A Nonexistence Result for Abelian Menon Difference Sets Using Perfect Binary Arrays

A Menon difference set has the parameters (4N2, 2N2-N, N2-N). In the abelian case it is equivalent to a perfect binary array, which is a multi-dimensional matrix with elements ±1 such that all out-of-phase periodic autocorrelation coefficients are zero. Suppose that the abelian group H×K×Zpα contains a Menon difference set, where p is an odd prime, |K|=pα, and pj≡−1 (mod exp (H)) for some j. Using the viewpoint of perfect binary arrays we prove that K must be cyclic. A corollary is that there exists a Menon difference set in the abelian group H×K×Z3α, where exp (H)=2 or 4 and |K|=3α, if and only if K is cyclic

Some Non-Existence Results on Divisible Difference Sets

In this paper, we shall prove several non-existence results for divisible difference sets, using three approaches: (i) character sum arguments similar to the work of Turyn [25] for ordinary difference sets, (ii) involution arguments, and (iii) multipliers in conjunction with results on ordinary difference sets. Among other results, we show that an abelian affine difference set of odd order s (s not a perfect square) in G can exist only if the Sylow 2-subgroup of G is cyclic. We also obtain a non-existence result for non-cyclic (n, n, n, 1) relative difference sets of odd order n

A Note on Intersection Numbers of Difference Sets

We present a condition on the intersection numbers of difference sets which follows from a result of Jungnickel and Pott [3]. We apply this condition to rule out several putative (non-abelian) difference sets and to correct erroneous proofs of Lander [4] for the nonexistence of (352, 27, 2)- and (122, 37, 12)-difference sets

A Note on Intersection Numbers of Difference Sets

We present a condition on the intersection numbers of difference sets which follows from a result of Jungnickel and Pott [3]. We apply this condition to rule out several putative (non-abelian) difference sets and to correct erroneous proofs of Lander [4] for the nonexistence of (352, 27, 2)- and (122, 37, 12)-difference sets

New Constructions of Menon Difference Sets

Menon difference sets have parameters (4N2, 2N2 − N, N2 − N). These have been constructed for N = 2a3b, 0 ⩽ a,b, but the only known constructions in abelian groups require that the Sylow 3-subgroup be elementary abelian (there are some nonabelian examples). This paper provides a construction of difference sets in higher exponent groups, and this provides new examples of perfect binary arrays

Scalability and Total Recall with Fast CoveringLSH

Locality-sensitive hashing (LSH) has emerged as the dominant algorithmic technique for similarity search with strong performance guarantees in high-dimensional spaces. A drawback of traditional LSH schemes is that they may have \emph{false negatives}, i.e., the recall is less than 100\%. This limits the applicability of LSH in settings requiring precise performance guarantees. Building on the recent theoretical "CoveringLSH" construction that eliminates false negatives, we propose a fast and practical covering LSH scheme for Hamming space called \emph{Fast CoveringLSH (fcLSH)}. Inheriting the design benefits of CoveringLSH our method avoids false negatives and always reports all near neighbors. Compared to CoveringLSH we achieve an asymptotic improvement to the hash function computation time from $\mathcal{O}(dL)$ to $\mathcal{O}(d + L\log{L})$, where $d$ is the dimensionality of data and $L$ is the number of hash tables. Our experiments on synthetic and real-world data sets demonstrate that \emph{fcLSH} is comparable (and often superior) to traditional hashing-based approaches for search radius up to 20 in high-dimensional Hamming space.Comment: Short version appears in Proceedings of CIKM 201

Exhaust gas treatment for reducing cold start emissions of a motorcycle engine fuelled with gasoline-ethanol blends

In countries like India, transportation by a two wheeled motorcycle is very common owing to affordable cost, easy handling and traffic congestion. Most of these bikes use single cylinder air cooled four-stroke spark ignition (SI) engines of displacement volume ranging from 100 cm3 to 250 cm3. CO and HC emissions from such engines when started after a minimum stop-time of 12 hours or more (cold-start emissions) are higher than warmed-up emissions. In the present study, a 150 cm3 single cylinder air cooled SI engine was tested for cold start emissions and exhaust gas temperature. Different gasoline-ethanol blends (E0 to E20) were used as fuel expecting better oxidation of HC and CO emissions with additional oxygen present in ethanol. The effect of glow plug assisted exhaust gas ignition (EGI) and use of catalytic converter on cold start emissions were studied separately using the same blends. Results show that with gasoline-ethanol blends, cold start CO and HC emissions were less than that with neat gasoline. And at an ambient temperature of 30±1°C, highest emission reductions were observed with E10. EGI without a catalytic converter had no significant effect on emissions except increasing the exhaust gas temperature. The catalytic converter was found to be active only after 120 seconds in converting cold start CO, HC and NOx. Use of a catalytic converter proves to be a better option than EGI in controlling cold start emissions with neat gasoline or gasoline-ethanol blends