The emergence of 4-cycles in polynomial maps over the extended integers

Let $f(x) \in \mathbb{Z}[x]$; for each integer $\alpha$ it is interesting to consider the number of iterates $n_{\alpha}$, if possible, needed to satisfy $f^{n_{\alpha}}(\alpha) = \alpha$. The sets $\{\alpha, f(\alpha), \ldots, f^{n_{\alpha} - 1}(\alpha), \alpha\}$ generated by the iterates of $f$ are called cycles. For $\mathbb{Z}[x]$ it is known that cycles of length 1 and 2 occur, and no others. While much is known for extensions to number fields, we concentrate on extending $\mathbb{Z}$ by adjoining reciprocals of primes. Let $\mathbb{Z}[1/p_1, \ldots, 1/p_n]$ denote $\mathbb{Z}$ extended by adding in the reciprocals of the $n$ primes $p_1, \ldots, p_n$ and all their products and powers with each other and the elements of $\mathbb{Z}$. Interestingly, cycles of length 4, called 4-cycles, emerge for polynomials in $\mathbb{Z}\left[1/p_1, \ldots, 1/p_n\right][x]$ under the appropriate conditions. The problem of finding criteria under which 4-cycles emerge is equivalent to determining how often a sum of four terms is zero, where the terms are $\pm 1$ times a product of elements from the list of $n$ primes. We investigate conditions on sets of primes under which 4-cycles emerge. We characterize when 4-cycles emerge if the set has one or two primes, and (assuming a generalization of the ABC conjecture) find conditions on sets of primes guaranteed not to cause 4-cycles to emerge.Comment: 14 pages, 1 figur

Dynamic polarizabilities and magic wavelengths for dysprosium

We theoretically study dynamic scalar polarizabilities of the ground and select long-lived excited states of dysprosium, a highly magnetic atom recently laser cooled and trapped. We demonstrate that there are a set of magic wavelengths of the unpoarized lattice laser field for each pair of states which includes the ground state and one of these excited states. At these wavelengths, the energy shift due to laser field is the same for both states, which can be useful for resolved sideband cooling on narrow transitions and precision spectroscopy. We present an analytical formula which, near resonances, allows for the determination of approximate values of the magic wavelengths without calculating the dynamic polarizabilities of the excited states.Comment: 6 papers, 3 figure

The impact of devegetated dune fields on North American climate during the late Medieval Climate Anomaly

During the Medieval Climate Anomaly, North America experienced severe droughts and widespread mobilization of dune fields that persisted for decades. We use an atmosphere general circulation model, forced by a tropical Pacific sea surface temperature reconstruction and changes in the land surface consistent with estimates of dune mobilization (conceptualized as partial devegetation), to investigate whether the devegetation could have exacerbated the medieval droughts. Presence of devegetated dunes in the model significantly increases surface temperatures, but has little impact on precipitation or drought severity, as defined by either the Palmer Drought Severity Index or the ratio of precipitation to potential evapotranspiration. Results are similar to recent studies of the 1930s Dust Bowl drought, suggesting bare soil associated with the dunes, in and of itself, is not sufficient to amplify droughts over North America

Atmospheric circulation anomalies during two persistent north american droughts: 1932-1939 and 1948-1957

We use an early twentieth century (1908-1958) atmospheric reanalysis, based on assimilation of surface and sea level pressure observations, to contrast atmospheric circulation during two periods of persistent drought in North America: 1932-1939 (the 'Dust Bowl') and 1948-1957. Primary forcing for both droughts is believed to come from anomalous sea surface temperatures (SSTs): a warm Atlantic and a cool eastern tropical Pacific. For boreal winter (October-March) in the 1950s, a stationary wave pattern originating from the tropical Pacific is present, with positive centers over the north Pacific and north Atlantic ocean basins and a negative center positioned over northwest North America and the tropical/subtropical Pacific. This wave train is largely absent for the 1930s drought; boreal winter height anomalies are organized much more zonally, with positive heights extending across northern North America. For boreal summer (April-September) during the 1930s, a strong upper level ridge is centered over the Great Plains; this feature is absent during the 1950s and appears to be linked to a weakening of the Great Plains low-level jet (GPLLJ). Subsidence anomalies are co-located over the centers of each drought: in the central Great Plains for the 1930s and in a band extending from the southwest to the southeastern United States for the 1950s. The location and intensity of this subsidence during the 1948-1957 drought is a typical response to a cold eastern tropical Pacific, but for 1932-1939 deviates in terms of the expected intensity, location, and spatial extent. Overall, circulation anomalies during the 1950s drought appear consistent with the expected response to the observed SST forcing. This is not the case for the 1930s, implying some other causal factor may be needed to explain the Dust Bowl drought anomalies. In addition to SST forcing, the 1930s were also characterized by massive alterations to the land surface, including regional-scale devegetation from crop failures and intensive wind erosion and dust storms. Incorporation of these land surface factors into a general circulation model greatly improves the simulation of precipitation and subsidence anomalies during this drought, relative to simulations with SST forcing alone. Even with additional forcing from the land surface, however, the model still has difficulty reproducing some of the other circulation anomalies, including weakening of the GPLLJ and strengthening of the upper level ridge during AMJJAS. This may be due to either weaknesses in the model or uncertainties in the boundary condition estimates. Still, analysis of the circulation anomalies supports the conclusion of an earlier paper (Cook et al. in Proc Natl Acad Sci 106:4997, 2009), demonstrating that land degradation factors are consistent with the anomalous nature of the Dust Bowl drought

Research culture: why every lab needs a handbook

A lab handbook is a flexible document that outlines the ethos of a research lab or group. A good handbook will outline the different roles within the lab, explain what is expected of all lab members, provide an overview of the culture the lab aims to create, and describe how the lab supports its members so that they can develop as researchers. Here we describe how we wrote a lab handbook for a large research group, and provide resources to help other labs write their own handbooks

Hamster oocyte membrane potential and ion permeability vary with preantral cumulus cell attachment and developmental stage

BACKGROUND: In vitro maturation of mammalian oocytes is an area of great interest due to its potential application in the treatment of infertility. The morphological and physiological changes that occur during oocyte development are poorly understood, and further studies are needed investigating the physiological changes associated with oocyte maturation. In this study we evaluated the membrane potential and the sodium/potassium permeability ratio of oocytes acutely isolated, and cumulus-oocyte complexes in metaphase II and preantral follicle stages. RESULTS: Intracellular electrical recordings revealed that cumulus-enclosed oocytes have a membrane potential significantly more negative at the preantral follicle stage than at metaphase II stage (-38.4 versus -19.7 mV, p < 0.0005). The membrane potential of the cumulus-free oocytes was not different between the preantral and metaphase II stages. The membrane potential of the cumulus cells forming preantral stage follicles was shown to be significantly different from that of the oocyte within the follicle (-28.6 versus -38.4 mV, p < 0.05). The sodium/potassium permeability measured in cumulus-enclosed oocytes at the preantral stage equaled a mean value of 0.33. The ratio was significantly lower when measured in oocytes denuded of cumulus cells or cumulus-enclosed metaphase II oocytes, 0.76, 0.79, 0.77 respectively (p < 0.001). CONCLUSIONS: These data show a change in the membrane potential and Na(+)/K(+) permeability ratio during ooycte development from the preantral stage oocyte to the metaphase II stage. We have also demonstrated a change in the preantral oocyte membrane potential when surrounding cumulus cells are removed; either due to membrane changes or loss of cumulus cells

Acceleration of energetic particles by large-scale compressible magnetohydrodynamic turbulence

Fast particles diffusing along magnetic field lines in a turbulent plasma can diffuse through and then return to the same eddy many times before the eddy is randomized in the turbulent flow. This leads to an enhancement of particle acceleration by large-scale compressible turbulence relative to previous estimates in which isotropic particle diffusion is assumed.Comment: 13 pages, 3 figures, accepted for publication in Ap

Against All Odds: Students' Interest in, and Perceived Value of, Research and Nonresearch Psychology Subjects

Although research literacy is necessary for the competent delivery of psychological services, many psychology students hold negative attitudes toward research subjects. The current study explored undergraduate students’ perceptions of research subjects relative to nonresearch subjects. A sample of 249 Australian (45.4%) and Singaporean (54.6%) first-year university students (Mage = 21.27, SDage = 5.14, females = 75.9%) indicated their interest in, and perceived value of, 32 psychology subjects (based on title and a short description). They also nominated their most/least interested and valued subject and provided a free-text explanation for their selections. Participants perceived research subjects as significantly less interesting and valuable relative to nonresearch subjects (d values were indicative of a large difference for interest and a small-to-medium different for value). Cluster analysis indicated that research subjects are seen as distinct, forming their own cluster. This finding was supported by thematic analysis of participants’ open-ended responses. Students considered research subjects to be especially difficult, requiring skills they did not possess or enjoy using (e.g., mathematics), and lacking relevance to their future studies and intended careers. The findings suggest that research methods instructors should aim to emphasize the relevance of research to practice in high interest areas (e.g., psychopathology)

Intensification of North American Megadroughts through Surface and Dust Aerosol Forcing

Tree-ring-based reconstructions of the Palmer drought severity index (PDSI) indicate that, during the Medieval Climate Anomaly (MCA), the central plains of North America experienced recurrent periods of drought spanning decades or longer. These megadroughts had exceptional persistence compared to more recent events, but the causes remain uncertain. The authors conducted a suite of general circulation model experiments to test the impact of sea surface temperature (SST) and land surface forcing on the MCA megadroughts over the central plains. The land surface forcing is represented as a set of dune mobilization boundary conditions, derived from available geomorphological evidence and modeled as increased bare soil area and a dust aerosol source (32deg-44degN, 105deg-95degW). In the experiments, cold tropical Pacific SST forcing suppresses precipitation over the central plains but cannot reproduce the overall drying or persistence seen in the PDSI reconstruction. Droughts in the scenario with dust aerosols, however, are amplified and have significantly longer persistence than in other model experiments, more closely matching the reconstructed PDSI. This additional drying occurs because the dust increases the shortwave planetary albedo, reducing energy inputs to the surface and boundary layer. The energy deficit increases atmospheric stability, inhibiting convection and reducing cloud cover and precipitation over the central plains. Results from this study provide the first model-based evidence that dust aerosol forcing and land surface changes could have contributed to the intensity and persistence of the central plains megadroughts, although uncertainties remain in the formulation of the boundary conditions and the future importance of these feedbacks