Lifetime risk and projected population prevalence of diabetes

Aims/hypothesis  With incidence rates for diabetes increasing rapidly worldwide, estimates of the magnitude of the impact on population health are required. We aimed to estimate the lifetime risk of diabetes, the number of years lived free of, and the number of years lived with diabetes for the Australian adult population from the year 2000, and to project prevalence of diabetes to the year 2025. Methods  Multi-state life-tables were constructed to simulate the progress of a cohort of 25-year-old Australians. National mortality rates were combined with incidence rates of diabetes and the RR of mortality in people with diabetes derived from the Australian Diabetes, Obesity and Lifestyle study (a national, population-based study of 11,247 adults aged ≥25 years). Results  If the rates of mortality and diabetes incidence observed over the period 2000–2005 continue, 38.0% (95% uncertainty interval 36.6–38.9) of 25-year-olds would be expected to develop diabetes at some time throughout their life. On average, a 25-year-old Australian will live a further 56 years, 48 of these free of diabetes. On average, a 45-year-old person with diabetes can expect to live 6 years less than a person free of diabetes. The prevalence of diabetes is projected to rise from 7.6% in 2000 to 11.4% by 2025. Conclusions/interpretation  If we maintain current diabetes incidence rates, more than a third of individuals will develop diabetes within their lifetime and in Australia there will an additional 1 million cases of diabetes by the year 2025.     

On randomly changing conformity bias in cultural transmission

Humans and nonhuman animals display conformist as well as anticonformist biases in cultural transmission. Whereas many previous mathematical models have incorporated constant conformity coefficients, empirical research suggests that the extent of (anti)conformity in populations can change over time. We incorporate stochastic time-varying conformity coefficients into a widely used conformity model, which assumes a fixed number n of “role models” sampled by each individual. We also allow the number of role models to vary over time (nt). Under anticonformity, nonconvergence can occur in deterministic and stochastic models with different parameter values. Even if strong anticonformity may occur, if conformity or random copying (i.e., neither conformity nor anticonformity) is expected, there is convergence to one of the three equilibria seen in previous deterministic models of conformity. Moreover, this result is robust to stochastic variation in nt. However, dynamic properties of these equilibria may be different from those in deterministic models. For example, with random conformity coefficients, all equilibria can be stochastically locally stable simultaneously. Finally, we study the effect of randomly changing weak selection. Allowing the level of conformity, the number of role models, and selection to vary stochastically may produce a more realistic representation of the wide range of group-level properties that can emerge under (anti)conformist biases. This promises to make interpretation of the effect of conformity on differences between populations, for example those connected by migration, rather difficult. Future research incorporating finite population sizes and migration would contribute added realism to these models.

Cavalli-Sforza and Feldman (1) studied the finite population dynamics of a trait whose transmission from one generation to the next depended on the mean value of that trait in the population. This “group transmission” constrained the within-group variability but could lead to increasing variance in the average trait value between groups. Other analyses of cultural transmission biases have incorporated characteristics of trait variation, such as the quality, and characteristics of transmitters, including success and prestige (2). Another class of transmission biases is couched in terms of the frequencies of the cultural variants in the population (3). These “frequency-dependent” biases include conformity and anticonformity, which occur when a more common variant is adopted at a rate greater or less than its population frequency, respectively (4).Humans have exhibited conformity in mental rotation (5), line discrimination (6), and numerical discrimination tasks (7). Anticonformity has been exhibited by young children performing numerical discrimination (7). Unbiased frequency-dependent transmission, known as random copying (8), has been suggested to account for choices of dog breeds (9), Neolithic pottery motifs, patent citations, and baby names (10, 11). However, baby name distributions appear more consistent with frequency-dependent (8, 12) and/or other (13, 14) biases.In nonhuman animals, conformity has been observed in nine-spined sticklebacks choosing a feeder (15) and great tits solving a puzzle box (16, 17) (but see ref. 18). Fruit flies displayed both conformist and anticonformist bias with respect to mate choice (19) (but these authors used a different definition of anticonformity from that of ref. 4, which we use, and therefore did not consider these behaviors to be anticonformist).Asch (20, 21) used a different definition of conformity from ref. 4, namely “the overriding of personal knowledge or behavioral dispositions by countervailing options observed in others” (ref. 22, p. 34). Aschian conformity (22) has been observed in chimpanzees (23, 24), capuchin monkeys (25, 26) (but see ref. 27), vervet monkeys (28), and great tits (16). It has also been empirically tested in at least 133 studies of humans and, in the United States, has declined from the 1950s to the 1990s (29).Temporal variation may also occur in forms of conformity other than Aschian. In ref. 12, popular US baby names from 1960 to 2010 show a concave turnover function indicative of negative frequency-dependent bias, but male baby names from earlier decades (1880 to 1930) show a convex turnover indicative of positive frequency-dependent or direct bias. However, most previous mathematical models of conformity have incorporated constant, rather than time-dependent, conformity coefficients.Cavalli-Sforza and Feldman (ref. 3, chap. 3) and Boyd and Richerson (ref. 4, chap. 7) studied models of frequency-dependent transmission of a cultural trait with two variants. Boyd and Richerson (4) incorporated conformist and anticonformist bias through a conformity coefficient denoted by D. In their simplest model, if the frequency of variant A is p and that of variant B is 1−p, then the frequency of variant A in the offspring generation, p′, isp′=p+Dp(1−p)(2p−1),[1]where D>0 entails conformity (A increases if its frequency is p>12), D<0 entails anticonformity, D=0 entails random copying, and −2<D<1. In this model, each offspring samples the cultural variants of n=3 members of the parental generation (hereafter, role models). Sampling n>3 role models requires different constraints and, if n>4, there are multiple conformity coefficients (Eq. 19).Many subsequent models have built upon Boyd and Richerson’s (4) simplest model (Eq. 1). These have incorporated individual learning, information inaccuracy due to environmental change (30–34), group selection (35), and other transmission biases, including payoff bias (36), direct bias, and prestige bias (37). Other models, which include a single conformity coefficient and preserve the essential features of Eq. 1, incorporate individual learning, environmental variability (32, 38), group selection (39), and multiple cultural variants (38).In agent-based statistical physics models, the up and down spins of an electron are analogous to cultural variants A and B (40, 41). Individuals are nodes in a network and choose among a series of actions with specified probabilities, such as independently acquiring a spin, or sampling neighboring individuals and adopting the majority or minority spin in the sample. The number of sampled role models can be greater than three (42, 43). (Anti)conformity may occur if all (42–47), or if at least r (40, 48), sampled individuals have the same variant. In contrast, Boyd and Richerson’s (4) general model (Eq. 19) allows, for example, stronger conformity to a 60% majority of role models and weaker conformity or anticonformity to a 95% majority (in humans, this might result from a perceived difference between “up-and-coming” and “overly popular” variants).In Boyd and Richerson’s (4) general model, individuals sample n role models, which is more realistic than restricting n to 3 (as in Eq. 1); individuals may be able to observe more than three members of the previous generation. With n>4, different levels of (anti)conformity may occur for different samples j of n role models with one variant. In addition to the example above with 60 and 95% majorities, other relationships between the level of conformity and the sample j of n are possible. For example, the strength of conformity might increase as the number of role models with the more common variant increases. In a recent exploration of Boyd and Richerson’s (4) general model, we found dynamics that departed significantly from those of Eq. 1 (49). If conformity and anticonformity occur for different majorities j of n role models (i.e., j>n2), polymorphic equilibria may exist that were not possible with Eq. 1. In addition, strong enough anticonformity can produce nonconvergence: With as few as 5 role models, stable cycles in variant frequencies may arise, and with as few as 10 role models, chaos is possible. Such complex dynamics may occur with or without selection.Here, we extend both Boyd and Richerson’s (4) simplest (Eq. 1) and general (Eq. 19) models to allow the conformity coefficient(s) to vary randomly across generations, by sampling them from probability distributions. Although some agent-based models allow individuals to switch between “conformist” and “non-” or “anticonformist” states over time (40, 42, 47, 50, 51), to our knowledge, random temporal variation in the conformity coefficients themselves has not been modeled previously. In reality, the degree to which groups of individuals conform may change over time, as illustrated by the finding that young children anti-conformed while older children conformed in a discrimination task (7); thus, it seems reasonable to expect that different generations may also exhibit different levels of conformity. Indeed, generational changes have occurred for Aschian conformity (29) and possibly in frequency-dependent copying of baby names (12). Our stochastic model may therefore produce more realistic population dynamics than previous deterministic models, and comparisons between the two can suggest when the latter is a reasonable approximation to the former.We also allow the number of role models, nt, to vary over time. Agent-based conformity models have incorporated temporal (43) and individual (43, 45, 46) variation in the number of sampled individuals, whereas here, all members of generation t sample the same number nt of role models. Causes of variation in nt are not explored here, but there could be several. For instance, different generations of animals may sample different numbers of role models due to variation in population density. In humans, changes in the use of social media platforms or their features may cause temporal changes in the number of observed individuals. For example, when Facebook added the feature “People You May Know,” the rate of new Facebook connections in a New Orleans dataset nearly doubled (52).In the stochastic model without selection, regardless of the fluctuation in the conformity coefficient(s), if there is conformity on average, the population converges to one of the three equilibria present in Boyd and Richerson’s (4) model with conformity (D(j)>0 for n2<j<n in Eq. 19). These are p*=1 (fixation on variant A), p*=0 (fixation on variant B), and p*=12 (equal representation of A and B). However, their stability properties may differ from those in the deterministic case. In Boyd and Richerson’s (4) model with random copying, every initial frequency p0 is an equilibrium. Here, with random copying expected and independent conformity coefficients, there is convergence to p*=0,12, or 1. In this case, and in the case with conformity expected, convergence to p*=0,12, or 1 also holds with stochastic variation in the number of role models, nt. With either stochastic or constant weak selection in Boyd and Richerson’s (4) simplest model (Eq. 1) and random copying expected, there is convergence to a fixation state (p*=0 or 1). Finally, with anticonformity in the deterministic model or anticonformity expected in the stochastic model, nonconvergence can occur.     

Fatigue, inflammation, and projected mortality in heart failure

BackgroundFatigue is a prominent and poorly understood symptom of heart failure with reduced ejection fraction (HFrEF). The purpose of this study was to determine whether fatigue correlated with immune biomarkers and prognosis.Methods/ResultsIn patients with HFrEF (N = 59) and healthy controls (N = 25), we prospectively measured fatigue (Profile of Mood States), depressive symptoms (Patient Health Questionnaire-8), sleep quality (Pittsburgh Sleep Quality Index), and immune biomarkers (plasma C-reactive protein [CRP], tumor necrosis factor-α [TNFα], and interleukins [IL-6 and IL-10]). Seattle Heart Failure Model (SHFM) mortality risk scores were determined. Patients with HFrEF had significantly greater fatigue and depressive symptoms and poorer sleep quality compared to control subjects. When controlling for depressive symptoms, however, fatigue did not differ significantly between patients with HFrEF and controls. Patients with HFrEF had significantly lower levels of IL-10 compared to controls. Cytokines did not correlate significantly with fatigue, but fatigue was significantly associated with higher SHFM scores.ConclusionsDepressive symptoms were an important covariate of fatigue in patients with HFrEF. Our study findings were the first to show a positive association between fatigue and the SHFM score, indicating that fatigue was associated with poorer prognosis.     

Prevalence of benign anorectal disease in a randomly selected population

BACKGROUND: The prevalence of benign anorectal diseases (BAD) in the general population has been difficult to establish, either because the individual diseases themselves were difficult to characterize in surveys or because of bias in the selection of the survey population. Reported herein is a prevalence survey of BAD symptoms and treatment history of a sample of the general population, selected by random digit dialing. METHOD: A survey instrument that inquired into symptoms of BAD, BAD treatment history, and health-seeking behaviors was administered by telephone interview with 102 individuals, between the ages of 21 and 65 of both genders and all races, chosen by random digit dialing in the Joliet, Illinois area. For selected variables (gender, education level, obesity, previous BAD treatment, fiber supplementation, time for defecation and reading during defecation all related to BAD symptoms) odds ratios and 95 percent confidence intervals were calculated. RESULTS: Of the 102 individuals, 9 had been previously treated for hemorrhoids, 4 by surgery, and 5 medically. Twenty individuals currently have BAD symptoms, six of these have multiple symptoms frequently, implying established BAD, and four of these have been previously treated for hemorrhoids. Seven of eight individuals with rectal bleeding in the past year have not sought medical evaluation. Of the associations tested, statistical significance was found only between female gender and BAD symptoms (odds ratio=4.6; 95 percent confidence interval=1.3 – 20.4). CONCLUSIONS: History of hemorrhoidal treatment and current BAD symptomatology are highly prevalent in a randomly selected population, and 80 percent of the subjects with symptoms of BAD have not consulted a physician regarding BAD. Some previously held correlates of hemorrhoidal symptoms, such as obesity and extended time for defecation, showed no apparent association with hemorrhoid treatment history or current BAD symptoms. The best predictors of current BAD symptoms were female gender (odds ratio=4.6; 95 percent confidence interval=1.3–20.4) and previous hemorrhoid treatment (odds ratio=3.9; 95 percent confidence interval=0.7–20).Supported by grants from The American Society of Colon and Rectal Surgeons Research Foundation and Konsyl Pharmaceuticals.     

Differentiation of integrals in higher dimensions

We prove a localization principle for directional maximal operators in L^p(ℝⁿ), with p > 1. The resulting bounds, which we conjecture hold for the largest possible class of directions, imply Lebesgue-type differentiation of integrals over tubes that point in the given directions.     

DNA condensation in two dimensions

We have found that divalent electrolyte counterions common in biological cells (Ca(2+), Mg(2+), and Mn(2+) ) can condense anionic DNA molecules confined to two-dimensional cationic surfaces. DNA-condensing agents in vivo include cationic histones and polyamines spermidine and spermine with sufficiently high valence (Z) 3 or larger. In vitro studies show that electrostatic forces between DNA chains in bulk aqueous solution containing divalent counterions remain purely repulsive, and DNA condensation requires counterion valence Z >/= 3. In striking contrast to bulk behavior, synchrotron x-ray diffraction and optical absorption experiments show that above a critical divalent counterion concentration the electrostatic forces between DNA chains adsorbed on surfaces of cationic membranes reverse from repulsive to attractive and lead to a chain collapse transition into a condensed phase of DNA tethered by divalent counterions. This demonstrates the importance of spatial dimensionality to intermolecular interactions where nonspecific counterion-induced electrostatic attractions between the like-charged polyelectrolytes overwhelm the electrostatic repulsions on a surface for Z = 2. This new phase, with a one-dimensional counterion liquid trapped between DNA chains at a density of 0.63 counterions per DNA bp, represents the most compact state of DNA on a surface in vitro and suggests applications in high-density storage of genetic information and organo-metallic materials processing.     

Fourier uniqueness in even dimensions

In recent work, methods from the theory of modular forms were used to obtain Fourier uniqueness results in several key dimensions (d=1,8,24), in which a function could be uniquely reconstructed from the values of it and its Fourier transform on a discrete set, with the striking application of resolving the sphere packing problem in dimensions d=8 and d=24. In this short note, we present an alternative approach to such results, viable in even dimensions, based instead on the uniqueness theory for the Klein–Gordon equation. Since the existing method for the Klein–Gordon uniqueness theory is based on the study of iterations of Gauss-type maps, this suggests a connection between the latter and methods involving modular forms. The derivation of Fourier uniqueness from the Klein–Gordon theory supplies conditions on the given test function for Fourier interpolation, which are hoped to be optimal or close to optimal.     

Tracheal dimensions in young twins

Tracheal dimensions were analyzed radiographically in 17 pairs of healthy high school boys (12 pairs of monozygotic twins and 5 pairs of dizygotic twins). Coefficients of variation in interindividual extra- and intrathoracic tracheal widths, tracheal depth, tracheal length, and cross sectional area ranged from 9.6 to 17.3%. Genetic influence was found in intrathoracic as well as extrathoracic tracheal widths at maximal expiration and in extrathoracic tracheal width at maximal inspiration. Intrathoracic tracheal width remained the same at either maximal inspiration or expiration. However, extrathoracic tracheal width became larger at maximal inspiration regardless of great changes in pleural pressure. These results indicate that tracheal rings may be influenced by genetic factors and that extrathoracic width may be enlarged during maximal inspiration.     

Functional assembly of a randomly cleaved protein.

The sequence of a 939-amino acid polypeptide that is a member of the aminoacyl-tRNA synthetase class of enzymes has been aligned with sequences of 15 related proteins. This alignment guided the design of 18 fragment pairs that were tested for internal sequence complementarity by reconstitution of enzyme activity. Reconstitution was achieved with fragments that divide the protein at both nonconserved and conserved sequences, including locations proximal to or within elements believed to form critical elements of secondary structure. Structure assembly is sufficiently flexible to accommodate fusion of short segments of unrelated sequences at fragment junctions. Complementary chain packing interactions and chain flexibility appear to be widely distributed throughout the sequence and are sufficient to reconstruct large three-dimensional structures from an array of disconnected pieces. The results may have implications for the evolution and assembly of large proteins.     

Equilibrium phase diagram of a randomly pinned glass-former

We use computer simulations to study the thermodynamic properties of a glass-former in which a fraction c of the particles has been permanently frozen. By thermodynamic integration, we determine the Kauzmann, or ideal glass transition, temperature T_K(c) at which the configurational entropy vanishes. This is done without resorting to any kind of extrapolation, i.e., T_K(c) is indeed an equilibrium property of the system. We also measure the distribution function of the overlap, i.e., the order parameter that signals the glass state. We find that the transition line obtained from the overlap coincides with that obtained from the thermodynamic integration, thus showing that the two approaches give the same transition line. Finally, we determine the geometrical properties of the potential energy landscape, notably the T- and c dependence of the saddle index, and use these properties to obtain the dynamic transition temperature T_d(c). The two temperatures T_K(c) and T_d(c) cross at a finite value of c and indicate the point at which the glass transition line ends. These findings are qualitatively consistent with the scenario proposed by the random first-order transition theory.Upon cooling, glass-forming liquids show a dramatic increase of their viscosities and relaxation times before they eventually fall out of equilibrium at low temperatures (1, 2). This laboratory glass transition is a purely kinetic effect because it occurs at the temperature at which the relaxation time of the system crosses the time scale imposed by the experiment, e.g., via the cooling rate. Despite the intensive theoretical, numerical, and experimental studies of the last five decades, the mechanism responsible for the slowing down and thus for the (kinetic) glass transition is still under debate and hence a topic of intense research. From a fundamental point of view the ultimate goal of these studies is to find an answer to the big question in the field: Does a finite temperature exist at which the dynamics truly freezes and, if so, is this ideal glass transition associated with a thermodynamic singularity or is it of kinetic origin (3–6)?Support for the existence of a kinetic transition comes from certain lattice gas models with a “facilitated dynamics” (6). In these models, the dynamics is due to the presence of “defects” and hence for such systems the freezing is not related to any thermodynamic singularity. However, the first evidence that there does indeed exist a thermodynamic singularity goes back to Kauzmann, who found that the residual entropy (the difference of the entropy of the liquid state from that of the crystalline state) vanishes at a finite temperature T_K if it is extrapolated to temperatures below the laboratory glass transition (7). Subsequently many theoretical scenarios that invoke the presence of a thermodynamic transition have been proposed (8–10). One of these is the so-called “random first-order transition” (RFOT) theory which, inspired by the exact solution of a mean-field spin glass, predicts that at T_K the glass-former does indeed undergo a thermodynamic transition at which the residual, or configurational entropy S_c (the logarithm of the number of the states which are available to the system) vanishes and concomitantly breaks the replica symmetry (10, 11). A further appealing feature of RFOT is that it seems to reconcile in a natural way the (free) energy-landscape scenario and mode-coupling theory (MCT), a highly successful theory that describes the relaxation dynamics at intermediate temperatures (12).Despite all these advances, the arguments put forward in the various papers must be considered as phenomenological because compelling and undisputed experimental or numerical evidence to prove or disprove any of these theories and scenarios is still lacking. The only exception is hard spheres in infinite dimensions, for which mean-field theory should become exact (13), but even in this case some unexpected problems are present (see ref. 14). This lack of understanding is mainly due to the steep increase of the relaxation times which hampers the access to the transition point of thermally equilibrated systems, and hence most of the efforts to identifying the transition point, if it exists, resort to unreliable extrapolation.     

Future caregivers: projected family structures of older persons.

Elderly persons depend upon spouses and children for emotional, physical, and financial support. In particular, the use of institutional long-term care has been shown to vary by family status. Changes in past and future levels of mortality, fertility, marriage, and divorce will influence the probability that elderly persons of the future have surviving spouses and children. This research uses multiple decrement life tables and component projection methods to project the future family status of elderly persons until the year 2020. The high level of fertility among women during the 1950s will result in greater proportions of future elderly persons having surviving children. Declines in mortality, coupled with increases in rates of marriage, increase the probability that both men and women will have spouses surviving in their old age.