A number-theoretic approach to homotopy exponents of SU(n)

We use methods of combinatorial number theory to prove that, for each $n>1$ and any prime $p$, some homotopy group $\pi_i(SU(n))$ contains an element of order $p^{n-1+ord_p([n/p]!)}$, where $ord_p(m)$ denotes the largest integer $\alpha$ such that $p^{\alpha}$ divides $m$.Comment: 20 page

Local Polynomial Whittle Estimation of Long-range Dependence

The local Whittle (or Gaussian semiparametric) estimator of long range dependence, proposed by Kunsch (1987) and analyzed by Robinson (1995a), has a relatively slow rate of convergence and a finite sample bias that can be large. In this paper, we generalize the local Whittle estimator to circumvent those problems. Instead of approximating the short-run component of the spectrum, phi(lambda), by a constant in a shrinking neighborhood of frequency zero, we approximate its logarithm by a polynomial. This leads to a "local polynomial Whittle" (LPW) estimator. Following the work of Robinson (1995a), we establish the asymptotic bias, variance, mean-squared error (MSE), and normality of the LPW estimator. We determine the asymptotically MSE-optimal bandwidth, and specify a plug-in selection method for its practical implementation. When phi(lambda) is smooth enough near the origin, we find that the bias of the LPW estimator goes to zero at a faster rate than that of the local Whittle estimator, and its variance is only inflated by a multiplicative constant. In consequence, the rate of convergence of the LPW estimator is faster than that of the local Whittle estimator, given an appropriate choice of the bandwidth m. We show that the LPW estimator attains the optimal rate of convergence for a class of spectra containing those for which varphi(lambda) is smooth of order s > 1 near zero. When phi(lambda) is infinitely smooth near zero, the rate of convergence of the LPW estimator based on a polynomial of high degree is arbitrarily close to n^{-1/2}.Asymptotic bias, asymptotic normality, bias reduction, long memory, minimax rate, optimal bandwidth, Whittle likelihood

Forward-secure hierarchical predicate encryption

Secrecy of decryption keys is an important pre-requisite for security of any encryption scheme and compromised private keys must be immediately replaced. \emph{Forward Security (FS)}, introduced to Public Key Encryption (PKE) by Canetti, Halevi, and Katz (Eurocrypt 2003), reduces damage from compromised keys by guaranteeing confidentiality of messages that were encrypted prior to the compromise event. The FS property was also shown to be achievable in (Hierarchical) Identity-Based Encryption (HIBE) by Yao, Fazio, Dodis, and Lysyanskaya (ACM CCS 2004). Yet, for emerging encryption techniques, offering flexible access control to encrypted data, by means of functional relationships between ciphertexts and decryption keys, FS protection was not known to exist.\smallskip In this paper we introduce FS to the powerful setting of \emph{Hierarchical Predicate Encryption (HPE)}, proposed by Okamoto and Takashima (Asiacrypt 2009). Anticipated applications of FS-HPE schemes can be found in searchable encryption and in fully private communication. Considering the dependencies amongst the concepts, our FS-HPE scheme implies forward-secure flavors of Predicate Encryption and (Hierarchical) Attribute-Based Encryption.\smallskip Our FS-HPE scheme guarantees forward security for plaintexts and for attributes that are hidden in HPE ciphertexts. It further allows delegation of decrypting abilities at any point in time, independent of FS time evolution. It realizes zero-inner-product predicates and is proven adaptively secure under standard assumptions. As the ``cross-product" approach taken in FS-HIBE is not directly applicable to the HPE setting, our construction resorts to techniques that are specific to existing HPE schemes and extends them with what can be seen as a reminiscent of binary tree encryption from FS-PKE

MARKET CONDUCT UNDER GOVERNMENT PRICE INTERVENTION IN THE U.S. DAIRY INDUSTRY

The degree of market power exercised by fluid and manufactured processors in the U.S. dairy industry is estimated. AppelbaumÂ’'s quantity-setting conjectural variation approach is cast into a switching regime framework to account for the two market regimes created by the existence of the dairy price support program: (a) government supported regime (market price is at the support price) and (b) market equilibrium regime (market price is above the support price). The model is also used to test whether government price intervention has a pro-competitive to anti-competitive influence on market conduct.Agricultural and Food Policy,

The predictors to medication adherence among adults with diabetes in the United Arab Emirates.

BackgroundDiabetes is a chronic medical condition and adherence to medication in adults with diabetes is important. Identifying predictors to medication adherence in adults with diabetes would help identify vulnerable patients who are likely to benefit by improving their adherence levels.MethodsWe conducted a cross-sectional study at the Dubai Police Health Centre between February 2015 and November 2015. Questionnaires were used to collect socio-demographic, clinical and disease related variables and the primary measure of outcome was adherence levels as measured by the Morisky Medication Adherence Scale (MMAS-8©). Multivariate logistic regression was carried out to identify predictors to adherence.ResultsFour hundred and forty six patients were interviewed. Mean age 61 year +/- 11. 48.4 % were male. The mean time since diagnosis of diabetes was 3.2 years (Range 1-15 years). Two hundred and eighty eight (64.6 %) patients were considered non-adherent (MMAS-8© adherence score < 6) while 118 (26.5 %) had moderate adherence (MMAS-8© adherence score 6 = <8) and 40 (9.0 %) high adherence (MMAS-8© adherence scores <8) to their medication respectively. The strongest predictor for adherence as predicted by the multi-logistic regression model was the patient's level of education. A technical diploma certificate as compared to a primary school level of education was the strongest predictor of adherence (OR = 66.1 CI: 6.93 to 630.43); p < 0.001). The patient's age was also a predictor of adherence with older patients reporting higher levels of adherence (OR = 1.113 (CI: 1.045 to 1.185; p = 0.001 for every year increase in age). The duration of diabetes was also a predictor of adherence (OR = 1.830 (CI: 1.270 to 2.636; p = 0.001 for every year increase in the duration of diabetes). Other predictors to medication adherence include Insulin use, ethnicity and certain cultural behaviours.ConclusionA number of important predictors to medication adherence in diabetics were identified in this study. Such predictors could help develop policies for improving adherence in diabetics

House Price Changes and Idiosyncratic Risk: The Impact of Property Characteristics

While the average change in house prices is related to changes in fundamentals or perhaps market-wide bubbles, not all houses in a market appreciate at the same rate. The primary focus of our study is to investigate the reasons for these variations in price changes among houses within a market. We draw on two theories for guidance, one related to the optimal search strategy for sellers of atypical dwellings and the other focusing on the bargaining process between a seller and potential buyers. We hypothesize that houses will appreciate at different rates depending on the characteristics of the property and the change in the strength of the housing market. These hypotheses are supported using data from three New Zealand housing markets.Atypicality, Bargaining, Housing Risk, House Price Appreciation, Search Models

Adaptive Local Polynomial Whittle Estimation of Long-range Dependence

The local Whittle (or Gaussian semiparametric) estimator of long range dependence, proposed by Künsch (1987) and analyzed by Robinson (1995a), has a relatively slow rate of convergence and a finite sample bias that can be large. In this paper, we generalize the local Whittle estimator to circumvent these problems. Instead of approximating the short-run component of the spectrum, φ(λ), by a constant in a shrinking neighborhood of frequency zero, we approximate its logarithm by a polynomial. This leads to a “local polynomial Whittle” (LPW) estimator. We specify a data-dependent adaptive procedure that adjusts the degree of the polynomial to the smoothness of φ(λ) at zero and selects the bandwidth. The resulting “adaptive LPW” estimator is shown to achieve the optimal rate of convergence, which depends on the smoothness of φ(λ) at zero, up to a logarithmic factor

House Price Changes and Idiosyncratic Risk: The Impact of Property Characteristics

While the average change in house prices is related to changes in fundamentals or perhaps market-wide bubbles, not all houses in a market appreciate at the same rate.The primary focus of our study is to investigate the reasons for these variations in price changes among houses within a market. We draw on two theories for guidance, one related to the optimal search strategy for sellers of atypical dwellings and the other focusing on the bargaining process between a seller and potential buyers. We hypothesize that houses will appreciate at different rates depending on the characteristics of the property and the change in the strength of the housing market. These hypotheses are supported using data from three New Zealand housing markets.Atypicality; Bargaining; Housing Risk; House Price Appreciation; Search Models