M)^(nu). The number of links needed to collapse a polymer in three dimensions thus scales as N^(phi), with (phi) > 0.43.Comment: 6 pages, 3 Postscript figures, LaTe

Beating the random assignment on constraint satisfaction problems of bounded degree

We show that for any odd $k$ and any instance of the Max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a $\frac{1}{2} + \Omega(1/\sqrt{D})$ fraction of constraints, where $D$ is a bound on the number of constraints that each variable occurs in. This improves both qualitatively and quantitatively on the recent work of Farhi, Goldstone, and Gutmann (2014), which gave a \emph{quantum} algorithm to find an assignment satisfying a $\frac{1}{2} + \Omega(D^{-3/4})$ fraction of the equations. For arbitrary constraint satisfaction problems, we give a similar result for "triangle-free" instances; i.e., an efficient algorithm that finds an assignment satisfying at least a $\mu + \Omega(1/\sqrt{D})$ fraction of constraints, where $\mu$ is the fraction that would be satisfied by a uniformly random assignment.Comment: 14 pages, 1 figur

Magnetoresistance Induced by Rare Strong Scatterers in a High Mobility 2DEG

We observe a strong negative magnetoresistance at non-quantizing magnetic fields in a high-mobility two-dimensional electron gas (2DEG). This strong negative magnetoresistance consists of a narrow peak around zero magnetic field and a huge magnetoresistance at larger fields. The peak shows parabolic magnetic field dependence and is attributed to the interplay of smooth disorder and rare strong scatterers. We identify the rare strong scatterers as macroscopic defects in the material and determine their density from the peak curvature.Comment: 5 pages, 4 figure

Current and voltage based bit errors and their combined mitigation for the Kirchhoff-law-Johnson-noise secure key exchange

We classify and analyze bit errors in the current measurement mode of the Kirchhoff-law-Johnson-noise (KLJN) key distribution. The error probability decays exponentially with increasing bit exchange period and fixed bandwidth, which is similar to the error probability decay in the voltage measurement mode. We also analyze the combination of voltage and current modes for error removal. In this combination method, the error probability is still an exponential function that decays with the duration of the bit exchange period, but it has superior fidelity to the former schemes.Comment: 9 pages, accepted for publication in Journal of Computational Electronic

A Characterization of Approximation Resistance for Even kk-Partite CSPs

A constraint satisfaction problem (CSP) is said to be \emph{approximation resistant} if it is hard to approximate better than the trivial algorithm which picks a uniformly random assignment. Assuming the Unique Games Conjecture, we give a characterization of approximation resistance for $k$-partite CSPs defined by an even predicate