Dynamics with Infinitely Many Derivatives: The Initial Value Problem

Differential equations of infinite order are an increasingly important class of equations in theoretical physics. Such equations are ubiquitous in string field theory and have recently attracted considerable interest also from cosmologists. Though these equations have been studied in the classical mathematical literature, it appears that the physics community is largely unaware of the relevant formalism. Of particular importance is the fate of the initial value problem. Under what circumstances do infinite order differential equations possess a well-defined initial value problem and how many initial data are required? In this paper we study the initial value problem for infinite order differential equations in the mathematical framework of the formal operator calculus, with analytic initial data. This formalism allows us to handle simultaneously a wide array of different nonlocal equations within a single framework and also admits a transparent physical interpretation. We show that differential equations of infinite order do not generically admit infinitely many initial data. Rather, each pole of the propagator contributes two initial data to the final solution. Though it is possible to find differential equations of infinite order which admit well-defined initial value problem with only two initial data, neither the dynamical equations of p-adic string theory nor string field theory seem to belong to this class. However, both theories can be rendered ghost-free by suitable definition of the action of the formal pseudo-differential operator. This prescription restricts the theory to frequencies within some contour in the complex plane and hence may be thought of as a sort of ultra-violet cut-off.Comment: 40 pages, no figures. Added comments concerning fractional operators and the implications of restricting the contour of integration. Typos correcte

Molecular recognition between functionalized gold nanoparticles and healable, supramolecular polymer blends – a route to property enhancement

A new, healable, supramolecular nanocomposite material has been developed and evaluated. The material comprises a blend of three components: a pyrene-functionalized polyamide, a polydiimide and pyrene- functionalized gold nanoparticles (P-AuNPs). The polymeric components interact by forming well-defined p–p stacked complexes between p-electron rich pyrenyl residues and p-electron deficient polydiimide residues. Solution studies in the mixed solvent chloroform–hexafluoroisopropanol (6 : 1, v/v) show that mixing the three components (each of which is soluble in isolation), results in the precipitation of a supramolecular, polymer nanocomposite network. The precipitate thus formed can be re-dissolved on heating, with the thermoreversible dissolution/precipitation procedure repeatable over at least 5 cycles. Robust, self-supporting composite films containing up to 15 wt% P-AuNPs could be cast from 2,2,2- trichloroethanol. Addition of as little as 1.25 wt% P-AuNPs resulted in significantly enhanced mechanical properties compared to the supramolecular blend without nanoparticles. The nanocomposites showed a linear increase in both tensile moduli and ultimate tensile strength with increasing P-AuNP content. All compositions up to 10 wt% P-AuNPs exhibited essentially quantitative healing efficiencies. Control experiments on an analogous nanocomposite material containing dodecylamine-functionalized AuNPs (5 wt%) exhibited a tensile modulus approximately half that of the corresponding nanocomposite that incorporated 5 wt% pyrene functionalized-AuNPs, clearly demonstrating the importance of the designed interactions between the gold filler and the supramolecular polymer matrix

Beneath the beard : do facial morphometrics influence the strength of judgments of men's beardedness?

This study was supported by a University of Queensland Postdoctoral Research Fellowship awarded to BJWD.Converging evidence suggests men's beards, like many androgen-dependent masculine secondary sexual traits, communicate masculinity and dominance intra-sexually while effects of men's beardedness on attractiveness ratings are more equivocal. Beards may enhance perceived masculinity and dominance via amplifying aspects of underlying craniofacial masculinity, particularly the size of the lower face and jaw. Here we tested these predictions across two studies. In Study 1, we tested how three facial metrics - objectively measured craniofacial masculinity, facial-width-to-height ratio (fWHR), and jaw size - calculated while clean-shaven impacted on ratings of attractiveness, masculinity and dominance of 37 men photographed when clean-shaven and with full beards. Results showed that beards exerted significant and positive effects on masculinity, dominance and to a lesser extent attractiveness. However, fWHR did not significantly interact with beardedness to influence the directions of any of the ratings, and while some linear and nonlinear interactions were significant between objective craniofacial masculinity and beardedness as well as between jaw size and beardedness, they tended to be subtle and dwarfed by the large main effect of beardedness on perceptual ratings. In Study 2, we measured ratings of attractiveness, masculinity and dominance for composite clean-shaven and bearded stimuli experimentally manipulated in facial shape to represent ±50% the shape of a beard, essentially manipulating the size of the lower face and jaw of the stimuli. We found a strong main effect whereby bearded stimuli enhanced dominance and masculinity ratings over clean-shaven stimuli. Increasing the size of the lower face and jaw augmented ratings of masculinity and dominance in clean-shaven stimuli but did not exert strong effects within bearded stimuli. Attractiveness ratings were highest for bearded faces with smaller jaws followed by bearded and clean-shaven faces with larger jaws and lowest for clean-shaven faces with small jaws. Taken together, our findings suggest that beards exert main effects on masculinity and dominance possibly by amplifying male typical facial shape. Attractiveness ratings of facial hair may reflect a compromise between overly dominant looking faces with larger jaws and the additive effects beardedness has on these ratings.PostprintPeer reviewe

An IR Search for Extinguished Supernovae in Starburst Galaxies

IR and Radio band observations of heavily extinguished regions in starburst galaxies suggest a very high SN rate associated with such regions. Optically measured supernova (SN) rates may therefore underestimate the total SN rate by factors of up to 10, due to the high extinction to SNe in starburst regions. The IR/radio SN rates come from a variety of indirect means, however, which suffer from model dependence and other problems. We describe a direct measurement of the SN rate from a regular patrol of starburst galaxies done with K' band imaging to minimize the effects of extinction. A collection of K' measurements of core-collapse SNe near maximum light is presented. Results of a preliminary SN search using the MIRC camera at the Wyoming IR Observatory (WIRO), and an improved search using the ORCA optics are described. A monthly patrol of starburst galaxies within 25 Mpc should yield 1.6 - 9.6 SNe/year. Our MIRC search with low-resolution (2.2" pixels) failed to find extinguished SNe, limiting the SN rate outside the nucleus (at > 15" radius) to less than 3.8 Supernova Rate Units (SRU or SNe/century/10^10 L(solar); 90% confidence). The MIRC camera had insufficient resolution to search nuclear starburst regions, where SN activity is concentrated, explaining why we found no heavily obscured SNe. We conclude that high-resolution, small field SN searches in starburst nuclei are more productive than low resolution, large-field searches, even for our large galaxies. With our ORCA high-resolution optics, we could limit the total SN rate to < 1.3 SRU at 90% confidence in 3 years of observations, lower than the most pessimistic estimate.Comment: AJ Submitted 1998 Dec. 13. View figures and download all as one file at http://panisse.lbl.gov/public/bruce/irs

Women's preferences for men's beards show no relation to their ovarian cycle phase and sex hormone levels

According to the ovulatory shift hypothesis, women's mate preferences for male morphology indicative of competitive ability, social dominance, and/or underlying health are strongest at the peri-ovulatory phase of the menstrual cycle. However, recent meta-analyses are divided on the robustness of such effects and the validity of the often-used indirect estimates of fertility and ovulation has been called into question in methodological studies. In the current study, we test whether women's preferences for men's beardedness, a cue of male sexual maturity, androgenic development and social dominance, are stronger at the peri-ovulatory phase of the menstrual cycle compared to during the early follicular or the luteal phase. We also tested whether levels of estradiol, progesterone, and the estradiol to progesterone ratio at each phase were associated with facial hair preferences. Fifty-two heterosexual women completed a two-alternative forced choice preference test for clean-shaven and bearded male faces during the follicular, peri-ovulatory (validated by the surge in luteinizing hormone or the drop in estradiol levels) and luteal phases. Participants also provided for one entire menstrual cycle daily saliva samples for subsequent assaying of estradiol and progesterone. Results showed an overall preference for bearded over clean-shaven faces at each phase of the menstrual cycle. However, preferences for facial hair were not significantly different over the phases of menstrual cycle and were not significantly associated with levels of reproductive hormones. We conclude that women's preferences for men's beardedness may not be related to changes in their likelihood of conception

Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity

One of the greatest problems of standard cosmology is the Big Bang singularity. Previously it has been shown that non-local ghostfree higher-derivative modifications of Einstein gravity in the ultra-violet regime can admit non-singular bouncing solutions. In this paper we study in more details the dynamical properties of the equations of motion for these theories of gravity in presence of positive and negative cosmological constants and radiation. We find stable inflationary attractor solutions in the presence of a positive cosmological constant which renders inflation {\it geodesically complete}, while in the presence of a negative cosmological constant a cyclic universe emerges. We also provide an algorithm for tracking the super-Hubble perturbations during the bounce and show that the bouncing solutions are free from any perturbative instability.Comment: 38 pages, 6 figures. V2: Added: a word to the title, clarifications, an appendix, many references. To appear in JCA

Cross-Cultural Variation in Men's Beardedness

Objectives To test whether cross-cultural variation in men’s facial hair conforms to patterns predicted by processes of inter-sexual and intra-sexual selection. Methods Data were taken from the PEW Research Center’s World’s Muslims’ project that collected information from 14,032 men from 25 countries. An Independent Factor Analysis was used to analyse how suites of demographic factors predict men’s beardedness. Results Analyses replicated those from past research using the PEW data, showing that beardedness was more frequent under prevailing conditions of lower health and higher economic disparity. Conclusions These findings contribute to evidence that men’s decision to augment their masculinity via full beardedness occurs under conditions characterised by stronger inter-sexual and intra-sexual selection

The Maine Annex, vol. 2, no. 15

Following World War II, the federal G.I. Bill enabled approximately 2.3 million, predominantly white male Veterans to receive a post-secondary education. To accommodate increased enrollment in 1946, the University of Maine established the Brunswick Campus at the former Brunswick Naval Air Station. The remote campus operated until spring 1949, when Veteran registrations waned

The Maine Annex, vol. 2, no. 9

The Maine Annex Editor-in-Chief, Roy W. Nickerson investigates rising costs at the Annex campus bookstore including the price of Coca-Cola increasing from 5 to 7-cents

The Maine Annex, vol. 2, no. 20

The Maine Annex, published by the students of the University of Maine at the Brunswick Campus, was launched January 10, 1947. Editors introduced the publication as the product of a group of progressive students attending the Brunswick Campus. The goal of the publication, according to editors, was to tell the story of our life on this campus. The four-page, tabloid-sized paper included display advertising from area businesses