Anonymity in Predicting the Future

Consider an arbitrary set $S$ and an arbitrary function $f : \mathbb{R} \to S$. We think of the domain of $f$ as representing time, and for each $x \in \mathbb{R}$, we think of $f(x)$ as the state of some system at time $x$. Imagine that, at each time $x$, there is an agent who can see $f \upharpoonright (-\infty, x)$ and is trying to guess $f(x)$--in other words, the agent is trying to guess the present state of the system from its past history. In a 2008 paper, Christopher Hardin and Alan Taylor use the axiom of choice to construct a strategy that the agents can use to guarantee that, for every function $f$, all but countably many of them will guess correctly. In a 2013 monograph they introduce the idea of anonymous guessing strategies, in which the agents can see the past but don't know where they are located in time. In this paper we consider a number of variations on anonymity. For instance, what if, in addition to not knowing where they are located in time, agents also do not know the rate at which time is progressing? What if they have no sense of how much time elapses between any two events? We show that in some cases agents can still guess successfully, while in others they perform very poorly.Comment: 12 pages, 1 figur

Lifting of modular forms

The existence and construction of vector-valued modular forms (vvmf) for any arbitrary Fuchsian group $\mathrm{G}$, for any representation $\rho:\mathrm{G} \longrightarrow \mathrm{GL}_{d}(\mathbb{C})$ of finite image can be established by lifting scalar-valued modular forms of the finite index subgroup $Ker(\rho)$ of $\mathrm{G}$. In this article vvmf are explicitly constructed for any admissible multiplier (representation) $\rho$, see Section 3 for the definition of admissible multiplier. In other words, the following question has been partially answered: For which representations $\rho$ of a given $\mathrm{G}$, is there a vvmf with at least one nonzero component

Domain wall dynamics in a single CrO2_2 grain

Recently we have reported on the magnetization dynamics of a single CrO$_2$ grain studied by micro Hall magnetometry (P. Das \textit{et al.}, Appl. Phys. Lett. \textbf{97} 042507, 2010). For the external magnetic field applied along the grain's easy magnetization direction, the magnetization reversal takes place through a series of Barkhausen jumps. Supported by micromagnetic simulations, the ground state of the grain was found to correspond to a flux closure configuration with a single cross-tie domain wall. Here, we report an analysis of the Barkhausen jumps, which were observed in the hysteresis loops for the external field applied along both the easy and hard magnetization directions. We find that the magnetization reversal takes place through only a few configuration paths in the free-energy landscape, pointing to a high purity of the sample. The distinctly different statistics of the Barkhausen jumps for the two field directions is discussed.Comment: JEMS Conference, to appear in J. Phys. Conf. Se

Interface driven magnetoelectric effects in granular CrO2

Antiferromagnetic and magnetoelectric Cr2O3-surfaces strongly affect the electronic properties in half metallic CrO2. We show the presence of a Cr2O3 surface layer on CrO3 grains by high-resolution transmission electron microscopy. The effect of these surface layers is demonstrated by measurements of the temperature variation of the magnetoelectric susceptibility. A major observation is a sign change at about 100 K followed by a monotonic rise as a function of temperature. These electric field induced moments in CrO3 are correlated with the magnetoelectric susceptibility of pure Cr2O3. This study indicates that it is important to take into account the magnetoelectric character of thin surface layers of Cr2O3 in granular CrO2 for better understanding the transport mechanism in this system. The observation of a finite magnetoelectric susceptibility near room temperature may find utility in device applications.Comment: Figure 1 with strongly reduced resolutio

Boundary and Eisenstein cohomology of G2(Z)G_2(\mathbb{Z})

In this article, Eisenstein cohomology of the arithmetic group $G_2(\mathbb{Z})$ with coefficients in any finite dimensional highest weight irreducible representation has been determined. We accomplish this by studying the cohomology of the boundary of the Borel-Serre compactification

Formation of finite antiferromagnetic clusters and the effect of electronic phase separation in Pr{_0.5}Ca{_0.5}Mn{_0.975}Al{_0.025}O{_3}

We report the first experimental evidence of a magnetic phase arising due to the thermal blocking of antiferromagnetic clusters in the weakened charge and orbital ordered system Pr{_0.5}Ca{_0.5}Mn{_0.975}Al{_0.025}O{_3}. The third order susceptibility (\chi_3) is used to differentiate this transition from a spin or cluster glass like freezing mechanism. These clusters are found to be mesoscopic and robust to electronic phase separation which only enriches the antiphase domain walls with holes at the cost of the bulk, without changing the size of these clusters. This implies that Al substitution provides sufficient disorder to quench the length scales of the striped phases.Comment: 4 Post Script Figure

Commensurability and arithmetic equivalence for orthogonal hypergeometric monodromy groups

Invariants are computed of quadratic forms associated to orthogonal hypergeometric groups of degree five. Some commensurabilities are then determined between these groups, and it is established that some thin groups cannot be conjugate to each other

Whale origins as a poster child for macroevolution

This article does not have an abstract

How varying CD4 criteria for treatment initiation was associated with mortality of HIV-patients? A retrospective analysis of electronic health records from Andhra Pradesh, India

Background HIV treatment and care services were scaled up in 2007 in India with objective to increase HIV-care coverage. CD4 count based criteria was mainly used for treatment initiation with increasing threshold in later years. Therefore, this paper aimed to evaluate the survival by varying CD4 criteria for antiretroviral treatment (ART) initiation among of HIV-positive patients, and independent factors associated with the mortality. Methods This retrospective cohort study included 127 949 HIV-positive patients aged ≥15 years, who initiated ART between 2007 and 2013 in Andhra Pradesh state, India. The patient’s demographic and clinical characteristics were extracted from the patient’s health records from electronic Computerized Management Information System Software (CMIS). Incidence of mortality/100 person-years was calculated for CD4 and treatment initiation categories. Kaplan-Meier and multivariable Cox-regression analyses were used to explore the association. Results Median CD4 count was 172 (inter-quartile range (IQR) = 102-240) at the time of treatment initiation, and 19.3% of them had ≤ 100 CD4 count. Incidence of mortality for the period 2007-08 (CD4 ≤ 200 cells/mm3) was 8.5/100 person-years compared to 6.4/100 person-years at risk for the period 2012 onwards (CD4 ≤ 350 cells/mm3). Earlier thresholds for treatment initiation showed higher risk of mortality (2007-08 (CD4 ≤ 200 cells/mm3), adjusted hazard ratio (HR): 1.86, 95% confidence interval (CI): 1.68-2.07; 2009-11 (CD4 ≤ 250 cells/mm3), HR = 1.67, 95% CI = 1.51-1.85) compared to 2012 onwards (CD4 ≤ 350 cells/mm3) criteria for treatment initiation. Conclusions Increasing CD4 threshold for treatment initiation over time was independently associated with lower risk of mortality. More efforts are required to detect and treat early, monitoring of follow-ups, promote health education to improve ART adherence, and provide supportive environment that encourages HIV-infected patients to disclose their HIV status in confidence

Exponential sums in prime fields for modular forms

The main objective of this article is to study the exponential sums associated to Fourier coefficients of modular forms supported at numbers having a fixed set of prime factors. This is achieved by establishing an improvement on Shparlinski's bound for exponential sums attached to certain recurrence sequences over finite fields