On 1-factorizations of Bipartite Kneser Graphs

It is a challenging open problem to construct an explicit 1-factorization of the bipartite Kneser graph $H(v,t)$, which contains as vertices all $t$-element and $(v-t)$-element subsets of $[v]:=\{1,\ldots,v\}$ and an edge between any two vertices when one is a subset of the other. In this paper, we propose a new framework for designing such 1-factorizations, by which we solve a nontrivial case where $t=2$ and $v$ is an odd prime power. We also revisit two classic constructions for the case $v=2t+1$ --- the \emph{lexical factorization} and \emph{modular factorization}. We provide their simplified definitions and study their inner structures. As a result, an optimal algorithm is designed for computing the lexical factorizations. (An analogous algorithm for the modular factorization is trivial.)Comment: We design the first explicit 1-factorization of H(2,q), where q is a odd prime powe

Quantum fingerprinting

Classical fingerprinting associates with each string a shorter string (its fingerprint), such that, with high probability, any two distinct strings can be distinguished by comparing their fingerprints alone. The fingerprints can be exponentially smaller than the original strings if the parties preparing the fingerprints share a random key, but not if they only have access to uncorrelated random sources. In this paper we show that fingerprints consisting of quantum information can be made exponentially smaller than the original strings without any correlations or entanglement between the parties: we give a scheme where the quantum fingerprints are exponentially shorter than the original strings and we give a test that distinguishes any two unknown quantum fingerprints with high probability. Our scheme implies an exponential quantum/classical gap for the equality problem in the simultaneous message passing model of communication complexity. We optimize several aspects of our scheme.Comment: 8 pages, LaTeX, one figur

Perfect Secrecy Systems Immune to Spoofing Attacks

We present novel perfect secrecy systems that provide immunity to spoofing attacks under equiprobable source probability distributions. On the theoretical side, relying on an existence result for $t$-designs by Teirlinck, our construction method constructively generates systems that can reach an arbitrary high level of security. On the practical side, we obtain, via cyclic difference families, very efficient constructions of new optimal systems that are onefold secure against spoofing. Moreover, we construct, by means of $t$-designs for large values of $t$, the first near-optimal systems that are 5- and 6-fold secure as well as further systems with a feasible number of keys that are 7-fold secure against spoofing. We apply our results furthermore to a recently extended authentication model, where the opponent has access to a verification oracle. We obtain this way novel perfect secrecy systems with immunity to spoofing in the verification oracle model.Comment: 10 pages (double-column); to appear in "International Journal of Information Security

Lower bound for the quantum capacity of a discrete memoryless quantum channel

We generalize the random coding argument of stabilizer codes and derive a lower bound on the quantum capacity of an arbitrary discrete memoryless quantum channel. For the depolarizing channel, our lower bound coincides with that obtained by Bennett et al. We also slightly improve the quantum Gilbert-Varshamov bound for general stabilizer codes, and establish an analogue of the quantum Gilbert-Varshamov bound for linear stabilizer codes. Our proof is restricted to the binary quantum channels, but its extension of to l-adic channels is straightforward.Comment: 16 pages, REVTeX4. To appear in J. Math. Phys. A critical error in fidelity calculation was corrected by using Hamada's result (quant-ph/0112103). In the third version, we simplified formula and derivation of the lower bound by proving p(Gamma)+q(Gamma)=1. In the second version, we added an analogue of the quantum Gilbert-Varshamov bound for linear stabilizer code

The Threat of Capital Drain: A Rationale for Public Banks?

This paper yields a rationale for why subsidized public banks may be desirable from a regional perspective in a financially integrated economy. We present a model with credit rationing and heterogeneous regions in which public banks prevent a capital drain from poorer to richer regions by subsidizing local depositors, for example, through a public guarantee. Under some conditions, cooperative banks can perform the same function without any subsidization; however, they may be crowded out by public banks. We also discuss the impact of the political structure on the emergence of public banks in a political-economy setting and the role of interregional mobility

Negative Price Spikes at Power Markets: The Role of Energy Policy

In Germany, substantial drops in wholesale power prices have become a regular phenomenon. While such price drops have far-reaching implications for the functioning of the power market, their underlying determinants remain poorly understood. To fill this gap, we propose a Markov regime-switching model to investigate low-price events at the European Power Exchange. Our analysis focuses on the role of energy policies that promote renewable energies and have led to significant reductions of nuclear capacities after the Fukushima accident. We find that high electricity infeed from renewable sources increases negative price spike probabilities, while the decommissioning of nuclear plants under the Nuclear Moratorium had an opposing effect. Simulations of market outcomes under different energy policies indicate that reaching ambitious renewable energy targets increases the frequency of low-price events and compromises the financial viability of conventional generation units, while a nuclear phase-out or an increase in storage capacities mitigates these effects.Im deutsch-österreichischen Marktgebiet der Strombörse European Power Exchange (EPEX) kam es in den letzten Jahren zu einem vermehrten Auftreten sehr niedriger und sogar negativer Preise. Obwohl solche negativen Preisspitzen weitreichende Folgen für das Funktionieren des Strommarkts haben, gibt es bislang nur wenige Untersuchungen zu ihren treibenden Ursachen. Um diese Lücke zu füllen, entwickelt dieser Artikel ein Markov Regime Switching-Modell zur Analyse ihres Auftretens an der EPEX. Im Mittelpunkt der Analyse stehen die Effekte einer Förderung erneuerbarer Energien und einer Reduktion von Kapazitäten nuklearer Kraftwerke im Rahmen des Atom-Moratoriums nach dem Unfall in Fukushima. Die Modellergebnisse zeigen auf, dass ein Anstieg von Strom aus erneuerbaren Quellen die Wahrscheinlichkeit von negativen Preisspitzen erhöht, während das Atom-Moratorium einen gegensätzlichen Effekt hatte. Weitere Simulationen von Marktergebnissen unter unterschiedlichen Politik-Szenarien legen nahe, dass das Erreichen ambitionierter Ziele für den Ausbau erneuerbarer Energien das Aufkommen von negativen Preisspitzen weiter fördern und die Rentabilität vieler konventioneller Kraftwerke in Frage stellen würde. Diese Effekte könnten allerdings sowohl durch einen vollständiger Atomausstieg oder einen Ausbau an Speicherkapazitäten abgemildert werden