L\'evy-Schr\"odinger wave packets

We analyze the time--dependent solutions of the pseudo--differential L\'evy--Schr\"odinger wave equation in the free case, and we compare them with the associated L\'evy processes. We list the principal laws used to describe the time evolutions of both the L\'evy process densities, and the L\'evy--Schr\"odinger wave packets. To have self--adjoint generators and unitary evolutions we will consider only absolutely continuous, infinitely divisible L\'evy noises with laws symmetric under change of sign of the independent variable. We then show several examples of the characteristic behavior of the L\'evy--Schr\"odinger wave packets, and in particular of the bi-modality arising in their evolutions: a feature at variance with the typical diffusive uni--modality of both the L\'evy process densities, and the usual Schr\"odinger wave functions.Comment: 41 pages, 13 figures; paper substantially shortened, while keeping intact examples and results; changed format from "report" to "article"; eliminated Appendices B, C, F (old names); shifted Chapters 4 and 5 (old numbers) from text to Appendices C, D (new names); introduced connection between Relativistic q.m. laws and Generalized Hyperbolic law

Mixtures in non stable Levy processes

We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that -- at least for one particular type of Student processes suggested by recent empirical results, and for integral times -- the distribution of the process is a mixture of other types of Student distributions, randomized by means of a new probability distribution. The mixture is such that along the time the asymptotic behavior of the probability density functions always coincide with that of the generating Student law. We put forward the conjecture that this can be a general feature of the Student processes. We finally analyze the Ornstein--Uhlenbeck process driven by our Levy noises and show a few simulation of it.Comment: 28 pages, 3 figures, to be published in J. Phys. A: Math. Ge

Stochastic Reaction-diffusion Equations Driven by Jump Processes

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.Comment: See journal reference for teh final published versio

Adaptively Secure Garbling with Near Optimal Online Complexity

We construct an adaptively secure garbling scheme with an online communication complexity of $n+m+\mathsf{poly}(\log |C|, \sec)$ where $C: \{0,1\}^n \rightarrow \{0,1\}^{m}$ is the circuit being garbled, and $\sec$ is the security parameter. The security of our scheme can be based on (polynomial hardness of) the Computational Diffie-Hellman (CDH) assumption, or the Factoring assumption or the Learning with Errors assumption. This is nearly the best achievable in the standard model (i.e., without random oracles) as the online communication complexity must be larger than both $n$ and $m$. The online computational complexity of our scheme is $O(n+m)+\mathsf{poly}(\log |C|, \sec)$. Previously known standard model adaptively secure garbling schemes had asymptotically worse online cost or relied on exponentially hard computational assumptions

Deweyan tools for inquiry and the epistemological context of critical pedagogy

This article develops the notion of resistance as articulated in the literature of critical pedagogy as being both culturally sponsored and cognitively manifested. To do so, the authors draw upon John Dewey\u27s conception of tools for inquiry. Dewey provides a way to conceptualize student resistance not as a form of willful disputation, but instead as a function of socialization into cultural models of thought that actively truncate inquiry. In other words, resistance can be construed as the cognitive and emotive dimensions of the ongoing failure of institutions to provide ideas that help individuals both recognize social problems and imagine possible solutions. Focusing on Dewey\u27s epistemological framework, specifically tools for inquiry, provides a way to grasp this problem. It also affords some innovative solutions; for instance, it helps conceive of possible links between the regular curriculum and the study of specific social justice issues, a relationship that is often under-examined. The aims of critical pedagogy depend upon students developing dexterity with the conceptual tools they use to make meaning of the evidence they confront; these are background skills that the regular curriculum can be made to serve even outside social justice-focused curricula. Furthermore, the article concludes that because such inquiry involves the exploration and potential revision of students\u27 world-ordering beliefs, developing flexibility in how one thinks may be better achieved within academic subjects and topics that are not so intimately connected to students\u27 current social lives, especially where students may be directly implicated

Adaptively Secure Garbling Schemes for Parallel Computations

We construct the first adaptively secure garbling scheme based on standard public-key assumptions for garbling a circuit $C: \{0, 1\}^n \mapsto \{0, 1\}^m$ that simultaneously achieves a near-optimal online complexity $n + m + \textrm{poly}(\lambda, \log |C|)$ (where $\lambda$ is the security parameter) and \emph{preserves the parallel efficiency} for evaluating the garbled circuit; namely, if the depth of $C$ is $d$, then the garbled circuit can be evaluated in parallel time $d \cdot \textrm{poly}(\log|C|, \lambda)$. In particular, our construction improves over the recent seminal work of Garg et al. (Eurocrypt 2018), which constructs the first adaptively secure garbling scheme with a near-optimal online complexity under the same assumptions, but the garbled circuit can only be evaluated gate by gate in a sequential manner. Our construction combines their novel idea of linearization with several new ideas to achieve parallel efficiency without compromising online complexity. We take one step further to construct the first adaptively secure garbling scheme for parallel RAM (PRAM) programs under standard assumptions that preserves the parallel efficiency. Previous such constructions we are aware of is from strong assumptions like indistinguishability obfuscation. Our construction is based on the work of Garg et al. (Crypto 2018) for adaptively secure garbled RAM, but again introduces several new ideas to handle parallel RAM computation, which may be of independent interests. As an application, this yields the first constant round secure computation protocol for persistent PRAM programs in the malicious settings from standard assumptions

The solution to the Tullock rent-seeking game when R > 2: mixed-strategy equilibria and mean dissipation rates

In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium exists when R>2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete, and show that full rent dissipation occurs when the strategy space is continuous. Our results are shown to be consistent with recent experimental evidence on the dissipation of rents. An earlier version of this paper circulated under the title, No, Virginia, There is No Overdissipation of Rents. We are grateful to Dave Furth and Frans van Winden for stimulating conversations, and for comments provided by workshop participants from the CORE-ULB-KUL IUAP project, Purdue University, Pennsylvania State University, Rijksuniversiteit Limburg, and Washington State University. We also thank Max van de Sande Bakhuyzen and Ben Heijdra for useful discussions, and Geert Gielens for computational assistance. An earlier version of the paper was presented at the ESEM 1992 in Brussels and the Mid-West Mathematical Economics Conference in Pittsburgh. All three authors would like to thank CentER for its hospitality during the formative stages of the paper. The second author has also benefited from the financial support of the Katholieke Universitieit Leuven and the Jay N. Ross Young Faculty Scholar Award at Purdue University. The third author benefitted from visiting IGIER where part of the paper was written. The third author also benefitted from grant IUAP 26 of the Belgian Government

Antimalarial Therapy Selection for Quinolone Resistance among Escherichia coli in the Absence of Quinolone Exposure, in Tropical South America

BACKGROUND: Bacterial resistance to antibiotics is thought to develop only in the presence of antibiotic pressure. Here we show evidence to suggest that fluoroquinolone resistance in Escherichia coli has developed in the absence of fluoroquinolone use. METHODS: Over 4 years, outreach clinic attendees in one moderately remote and five very remote villages in rural Guyana were surveyed for the presence of rectal carriage of ciprofloxacin-resistant gram-negative bacilli (GNB). Drinking water was tested for the presence of resistant GNB by culture, and the presence of antibacterial agents and chloroquine by HPLC. The development of ciprofloxacin resistance in E. coli was examined after serial exposure to chloroquine. Patient and laboratory isolates of E. coli resistant to ciprofloxacin were assessed by PCR-sequencing for quinolone-resistance-determining-region (QRDR) mutations. RESULTS: In the very remote villages, 4.8% of patients carried ciprofloxacin-resistant E. coli with QRDR mutations despite no local availability of quinolones. However, there had been extensive local use of chloroquine, with higher prevalence of resistance seen in the villages shortly after a Plasmodium vivax epidemic (p<0.01). Antibacterial agents were not found in the drinking water, but chloroquine was demonstrated to be present. Chloroquine was found to inhibit the growth of E. coli in vitro. Replica plating demonstrated that 2-step QRDR mutations could be induced in E. coli in response to chloroquine. CONCLUSIONS: In these remote communities, the heavy use of chloroquine to treat malaria likely selected for ciprofloxacin resistance in E. coli. This may be an important public health problem in malarious areas