Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hat p$, its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters $a$ and $b$ for $\hat pp$ respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as $p$ tends to $0$, and which guarantee that, for any $p$ in $(0,1)$, the risk is lower than its asymptotic value. This allows selecting the required number of successes, $r$, to meet a prescribed quality irrespective of the unknown $p$. In addition, the proposed estimators are shown to be approximately minimax when $a/b$ does not deviate too much from $1$, and asymptotically minimax as $r$ tends to infinity when $a=b$.Comment: 4 figure

Geodesics and the competition interface for the corner growth model

We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, out- side of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as bound- ary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where the shape has some regularity. In a sequel to this paper the cocycles are used to prove results about semi-infinite geodesics and the competition interface

Stationary cocycles and Busemann functions for the corner growth model

We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, out- side of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as bound- ary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where the shape has some regularity. In a sequel to this paper the cocycles are used to prove results about semi-infinite geodesics and the competition interface

Self-avoiding walks and connective constants

The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the asymptotic growth rate of the number of self-avoiding walks (SAWs) on $G$ from a given starting vertex. We survey several aspects of the relationship between the connective constant and the underlying graph $G$. $\bullet$ We present upper and lower bounds for $\mu$ in terms of the vertex-degree and girth of a transitive graph. $\bullet$ We discuss the question of whether $\mu\ge\phi$ for transitive cubic graphs (where $\phi$ denotes the golden mean), and we introduce the Fisher transformation for SAWs (that is, the replacement of vertices by triangles). $\bullet$ We present strict inequalities for the connective constants $\mu(G)$ of transitive graphs $G$, as $G$ varies. $\bullet$ As a consequence of the last, the connective constant of a Cayley graph of a finitely generated group decreases strictly when a new relator is added, and increases strictly when a non-trivial group element is declared to be a further generator. $\bullet$ We describe so-called graph height functions within an account of "bridges" for quasi-transitive graphs, and indicate that the bridge constant equals the connective constant when the graph has a unimodular graph height function. $\bullet$ A partial answer is given to the question of the locality of connective constants, based around the existence of unimodular graph height functions. $\bullet$ Examples are presented of Cayley graphs of finitely presented groups that possess graph height functions (that are, in addition, harmonic and unimodular), and that do not. $\bullet$ The review closes with a brief account of the "speed" of SAW.Comment: Accepted version. arXiv admin note: substantial text overlap with arXiv:1304.721

Prediction of Optimal Folding Routes of Proteins That Satisfy the Principle of Lowest Entropy Loss: Dynamic Contact Maps and Optimal Control

An optimization model is introduced in which proteins try to evade high energy regions of the folding landscape, and prefer low entropy loss routes during folding. We make use of the framework of optimal control whose convenient solution provides practical and useful insight into the sequence of events during folding. We assume that the native state is available. As the protein folds, it makes different set of contacts at different folding steps. The dynamic contact map is constructed from these contacts. The topology of the dynamic contact map changes during the course of folding and this information is utilized in the dynamic optimization model. The solution is obtained using the optimal control theory. We show that the optimal solution can be cast into the form of a Gaussian Network that governs the optimal folding dynamics. Simulation results on three examples (CI2, Sso7d and Villin) show that folding starts by the formation of local clusters. Non-local clusters generally require the formation of several local clusters. Non-local clusters form cooperatively and not sequentially. We also observe that the optimal controller prefers “zipping” or small loop closure steps during folding. The folding routes predicted by the proposed method bear strong resemblance to the results in the literature

Microbial Reprogramming Inhibits Western Diet-Associated Obesity

A recent epidemiological study showed that eating ‘fast food’ items such as potato chips increased likelihood of obesity, whereas eating yogurt prevented age-associated weight gain in humans. It was demonstrated previously in animal models of obesity that the immune system plays a critical role in this process. Here we examined human subjects and mouse models consuming Westernized ‘fast food’ diet, and found CD4[superscript +] T helper (Th)17-biased immunity and changes in microbial communities and abdominal fat with obesity after eating the Western chow. In striking contrast, eating probiotic yogurt together with Western chow inhibited age-associated weight gain. We went on to test whether a bacteria found in yogurt may serve to lessen fat pathology by using purified Lactobacillus reuteri ATCC 6475 in drinking water. Surprisingly, we discovered that oral L. reuteri therapy alone was sufficient to change the pro-inflammatory immune cell profile and prevent abdominal fat pathology and age-associated weight gain in mice regardless of their baseline diet. These beneficial microbe effects were transferable into naïve recipient animals by purified CD4[superscript +] T cells alone. Specifically, bacterial effects depended upon active immune tolerance by induction of Foxp3[superscript +] regulatory T cells (Treg) and interleukin (Il)-10, without significantly changing the gut microbial ecology or reducing ad libitum caloric intake. Our finding that microbial targeting restored CD4[superscript +] T cell balance and yielded significantly leaner animals regardless of their dietary ‘fast food’ indiscretions suggests population-based approaches for weight management and enhancing public health in industrialized societies.National Institutes of Health (U.S.) (Grant P30-ES002109)National Institutes of Health (U.S.) (Grant RO1CA108854)National Institutes of Health (U.S.) (Grant P01 AI045757)National Institutes of Health (U.S.) (Grant U19 AI046130)National Institutes of Health (U.S.) (Grant U19 AI070352)National Institutes of Health (U.S.) (Grant P01 AI039671)National Institute of Neurological Disorders and Stroke (U.S.) (Jacob Javits Merit Award NS2427)The Penates FoundationNancy Taylor Foundation for Chronic Diseases, Inc

Prospect theory and tax evasion: a reconsideration of the Yitzhaki puzzle

The standard expected utility (EUT) model of tax evasion predicts that evasion is decreasing in the marginal tax rate (the Yitzhaki puzzle). Recent literature shows cases in which incorporating prospect theory (PT) does and does not overturn the Puzzle. In a general environment that nests both PT and EUT preferences, we provide a detailed study of how the elements of PT affect the Puzzle. PT does not always reverse the Puzzle, hence we give and interpret conditions for when it does and does not. When allowing for stigma and/or variable audit probability, PT reverses the Puzzle in the same way and with the same limitations as does EUT, if equally augmented

Probiotic Microbes Sustain Youthful Serum Testosterone Levels and Testicular Size in Aging Mice

The decline of circulating testosterone levels in aging men is associated with adverse health effects. During studies of probiotic bacteria and obesity, we discovered that male mice routinely consuming purified lactic acid bacteria originally isolated from human milk had larger testicles and increased serum testosterone levels compared to their age-matched controls. Further investigation using microscopy-assisted histomorphometry of testicular tissue showed that mice consuming Lactobacillus reuteri in their drinking water had significantly increased seminiferous tubule cross-sectional profiles and increased spermatogenesis and Leydig cell numbers per testis when compared with matched diet counterparts This showed that criteria of gonadal aging were reduced after routinely consuming a purified microbe such as L. reuteri. We tested whether these features typical of sustained reproductive fitness may be due to anti-inflammatory properties of L. reuteri, and found that testicular mass and other indicators typical of old age were similarly restored to youthful levels using systemic administration of antibodies blocking pro-inflammatory cytokine interleukin-17A. This indicated that uncontrolled host inflammatory responses contributed to the testicular atrophy phenotype in aged mice. Reduced circulating testosterone levels have been implicated in many adverse effects; dietary L. reuteri or other probiotic supplementation may provide a viable natural approach to prevention of male hypogonadism, absent the controversy and side-effects of traditional therapies, and yield practical options for management of disorders typically associated with normal aging. These novel findings suggest a potential high impact for microbe therapy in public health by imparting hormonal and gonad features of reproductive fitness typical of much younger healthy individuals.National Institutes of Health (U.S.) (Grant P30-ES002109)National Institutes of Health (U.S.) (Grant U01 CA164337)National Institutes of Health (U.S.) (Grant RO1CA108854

DNA Damage Triggers Genetic Exchange in Helicobacter pylori

Many organisms respond to DNA damage by inducing expression of DNA repair genes. We find that the human stomach pathogen Helicobacter pylori instead induces transcription and translation of natural competence genes, thus increasing transformation frequency. Transcription of a lysozyme-like protein that promotes DNA donation from intact cells is also induced. Exogenous DNA modulates the DNA damage response, as both recA and the ability to take up DNA are required for full induction of the response. This feedback loop is active during stomach colonization, indicating a role in the pathogenesis of the bacterium. As patients can be infected with multiple genetically distinct clones of H. pylori, DNA damage induced genetic exchange may facilitate spread of antibiotic resistance and selection of fitter variants through re-assortment of preexisting alleles in this important human pathogen

Maturation of the angiotensin II cardiovascular response in the embryonic White Leghorn chicken (Gallus gallus)

Angiotensin II (Ang II) is an important regulator of cardiovascular function in adult vertebrates. Although its role in regulating the adult system has been extensively investigated, the cardiovascular response to Ang II in embryonic vertebrates is relatively unknown. We investigated the potential of Ang II as a regulator of cardiovascular function in embryonic chickens, which lack central nervous system control of cardiovascular function throughout the majority of incubation. The cardiovascular response to Ang II in embryonic chickens was investigated over the final 50% of their development. Ang II produced a dose-dependent increase in arterial pressure on each day of development studied, and the response increased in intensity as development progressed. The Ang II type-1 receptor nonspecific competitive peptide antagonist [Sar1 ile8] Ang II blocked the cardiovascular response to subsequent injections of Ang II on day 21 only. The embryonic pressure response to Ang II (hypertension only) differed from that of adult chickens, in which initial hypotension is followed by hypertension. The constant level of gene expression for the Ang II receptor, in conjunction with an increasing pressure response to the peptide, suggests that two Ang II receptor subtypes are present during chicken development. Collectively, the data indicate that Ang II plays an important role in the cardiovascular development of chickens; however, its role in maintaining basal function requires further study