Computational problems in the theory of Abelian groups

In this thesis, the worst-case time complexity bounds on the algorithms for the problems mentioned below have been improved. A. Algorithms on abelian groups represented by a set of defining relations for computing: (I) a canonical basis for finite abelian groups (II) a canonical basis for Infinite abelian group B. Algorithms for computing: (I) Hermite normal form of an Integer matrix (II) The Smith normal form of an Integer matrix (III) The set of all solutions of a system of Diophantine Equations C. Algorithms on abelian groups represented by an explicit set of generators for computing: (I) the order of an element (space complexity 1s only improved) (II) a complete basis for a finite abelian group (III) membership-Inclusion testing (IV) the union and Intersection of two finite abelian groups D. A classification of the relative complexity of computational problems on abelian groups (as above) factorization and primility testing. E. Algorithms on abelian subgroups of the symmetric group for computing: (I) the complete structure of a group (II) membership-Indus Ion testing (III) the union of two abelian groups (IV) the Intersection of two abelian groups

Finding the Anticover of a String

A k-anticover of a string x is a set of pairwise distinct factors of x of equal length k, such that every symbol of x is contained into an occurrence of at least one of those factors. The existence of a k-anticover can be seen as a notion of non-redundancy, which has application in computational biology, where they are associated with various non-regulatory mechanisms. In this paper we address the complexity of the problem of finding a k-anticover of a string x if it exists, showing that the decision problem is NP-complete on general strings for k-3. We also show that the problem admits a polynomial-time solution for k = 2. For unbounded k, we provide an exact exponential algorithm to find a k-anticover of a string of length n (or determine that none exists), which runs in O(min{3 n-k 3 , ( k(k+1) 2 ) n k+1 }) time using polynomial space. 2012 ACM Subject Classification Mathematics of computing ! Combinatorics on words

Entropic Elasticity of Double-Strand DNA Subject to Simple Spatial Constraints

The aim of the present paper is the study of the entropic elasticity of the dsDNA molecule, having a cristallographic length L of the order of 10 to 30 persistence lengths A, when it is subject to spatial obstructions. We have not tried to obtain the single molecule partition function by solving a Schodringer-like equation. We prefer to stay within a discretized version of the WLC model with an added one-monomer potential, simulating the spatial constraints. We derived directly from the discretized Boltzmann formula the transfer matrix connecting the partition functions relative to adjacent "effective monomers". We have plugged adequate Dirac delta-functions in the functional integral to ensure that the monomer coordinate and the tangent vector are independent variables. The partition function is, then, given by an iterative process which is both numerically efficient and physically transparent. As a test of our discretized approach, we have studied two configurations involving a dsDNA molecule confined between a pair of parallel plates.Comment: The most formal developments of Section I have been moved into an appendix and replaced by a direct derivation of the transfer matrix used in the applications. of Section II. Two paragraphs and two figures have been added to clarify the physical interpretation of the result

Genome sequences and great expectations

To assess how automatic function assignment will contribute to genome annotation in the next five years, we have performed an analysis of 31 available genome sequences. An emerging pattern is that function can be predicted for almost two-thirds of the 73,500 genes that were analyzed. Despite progress in computational biology, there will always be a great need for large-scale experimental determination of protein function

Establishment of computational biology in Greece and Cyprus: Past, present, and future.

We review the establishment of computational biology in Greece and Cyprus from its inception to date and issue recommendations for future development. We compare output to other countries of similar geography, economy, and size—based on publication counts recorded in the literature—and predict future growth based on those counts as well as national priority areas. Our analysis may be pertinent to wider national or regional communities with challenges and opportunities emerging from the rapid expansion of the field and related industries. Our recommendations suggest a 2-fold growth margin for the 2 countries, as a realistic expectation for further expansion of the field and the development of a credible roadmap of national priorities, both in terms of research and infrastructure funding

Nonperturbative Vertices in Supersymmetric Quantum Electrodynamics

We derive the complete set of supersymmetric Ward identities involving only two- and three- point proper vertices in supersymmetric QED. We also present the most general form of the proper vertices consistent with both the supersymmetric and U(1) gauge Ward identities. These vertices are the supersymmetric equivalent of the non supersymmetric Ball-Chiu vertices.Comment: seventeen pages late

The Robustness of Quintessence

Recent observations seem to suggest that our Universe is accelerating implying that it is dominated by a fluid whose equation of state is negative. Quintessence is a possible explanation. In particular, the concept of tracking solutions permits to adress the fine-tuning and coincidence problems. We study this proposal in the simplest case of an inverse power potential and investigate its robustness to corrections. We show that quintessence is not affected by the one-loop quantum corrections. In the supersymmetric case where the quintessential potential is motivated by non-perturbative effects in gauge theories, we consider the curvature effects and the K\"ahler corrections. We find that the curvature effects are negligible while the K\"ahler corrections modify the early evolution of the quintessence field. Finally we study the supergravity corrections and show that they must be taken into account as $Q\approx m_{\rm Pl}$ at small red-shifts. We discuss simple supergravity models exhibiting the quintessential behaviour. In particular, we propose a model where the scalar potential is given by $V(Q)=\frac{\Lambda^{4+\alpha }}{Q^{\alpha}}e^{\frac{\kappa}{2}Q^2}$. We argue that the fine-tuning problem can be overcome if $\alpha \ge 11$. This model leads to $\omega_Q\approx -0.82$ for $\Omega_{\rm m}\approx 0.3$ which is in good agreement with the presently available data.Comment: 16 pages, 7 figure

Transcriptomic and CRISPR/Cas9 technologies reveal FOXA2 as a tumor suppressor gene in pancreatic cancer

Pancreatic ductal adenocarcinoma (PDAC) is an aggressive cancer with low survival rates and limited therapeutic options. Thus elucidation of signaling pathways involved in PDAC pathogenesis is essential for identifying novel potential therapeutic gene targets. Here, we used a systems approach to elucidate those pathways by integrating gene and microRNA profiling analyses together with CRISPR/Cas9 technology to identify novel transcription factors involved in PDAC pathogenesis. FOXA2 transcription factor was found to be significantly downregulated in PDAC relative to control pancreatic tissues. Functional experiments revealed that FOXA2 has a tumor suppressor function through inhibition of pancreatic cancer cell growth, migration, invasion, and colony formation. In situ hybridization analysis revealed miR-199a to be significantly upregulated in pancreatic cancer. Bioinformatics and luciferase analyses showed that miR-199a negatively but directly regulates FOXA2 expression through binding in its 3′-untranslated region (UTR). Evaluation of the functional importance of miR-199a on pancreatic cancer revealed that miR-199a acts as an inhibitor of FOXA2 expression, inducing an increase in pancreatic cancer cell proliferation, migration, and invasion. Additionally, gene ontology and network analyses in PANC-1 cells treated with a small interfering RNA (siRNA) against FOXA2 revealed an enrichment for cell invasion mechanisms through PLAUR and ERK activation. FOXA2 deletion (FOXA2Δ) by using two CRISPR/Cas9 vectors in PANC-1 cells induced tumor growth in vivo resulting in upregulation of PLAUR and ERK pathways in FOXA2Δ xenograft tumors. We have identified FOXA2 as a novel tumor suppressor in pancreatic cancer and it is regulated directly by miR-199a, thereby enhancing our understanding of how microRNAs interplay with the transcription factors to affect pancreatic oncogenesis

Flow Equations for U_k and Z_k

By considering the gradient expansion for the wilsonian effective action S_k of a single component scalar field theory truncated to the first two terms, the potential U_k and the kinetic term Z_k, I show that the recent claim that different expansion of the fluctuation determinant give rise to different renormalization group equations for Z_k is incorrect. The correct procedure to derive this equation is presented and the set of coupled differential equations for U_k and Z_k is definitely established.Comment: 5 page

One Loop Back Reaction On Chaotic Inflation

We extend, for the case of a general scalar potential, the inflaton-graviton Feynman rules recently developed by Iliopoulos {\it et al.} As an application we compute the leading term, for late co-moving times, of the one loop back reaction on the expansion rate for $V(\phi) = \frac12 m^2 \phi^2$. This is expressed as the logarithmic time derivative of the scale factor in the coordinate system for which the expectation value of the metric has the form: $dx^{\mu} dx^{\nu} = - d{\bar t}^2 + a^2({\bar t}) d{\vec x} \cdot d{\vec x}$. This quantity should be a gauge independent observable. Our result for it agrees exactly with that inferred from the effect previously computed by Mukhanov {\it et al.} using canonical quantization. It is significant that the two calculations were made with completely different schemes for fixing the gauge, and that our computation was done using the standard formalism of covariant quantization. This should settle some of the issues recently raised by Unruh.Comment: 41 pages, LaTeX 2 epsilo