Distribution testing lower bounds via reductions from communication complexity

We present a new methodology for proving distribution testing lower bounds, establishing a connection between distribution testing and the simultaneous message passing (SMP) communication model. Extending the framework of Blais, Brody, and Matulef (Computational Complexity, 2012), we show a simple way to reduce (private-coin) SMP problems to distribution testing problems. This method allows us to prove new distribution testing lower bounds, as well as to provide simple proofs of known lower bounds. Our main result is concerned with testing identity to a specific distribution p, given as a parameter. In a recent and influential work, Valiant and Valiant (FOCS, 2014) showed that the sample complexity of the aforementioned problem is closely related to the 2/3-quasinorm of p. We obtain alternative bounds on the complexity of this problem in terms of an arguably more intuitive measure and using simpler proofs. More specifically, we prove that the sample complexity is essentially determined by a fundamental operator in the theory of interpolation of Banach spaces, known as Peetre's K-functional. We show that this quantity is closely related to the size of the effective support of p (loosely speaking, the number of supported elements that constitute the vast majority of the mass of p). This result, in turn, stems from an unexpected connection to functional analysis and refined concentration of measure inequalities, which arise naturally in our reduction

An adaptivity hierarchy theorem for property testing

Adaptivity is known to play a crucial role in property testing. In particular, there exist properties for which there is an exponential gap between the power of adaptive testing algorithms, wherein each query may be determined by the answers received to prior queries, and their non-adaptive counterparts, in which all queries are independent of answers obtained from previous queries. In this work, we investigate the role of adaptivity in property testing at a finer level. We first quantify the degree of adaptivity of a testing algorithm by considering the number of "rounds of adaptivity" it uses. More accurately, we say that a tester is k-(round) adaptive if it makes queries in k+1 rounds, where the queries in the i'th round may depend on the answers obtained in the previous i-1 rounds. Then, we ask the following question: Does the power of testing algorithms smoothly grow with the number of rounds of adaptivity? We provide a positive answer to the foregoing question by proving an adaptivity hierarchy theorem for property testing. Specifically, our main result shows that for every n in N and 0 <= k <= n^{0.99} there exists a property Pi_{n,k} of functions for which (1) there exists a k-adaptive tester for Pi_{n,k} with query complexity tilde O(k), yet (2) any (k-1)-adaptive tester for Pi_{n,k} must make Omega(n) queries. In addition, we show that such a qualitative adaptivity hierarchy can be witnessed for testing natural properties of graphs

An adaptivity hierarchy theorem for property testing

Adaptivity is known to play a crucial role in property testing. In particular, there exist properties for which there is an exponential gap between the power of adaptive testing algorithms, wherein each query may be determined by the answers received to prior queries, and their non-adaptive counterparts, in which all queries are independent of answers obtained from previous queries. In this work, we investigate the role of adaptivity in property testing at a finer level. We first quantify the degree of adaptivity of a testing algorithm by considering the number of "rounds of adaptivity" it uses. More accurately, we say that a tester is k-(round) adaptive if it makes queries in k+1 rounds, where the queries in the i'th round may depend on the answers obtained in the previous i-1 rounds. Then, we ask the following question: Does the power of testing algorithms smoothly grow with the number of rounds of adaptivity? We provide a positive answer to the foregoing question by proving an adaptivity hierarchy theorem for property testing. Specifically, our main result shows that for every n in N and 0 <= k <= n^{0.99} there exists a property Pi_{n,k} of functions for which (1) there exists a k-adaptive tester for Pi_{n,k} with query complexity tilde O(k), yet (2) any (k-1)-adaptive tester for Pi_{n,k} must make Omega(n) queries. In addition, we show that such a qualitative adaptivity hierarchy can be witnessed for testing natural properties of graphs

Renormalization group approach to vibrational energy transfer in protein

Renormalization group method is applied to the study of vibrational energy transfer in protein molecule. An effective Lagrangian and associated equations of motion to describe the resonant energy transfer are analyzed in terms of the first-order perturbative renormalization group theory that has been developed as a unified tool for global asymptotic analysis. After the elimination of singular terms associated with the Fermi resonance, amplitude equations to describe the slow dynamics of vibrational energy transfer are derived, which recover the result obtained by a technique developed in nonlinear optics [S.J. Lade, Y.S. Kivshar, Phys. Lett. A 372 (2008) 1077].Comment: 11 page

d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories

We study three dimensional O(N)_k and U(N)_k Chern-Simons theories coupled to a scalar field in the fundamental representation, in the large N limit. For infinite k this is just the singlet sector of the O(N) (U(N)) vector model, which is conjectured to be dual to Vasiliev's higher spin gravity theory on AdS_4. For large k and N we obtain a parity-breaking deformation of this theory, controlled by the 't Hooft coupling lambda = 4 \pi N / k. For infinite N we argue (and show explicitly at two-loop order) that the theories with finite lambda are conformally invariant, and also have an exactly marginal (\phi^2)^3 deformation. For large but finite N and small 't Hooft coupling lambda, we show that there is still a line of fixed points parameterized by the 't Hooft coupling lambda. We show that, at infinite N, the interacting non-parity-invariant theory with finite lambda has the same spectrum of primary operators as the free theory, consisting of an infinite tower of conserved higher-spin currents and a scalar operator with scaling dimension \Delta=1; however, the correlation functions of these operators do depend on lambda. Our results suggest that there should exist a family of higher spin gravity theories, parameterized by lambda, and continuously connected to Vasiliev's theory. For finite N the higher spin currents are not conserved.Comment: 34 pages, 29 figures. v2: added reference

Pyrite nanocrystals: shape-controlled synthesis and tunable optical properties via reversible self-assembly

Nanocrystals from non-toxic, earth abundant materials have recently received great interest for their potential large-scale application in photovoltaics and photocatalysis. Here, we report for the first time on the shape-controlled and scalable synthesis of phase-pure pyrite (FeS2) nanocrystals employing the simple, inexpensive, thermal reaction of iron–oleylamine complexes with sulfur in oleylamine. Either dendritic nanocrystals (nanodendrites) or nanocubes are obtained by adjusting the iron-oleylamine concentration and thereby controlling the nucleus concentration and kinetics of the nanocrystal growth. Pyrite nanodendrites are reversibly assembled by washing with toluene and redispersed by adding the ligand oleylamine. The assembly–redispersion-process is accompanied by an increased absorption in the red/near-infrared spectral region for the aggregated state. This increased low-energy absorption is due to interactions between the closed-packed nanocrystals. High-concentration nanodendrite dispersions are used to prepare pyrite thin films with strong broadband extinction in the visible and near-infrared. These films are attractive candidates for light harvesting in all inorganic solar cells based on earth abundant, non-toxic materials as well as for photocatalytic applications

cAMP Response Element-Binding Protein Deficiency Allows for Increased Neurogenesis and a Rapid Onset of Antidepressant Response

cAMP response element-binding protein (CREB) has been implicated in the molecular and cellular mechanisms of chronic antidepressant (AD) treatment, although its role in the behavioral response is unclear. CREB-deficient (CREBαΔ mutant) mice demonstrate an antidepressant phenotype in the tail suspension test (TST) and forced-swim test. Here, we show that, at baseline, CREBαΔ mutant mice exhibited increased hippocampal cell proliferation and neurogenesis compared with wild-type (WT) controls, effects similar to those observed in WT mice after chronic desipramine (DMI) administration. Neurogenesis was not further augmented by chronic DMI treatment in CREBαΔ mutant mice. Serotonin depletion decreased neurogenesis in CREBαΔ mutant mice toWTlevels, which correlated with a reversal of the antidepressant phenotype in the TST. This effect was specific for the reversal of the antidepressant phenotype in these mice, because serotonin depletion did not alter a baseline anxiety-like behavior in CREB mutant mice. The response to chronic AD treatment in the novelty-induced hypophagia (NIH) test may rely on neurogenesis. Therefore, we used this paradigm to evaluate chronic AD treatment in CREB mutant mice to determine whether the increased neurogenesis in these mice alters their response in the NIH paradigm. Whereas both WT and CREBαΔ mutant mice responded to chronic AD treatment in the NIH paradigm, only CREBαΔ mutant mice responded to acute AD treatment. However, in the elevated zero maze, DMI did not reverse anxiety behavior in mutant mice. Together, these data show that increased hippocampal neurogenesis allows for an antidepressant phenotype as well as a rapid onset of behavioral responses to AD treatment

The Higher Spin/Vector Model Duality

This paper is mainly a review of the dualities between Vasiliev's higher spin gauge theories in AdS4 and three dimensional large N vector models, with focus on the holographic calculation of correlation functions of higher spin currents. We also present some new results in the computation of parity odd structures in the three point functions in parity violating Vasiliev theories.Comment: 55 pages, 1 figure. Contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasiliev. v2: references adde

Short-term efficacy of physical interventions in osteoarthritic knee pain. A systematic review and meta-analysis of randomised placebo-controlled trials.

BACKGROUND: Treatment efficacy of physical agents in osteoarthritis of the knee (OAK) pain has been largely unknown, and this systematic review was aimed at assessing their short-term efficacies for pain relief. METHODS: Systematic review with meta-analysis of efficacy within 1-4 weeks and at follow up at 1-12 weeks after the end of treatment. RESULTS: 36 randomised placebo-controlled trials (RCTs) were identified with 2434 patients where 1391 patients received active treatment. 33 trials satisfied three or more out of five methodological criteria (Jadad scale). The patient sample had a mean age of 65.1 years and mean baseline pain of 62.9 mm on a 100 mm visual analogue scale (VAS). Within 4 weeks of the commencement of treatment manual acupuncture, static magnets and ultrasound therapies did not offer statistically significant short-term pain relief over placebo. Pulsed electromagnetic fields offered a small reduction in pain of 6.9 mm [95% CI: 2.2 to 11.6] (n = 487). Transcutaneous electrical nerve stimulation (TENS, including interferential currents), electro-acupuncture (EA) and low level laser therapy (LLLT) offered clinically relevant pain relieving effects of 18.8 mm [95% CI: 9.6 to 28.1] (n = 414), 21.9 mm [95% CI: 17.3 to 26.5] (n = 73) and 17.7 mm [95% CI: 8.1 to 27.3] (n = 343) on VAS respectively versus placebo control. In a subgroup analysis of trials with assumed optimal doses, short-term efficacy increased to 22.2 mm [95% CI: 18.1 to 26.3] for TENS, and 24.2 mm [95% CI: 17.3 to 31.3] for LLLT on VAS. Follow-up data up to 12 weeks were sparse, but positive effects seemed to persist for at least 4 weeks after the course of LLLT, EA and TENS treatment was stopped. CONCLUSION: TENS, EA and LLLT administered with optimal doses in an intensive 2-4 week treatment regimen, seem to offer clinically relevant short-term pain relief for OAK