The Lambek calculus with iteration: two variants

Formulae of the Lambek calculus are constructed using three binary connectives, multiplication and two divisions. We extend it using a unary connective, positive Kleene iteration. For this new operation, following its natural interpretation, we present two lines of calculi. The first one is a fragment of infinitary action logic and includes an omega-rule for introducing iteration to the antecedent. We also consider a version with infinite (but finitely branching) derivations and prove equivalence of these two versions. In Kleene algebras, this line of calculi corresponds to the *-continuous case. For the second line, we restrict our infinite derivations to cyclic (regular) ones. We show that this system is equivalent to a variant of action logic that corresponds to general residuated Kleene algebras, not necessarily *-continuous. Finally, we show that, in contrast with the case without division operations (considered by Kozen), the first system is strictly stronger than the second one. To prove this, we use a complexity argument. Namely, we show, using methods of Buszkowski and Palka, that the first system is $\Pi_1^0$-hard, and therefore is not recursively enumerable and cannot be described by a calculus with finite derivations

Quantum dimer models and exotic orders

We discuss how quantum dimer models may be used to provide "proofs of principle" for the existence of exotic magnetic phases in quantum spin systems.Comment: 12 pages, 6 figures. Contributed talk at the PITP-Les Houches Summer School on "Quantum Magnetism", June 200

A novel long non-coding natural antisense RNA is a negative regulator of Nos1 gene expression

Long non-coding natural antisense transcripts (NATs) are widespread in eukaryotic species. Although recent studies indicate that long NATs are engaged in the regulation of gene expression, the precise functional roles of the vast majority of them are unknown. Here we report that a long NAT (Mm-antiNos1 RNA) complementary to mRNA encoding the neuronal isoform of nitric oxide synthase (Nos1) is expressed in the mouse brain and is transcribed from the non-template strand of the Nos1 locus. Nos1 produces nitric oxide (NO), a major signaling molecule in the CNS implicated in many important functions including neuronal differentiation and memory formation. We show that the newly discovered NAT negatively regulates Nos1 gene expression. Moreover, our quantitative studies of the temporal expression profiles of Mm-antiNos1 RNA in the mouse brain during embryonic development and postnatal life indicate that it may be involved in the regulation of NO-dependent neurogenesis

Efficient noninteractive certification of RSA moduli and beyond

In many applications, it is important to verify that an RSA public key (N; e) speci es a permutation over the entire space ZN, in order to prevent attacks due to adversarially-generated public keys. We design and implement a simple and e cient noninteractive zero-knowledge protocol (in the random oracle model) for this task. Applications concerned about adversarial key generation can just append our proof to the RSA public key without any other modi cations to existing code or cryptographic libraries. Users need only perform a one-time veri cation of the proof to ensure that raising to the power e is a permutation of the integers modulo N. For typical parameter settings, the proof consists of nine integers modulo N; generating the proof and verifying it both require about nine modular exponentiations. We extend our results beyond RSA keys and also provide e cient noninteractive zero- knowledge proofs for other properties of N, which can be used to certify that N is suitable for the Paillier cryptosystem, is a product of two primes, or is a Blum integer. As compared to the recent work of Auerbach and Poettering (PKC 2018), who provide two-message protocols for similar languages, our protocols are more e cient and do not require interaction, which enables a broader class of applications.https://eprint.iacr.org/2018/057First author draf

Growth dynamics and the evolution of cooperation in microbial populations

Microbes providing public goods are widespread in nature despite running the risk of being exploited by free-riders. However, the precise ecological factors supporting cooperation are still puzzling. Following recent experiments, we consider the role of population growth and the repetitive fragmentation of populations into new colonies mimicking simple microbial life-cycles. Individual-based modeling reveals that demographic fluctuations, which lead to a large variance in the composition of colonies, promote cooperation. Biased by population dynamics these fluctuations result in two qualitatively distinct regimes of robust cooperation under repetitive fragmentation into groups. First, if the level of cooperation exceeds a threshold, cooperators will take over the whole population. Second, cooperators can also emerge from a single mutant leading to a robust coexistence between cooperators and free-riders. We find frequency and size of population bottlenecks, and growth dynamics to be the major ecological factors determining the regimes and thereby the evolutionary pathway towards cooperation.Comment: 26 pages, 6 figure

Gauge and Supersymmetric Invariance of a Boundary Bagger-Lambert-Gustavsson Theory

In this paper we will discuss the effect of a having a boundary on the supersymmetric invariance and gauge invariance of the Bagger-Lambert-Gustavsson (BLG) Theory. We will show that even though the supersymmetry and gauge invariance of the original BLG theory is broken due to the presence of a boundary, it restored by the addition of suitable boundary terms. In fact, to achieve the gauge invariance of this theory, we will have to introduce new boundary degrees of freedom. The boundary theory obeyed by these new boundary degrees of freedom will be shown to be a generalization of the gauged Wess-Zumino-Witten model, with the generators of the Lie algebra replaced by the generators of the Lie 3-algebra. The gauge and supersymmetry variations of the boundary theory will exactly cancel the boundary terms generated by the gauge and supersymmetric variations of the bulk theory.Comment: 15 pages, 0 figures, accepted for publication in JHE

Statistical Signatures of Photon Localization

The realization that electron localization in disordered systems (Anderson localization) is ultimately a wave phenomenon has led to the suggestion that photons could be similarly localized by disorder. This conjecture attracted wide interest because the differences between photons and electrons - in their interactions, spin statistics, and methods of injection and detection - may open a new realm of optical and microwave phenomena, and allow a detailed study of the Anderson localization transition undisturbed by the Coulomb interaction. To date, claims of three-dimensional photon localization have been based on observations of the exponential decay of the electromagnetic wave as it propagates through the disordered medium. But these reports have come under close scrutiny because of the possibility that the decay observed may be due to residual absorption, and because absorption itself may suppress localization. Here we show that the extent of photon localization can be determined by a different approach - measurement of the relative size of fluctuations of certain transmission quantities. The variance of relative fluctuations accurately reflects the extent of localization, even in the presence of absorption. Using this approach, we demonstrate photon localization in both weakly and strongly scattering quasi-one-dimensional dielectric samples and in periodic metallic wire meshes containing metallic scatterers, while ruling it out in three-dimensional mixtures of aluminum spheres.Comment: 5 pages, including 4 figure

An analytic approximation to the Diffusion Coefficient for the periodic Lorentz Gas

An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as a function of the lattice spacing. This approximation is superior to the popular Machta and Zwanzig result and agrees well with a range of numerical estimates.Comment: 13 pages, 4 figure

Deformations of Lifshitz holography

The simplest gravity duals for quantum critical theories with z=2 `Lifshitz' scale invariance admit a marginally relevant deformation. Generic black holes in the bulk describe the field theory with a dynamically generated momentum scale Lambda as well as finite temperature T. We describe the thermodynamics of these black holes in the quantum critical regime where T >> Lambda^2. The deformation changes the asymptotics of the spacetime mildly and leads to intricate UV sensitivities of the theory which we control perturbatively in Lambda^2/T.Comment: 1+27 pages, 12 figure

Increased use of malaria rapid diagnostic tests improves targeting of anti-malarial treatment in rural Tanzania: implications for nationwide rollout of malaria rapid diagnostic tests.

ABSTRACT: BACKGROUND: The World Health Organization recommends parasitological confirmation of all malaria cases. Tanzania is implementing a phased rollout of malaria rapid diagnostic tests (RDTs) for routine use in all levels of care as one strategy to increase parasitological confirmation of malaria diagnosis. This study was carried out to evaluated artemisinin combination therapy (ACT) prescribing patterns in febrile patients with and without uncomplicated malaria in one pre-RDT implementation and one post-RDT implementation area. METHODS: A cross-sectional health facility surveys was conducted during high and low malaria transmission seasons in 2010 in both areas. Clinical information and a reference blood film on all patients presenting for an initial illness consultation were collected. Malaria was defined as a history of fever in the past 48 hours and microscopically confirmed parasitaemia. Routine diagnostic testing was defined as RDT or microscopy ordered by the health worker and performed at the health facility as part of the health worker-patient consultation. Correct diagnostic testing was defined as febrile patient tested with RDT or microscopy. Over-testing was defined as a febrile patient tested with RDT or microscopy. Correct treatment was defined as patient with malaria prescribed ACT. Over-treatment was defined as patient without malaria prescribed ACT. RESULTS: A total of 1,247 febrile patients (627 from pre-implementation area and 620 from post-implementation area) were included in the analysis. In the post-RDT implementation area, 80.9% (95% CI, 68.2-89.3) of patients with malaria received recommended treatment with ACT compared to 70.3% (95% CI, 54.7-82.2) of patients in the pre-RDT implementation area. Correct treatment was significantly higher in the post-implementation area during high transmission season (85.9% (95%CI, 72.0-93.6) compared to 58.3% (95%CI, 39.4-75.1) in pre-implementation area (p=0.01). Over-treatment with ACT of patients without malaria was less common in the post-RDT implementation area (20.9%; 95% CI, 14.7-28.8) compared to the pre-RDT implementation area (45.8%; 95% CI, 37.2-54.6) (p<0.01) in high transmission. The odds of overtreatment was significantly lower in post- RDT area (adjusted Odds Ratio (OR: 95%CI) 0.57(0.36-0.89); and much higher with clinical diagnosis adjusted OR (95%CI) 2.24(1.37-3.67) CONCLUSION: Implementation of RDTs increased use of RDTs for parasitological confirmation and reduced over-treatment with ACT during high malaria transmission season in one area in Tanzania. Continued monitoring of the national RDT rollout will be needed to assess whether these changes in case management practices will be replicated in other areas and sustained over time. Additional measures (such as refresher trainings, closer supervisions, etc) may be needed to improve ACT targeting during low transmission seasons