Space--Time Tradeoffs for Subset Sum: An Improved Worst Case Algorithm

The technique of Schroeppel and Shamir (SICOMP, 1981) has long been the most efficient way to trade space against time for the SUBSET SUM problem. In the random-instance setting, however, improved tradeoffs exist. In particular, the recently discovered dissection method of Dinur et al. (CRYPTO 2012) yields a significantly improved space--time tradeoff curve for instances with strong randomness properties. Our main result is that these strong randomness assumptions can be removed, obtaining the same space--time tradeoffs in the worst case. We also show that for small space usage the dissection algorithm can be almost fully parallelized. Our strategy for dealing with arbitrary instances is to instead inject the randomness into the dissection process itself by working over a carefully selected but random composite modulus, and to introduce explicit space--time controls into the algorithm by means of a "bailout mechanism"

Generalized Fock spaces and the Stirling numbers

The Bargmann-Fock-Segal space plays an important role in mathematical physics, and has been extended into a number of directions. In the present paper we imbed this space into a Gelfand triple. The spaces forming the Fr\'echet part (i.e. the space of test functions) of the triple are characterized both in a geometric way and in terms of the adjoint of multiplication by the complex variable, using the Stirling numbers of the second kind. The dual of the space of test functions has a topological algebra structure, of the kind introduced and studied by the first named author and G. Salomon.Comment: revised versio

Gauge-invariant gluon mass, infrared Abelian dominance and stability of magnetic vacuum

We give an argument for deriving analytically the infrared ``Abelian'' dominance in a gauge invariant way for the Wilson loop average in SU(2) Yang--Mills theory. In other words, we propose a possible mechanism for realizing the dynamical Abelian projection in the SU(2) gauge-invariant manner without breaking color symmetry. This supports validity of the dual superconductivity picture for quark confinement. We also discuss the stability of the vacuum with magnetic condensation as a by-product of this result.Comment: 25 pages, 3 figures (4 eps files); version accepted for publication in Phys.Rev.D; One paragraph is added at each end of sections 3,4 and 5 for comparing the analytical result with the lattice results of my group based on the new formulation, together with the results in the conventional MAG if available. footnote 4 is added, and a reference is added. A number of sentences and phrases are improve

Approximately coloring graphs without long induced paths

It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on $t$ vertices, for fixed $t$. We propose an algorithm that, given a 3-colorable graph without an induced path on $t$ vertices, computes a coloring with $\max\{5,2\lceil{\frac{t-1}{2}}\rceil-2\}$ many colors. If the input graph is triangle-free, we only need $\max\{4,\lceil{\frac{t-1}{2}}\rceil+1\}$ many colors. The running time of our algorithm is $O((3^{t-2}+t^2)m+n)$ if the input graph has $n$ vertices and $m$ edges

Are Political Attacks a Laughing Matter? Three Experiments on Political Humor and the Effectiveness of Negative Campaigning

Research on the effectiveness of negative campaigning offers mixed results. Negative messages can sometimes work to depress candidate evaluations, but they can also backfire against the attacker. In this article, we examine how humor can help mitigate the unintended effects of negative campaigning using data from three experimental studies in the Netherlands and the USA. Our results show that (i) political attacks combined with “other-deprecatory humor” (i.e., jokes against the opponents) are less likely to backfire against the attacker, and can even increase positive evaluations of this latter - especially when the attack is perceived as amusing. At the same time (ii), and contrary to what we expected, humor does not take away the edge of the attack: funny attacks do not work less well against the target than non-funny attacks. All in all, these results suggest that humor can be a good frame for political attacks: it reduces harmful backlash effects against the attacker and they are just as effective as humorless attacks.Amsterdam School of Communication Research (ASCoR

Sparse Kneser graphs are Hamiltonian

For integers k≥1 and n≥2k+1, the Kneser graph K(n,k) is the graph whose vertices are the k-element subsets of {1,…,n} and whose edges connect pairs of subsets that are disjoint. The Kneser graphs of the form K(2k+1,k) are also known as the odd graphs. We settle an old problem due to Meredith, Lloyd, and Biggs from the 1970s, proving that for every k≥3, the odd graph K(2k+1,k) has a Hamilton cycle. This and a known conditional result due to Johnson imply that all Kneser graphs of the form K(2k+2a,k) with k≥3 and a≥0 have a Hamilton cycle. We also prove that K(2k+1,k) has at least 22k−6 distinct Hamilton cycles for k≥6. Our proofs are based on a reduction of the Hamiltonicity problem in the odd graph to the problem of finding a spanning tree in a suitably defined hypergraph on Dyck words

Biotechnological Production of Carotenoids and Their Applications in Food and Pharmaceutical Products

Pigments can be divided into four categories: natural, nature-identical, synthetic, and inorganic colors. Artificial colorants are the most used in food and pharmaceutical industries because of their advantages related to color range, price, resistance to oxygen degradation, and solubility. However, many natural pigments present health-promoting activities that make them an interesting option for human use and consumption. Natural colorants are derived from sources such as plants, insects, and microorganisms. Carotenoids are natural pigments with important biological activities, such as antioxidant and pro-vitamin A activity, that can be either extracted from plants and algae or synthesized by various microorganisms, including bacteria, yeasts, filamentous fungi, and microalgae. Advantages of microbial production include the ability of microorganisms to use a wide variety of low cost substrates, the better control of cultivation, and the minimized production time. After fermentation, carotenoids are usually recovered by cell disruption, solvent extraction, and concentration. Subsequent purification steps are followed depending on the application. The most prominent industrial applications of carotenoids, considering their health benefits, are in the food, feed, and pharmaceutical industries

Travelling on Graphs with Small Highway Dimension

We study the Travelling Salesperson (TSP) and the Steiner Tree problem (STP) in graphs of low highway dimension. This graph parameter was introduced by Abraham et al. [SODA 2010] as a model for transportation networks, on which TSP and STP naturally occur for various applications in logistics. It was previously shown [Feldmann et al. ICALP 2015] that these problems admit a quasi-polynomial time approximation scheme (QPTAS) on graphs of constant highway dimension. We demonstrate that a significant improvement is possible in the special case when the highway dimension is 1, for which we present a fully-polynomial time approximation scheme (FPTAS). We also prove that STP is weakly NP-hard for these restricted graphs. For TSP we show NP-hardness for graphs of highway dimension 6, which answers an open problem posed in [Feldmann et al. ICALP 2015]