The Little Randall-Sundrum Model at the Large Hadron Collider

We present a predictive warped model of flavor that is cut off at an ultraviolet scale O(10^3) TeV. This "Little Randall-Sundrum (LRS)" model is a volume-truncation, by a factor $y \approx 6$, of the RS scenario and is holographically dual to dynamics with number of colors larger by $y$. The LRS couplings between Kaluza-Klein states and the Standard Model fields, including the proton constituents, are explicitly calculable without ad hoc assumptions. Assuming separate gauge and flavor dynamics, a number of unwanted contributions to precision electroweak, $Z b\bar b$ and flavor observables are suppressed in the LRS framework, compared with the corresponding RS case. An important consequence of the LRS truncation, independent of precise details, is a significant enhancement of the clean (golden) di-lepton LHC signals, by O(y^3), due to a larger "$\rho$-photon" mixing and a smaller inter-composite coupling.Comment: Revtex4, 6 pages, two tables. Typos in the text and reference list correcte

Constructing non-trivial elements of the Shafarevich-Tate group of an Abelian Variety over a Number Field

The second part of the Birch and Swinnerton-Dyer (BSD) conjecture gives a conjectural formula for the order of the Shafarevich-Tate group of an elliptic curve in terms of other computable invariants of the curve. Cremona and Mazur initiated a theory that can often be used to verify the BSD conjecture by constructing non-trivial elements of the Shafarevich-Tate group of an elliptic curve by means of the Mordell-Weil group of an ambient curve. In this paper, we generalize Cremona and Mazur's work and give precise conditions under which such a construction can be made for the Shafarevich-Tate group of an abelian variety over a number field. We then give an extension of our general result that provides new theoretical evidence for the BSD conjecture.Comment: 18 page

The Stabilizing Effect Of Intraspecific Genetic Variation On Population Dynamics In Novel And Ancestral Habitats

Recent studies show that intraspecific genetic variation in asexual species may have large effects on community and ecosystem functions, increasing their stability, productivity, and species richness. However, major questions regarding its population-level impact remain empirically unanswered: (a) How does intraspecific genetic diversity affect the ecological characteristics of sexual species, in which recombination can alter the outcome of causal mechanisms such as selection and niche diversification? (b) Does genetic diversity increase population dynamic stability? (c) Is the impact of genetic diversity dependent on the selective environment? To answer these questions, I founded replicate flour beetle (Tribolium castaneum) populations with different degrees of ecologically relevant, heritable trait variation and monitored their dynamics for approximately eight generations. I show that population stability and persistence increased with greater genetic variation but that the stabilizing effect was independent of the selective habitat (different proportions of ancestral and novel resources). Alleles from a single founding strain underwent a selective sweep in the homogeneous ancestral habitat but not in a novel heterogeneous habitat. These results expand current understanding of the ecological impacts of genetic diversity by showing that genetically more diverse sexual populations persist longer and are more stable but that the selective environment determines the mechanistic basis of increased stability.Integrative Biolog

Combining Direct & Indirect Kaon CP Violation to Constrain the Warped KK Scale

The Randall-Sundrum (RS) framework has a built in protection against flavour violation, but still generically suffers from little CP problems. The most stringent bound on flavour violation is due to epsilon_K, which is inversely proportional to the fundamental Yukawa scale. Hence the RS epsilon_K problem can be ameliorated by effectively increasing the Yukawa scale with a bulk Higgs, as was recently observed in arXiv:0810.1016. We point out that incorporating the constraint from epsilon'/\epsilon_K, which is proportional to the Yukawa scale, raises the lower bound on the KK scale compared to previous analyses. The bound is conservatively estimated to be 5.5 TeV, choosing the most favorable Higgs profile, and 7.5 TeV in the two-site limit. Relaxing this bound might require some form of RS flavour alignment. As a by-product of our analysis, we also provide the leading order flavour structure of the theory with a bulk Higgs.Comment: 15 pages, 2 figure

Associated production of a Kaluza-Klein excitation of a gluon with a t t(bar) pair at the LHC

In Randall-Sundrum models, the Kaluza-Klein (KK) excitations of the gluon, g_{KK} have enhanced couplings to the right-handed quarks. In the absence of a gg g_{KK} coupling in these models, the single production of a g_{KK} from an initial gg state is not possible. The search for other production mechanisms at the LHC, therefore, becomes important. We suggest that the associated production of a g_{KK} with a t t(bar) pair is such a mechanism. Our study shows that through this process the LHC can probe KK gluon masses in the range of 2.8 -- 2.9 TeV.Comment: 11 pages, 3 figure

Web Security Detection Tool

According to Government Computer News (GCN) web attacks have been marked as all- time high this year. GCN says that some of the leading security software like SOPHOS detected about 15,000 newly infected web pages daily in initial three months of 2008 [13]. This has lead to the need of efficient software to make web applications robust and sustainable to these attacks. While finding information on different types of attacks, I found that SQL injection and cross site scripting are the most famous among attackers. These attacks are used extensively since, they can be performed using different techniques and it is difficult to make a web application completely immune to these attacks. There are myriad detection tools available which help to detect vulnerabilities in web applications. These tools are mainly categorized as white-box and black-box testing tools. In this writing project, we aim to develop a detection tool which would be efficient and helpful for the users to pinpoint possible vulnerabilities in his/her PHP scripts. We propose a technique to integrate the aforementioned categories of tools under one framework to achieve better detection against possible vulnerabilities. Our system focuses on giving the developer a simple and concise tool which would help him/her to correct possible loopholes in the PHP code snippets

Visibility and the Birch and Swinnerton-Dyer conjecture for analytic rank one

Let $E$ be an optimal elliptic curve over \Q of conductor $N$ having analytic rank one, i.e., such that the $L$-function $L_E(s)$ of $E$ vanishes to order one at $s=1$. Let $K$ be a quadratic imaginary field in which all the primes dividing $N$ split and such that the $L$-function of $E$ over $K$ vanishes to order one at $s=1$. Suppose there is another optimal elliptic curve over \Q of the same conductor $N$ whose Mordell-Weil rank is greater than one and whose associated newform is congruent to the newform associated to $E$ modulo an integer $r$. The theory of visibility then shows that under certain additional hypotheses, $r$ divides the order of the Shafarevich-Tate group of $E$ over $K$. We show that under somewhat similar hypotheses, $r$ divides the order of the Shafarevich-Tate group of $E$ over $K$. We show that under somewhat similar hypotheses, $r$ also divides the Birch and Swinnerton-Dyer {\em conjectural} order of the Shafarevich-Tate group of $E$ over $K$, which provides new theoretical evidence for the second part of the Birch and Swinnerton-Dyer conjecture in the analytic rank one case