The arithmetic of genus two curves with (4,4)-split Jacobians

In this paper we study genus 2 curves whose Jacobians admit a polarized (4,4)-isogeny to a product of elliptic curves. We consider base fields of characteristic different from 2 and 3, which we do not assume to be algebraically closed. We obtain a full classification of all principally polarized abelian surfaces that can arise from gluing two elliptic curves along their 4-torsion and we derive the relation their absolute invariants satisfy. As an intermediate step, we give a general description of Richelot isogenies between Jacobians of genus 2 curves, where previously only Richelot isogenies with kernels that are pointwise defined over the base field were considered. Our main tool is a Galois theoretic characterization of genus 2 curves admitting multiple Richelot isogenies.Comment: 30 page

Involving users in OPAC interface design: Perspective from a UK study

This is the post-print versoin of the Article. The official published version can be accessed from the link below - Copyright @ 2007 SpringerThe purpose of this study was to determine user suggestions for a typical OPAC (Online Public Library Catalogue) application’s functionality and features. An experiment was undertaken to find out the type of interactions features that users prefer to have in an OPAC. The study revealed that regardless of users’ Information Technology (IT) backgrounds, their functionality expectations of OPACs are the same. However, based on users’ previous experiences with OPACs, their requirements with respect to specific features may change. Users should be involved early in the OPAC development cycle process in order to ensure usable and functional interface

Stringy K-theory and the Chern character

For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new ring called the full orbifold K-theory of Y. For a global quotient Y=[X/G], the ring of G-invariants of the stringy K-theory of X is a subalgebra of the full orbifold K-theory of the the stack Y and is linearly isomorphic to the ``orbifold K-theory'' of Adem-Ruan (and hence Atiyah-Segal), but carries a different, ``quantum,'' product, which respects the natural group grading. We prove there is a ring isomorphism, the stringy Chern character, from stringy K-theory to stringy cohomology, and a ring homomorphism from full orbifold K-theory to Chen-Ruan orbifold cohomology. These Chern characters satisfy Grothendieck-Riemann-Roch for etale maps. We prove that stringy cohomology is isomorphic to Fantechi and Goettsche's construction. Since our constructions do not use complex curves, stable maps, admissible covers, or moduli spaces, our results simplify the definitions of Fantechi-Goettsche's ring, of Chen-Ruan's orbifold cohomology, and of Abramovich-Graber-Vistoli's orbifold Chow. We conclude by showing that a K-theoretic version of Ruan's Hyper-Kaehler Resolution Conjecture holds for symmetric products. Our results hold both in the algebro-geometric category and in the topological category for equivariant almost complex manifolds.Comment: Exposition improved and additional details provided. To appear in Inventiones Mathematica

Analytic curves in algebraic varieties over number fields

We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'olya-Bertrandias valid over the projective line to arbitrary algebraic curves over a number field. The formulation and the proof of these criteria involve some basic notions in Arakelov geometry, combined with complex and rigid analytic geometry (notably, potential theory over complex and $p$-adic curves). We also discuss geometric analogues, pertaining to the algebraic geometry of projective surfaces, of these arithmetic criteria.Comment: 55 pages. To appear in "Algebra, Arithmetic, and Geometry: In Honor of Y.i. Manin", Y. Tschinkel & Yu. Manin editors, Birkh\"auser, 200

Duality in Non-Trivially Compactified Heterotic Strings

We study the implications of duality symmetry on the analyticity properties of the partition function as it depends upon the compactification length. In order to obtain non-trivial compactifications, we give a physical prescription to get the Helmholtz free energy for any heterotic string supersymmetric or not. After proving that the free energy is always invariant under the duality transformation $R\rightarrow \alpha^{'}/(4R)$ and getting the zero temperature theory whose partition function corresponds to the Helmholtz potential, we show that the self-dual point $R_{0}=\sqrt{\alpha^{'}}/2$ is a generic singularity as the Hagedorn one. The main difference between these two critical compactification radii is that the term producing the singularity at the self-dual point is finite for any $R \neq R_{0}$. We see that this behavior at $R_{0}$ actually implies a loss of degrees of freedom below that point.Comment: (Preprint No. FTUAM-92/12) 17 page

Near Infrared Diode Laser THz Systems

The generation and detection of radiation in the THz frequency range can be achieved with many different electronic and photonic concepts. Among the many different photonic THz systems the most versatile are based on diode lasers. In this paper we describe and review the different concepts and optimization ideas for diode laser based THz systems in order to achieve the best performance for different types of THz setups.</p

Effect of sitagliptin on energy metabolism and brown adipose tissue in overweight individuals with prediabetes:a randomised placebo-controlled trial

Aims/hypothesis: The aim of this study was to evaluate the effect of sitagliptin on glucose tolerance, plasma lipids, energy expenditure and metabolism of brown adipose tissue (BAT), white adipose tissue (WAT) and skeletal muscle in overweight individuals with prediabetes (impaired glucose tolerance and/or impaired fasting glucose). Methods: We performed a randomised, double-blinded, placebo-controlled trial in 30 overweight, Europid men (age 45.9 \xc2\xb1 6.2\xc2\xa0years; BMI 28.8 \xc2\xb1 2.3\xc2\xa0kg/m2) with prediabetes in the Leiden University Medical Center and the Alrijne Hospital between March 2015 and September 2016. Participants were initially randomly allocated to receive sitagliptin (100\xc2\xa0mg/day) (n = 15) or placebo (n = 15) for 12\xc2\xa0weeks, using a randomisation list that was set up by an unblinded pharmacist. All people involved in the study as well as participants were blinded to group assignment. Two participants withdrew from the study prior to completion (both in the sitagliptin group) and were subsequently replaced with two new participants that were allocated to the same treatment. Before and after treatment, fasting venous blood samples and skeletal muscle biopsies were obtained, OGTT was performed and body composition, resting energy expenditure and [18F] fluorodeoxyglucose ([18F]FDG) uptake by metabolic tissues were assessed. The primary study endpoint was the effect of sitagliptin on BAT volume and activity. Results: One participant from the sitagliptin group was excluded from analysis, due to a distribution error, leaving 29 participants for further analysis. Sitagliptin, but not placebo, lowered glucose excursion (\xe2\x88\x9240%; p < 0.003) during OGTT, accompanied by an improved insulinogenic index (+38%; p < 0.003) and oral disposition index (+44%; p < 0.003). In addition, sitagliptin lowered serum concentrations of triacylglycerol (\xe2\x88\x9229%) and very large (\xe2\x88\x9246%), large (\xe2\x88\x9235%) and medium-sized (\xe2\x88\x9224%) VLDL particles (all p < 0.05). Body weight, body composition and energy expenditure did not change. In skeletal muscle, sitagliptin increased mRNA expression of PGC1\xce\xb2 (also known as PPARGC1B) (+117%; p < 0.05), a main controller of mitochondrial oxidative energy metabolism. Although the primary endpoint of change in BAT volume and activity was not met, sitagliptin increased [18F] FDG uptake in subcutaneous WAT (sWAT; +53%; p < 0.05). Reported side effects were mild and transient and not necessarily related to the treatment. Conclusions/interpretation: Twelve weeks of sitagliptin in overweight, Europid men with prediabetes improves glucose tolerance and lipid metabolism, as related to increased [18F] FDG uptake by sWAT, rather than BAT, and upregulation of the mitochondrial gene PGC1\xce\xb2 in skeletal muscle. Studies on the effect of sitagliptin on preventing or delaying the progression of prediabetes into type 2 diabetes are warranted. Trial registration: ClinicalTrials.gov NCT02294084. Funding: This study was funded by Merck Sharp & Dohme Corp, Dutch Heart Foundation, Dutch Diabetes Research Foundation, Ministry of Economic Affairs and the University of Granada

Finite Temperature Bosonic Closed Strings: Thermal Duality and the Kosterlitz Thouless Transition

We elucidate the properties of a gas of free closed bosonic strings in thermal equilibrium. Our starting point is the intensive generating functional of connected one-loop closed vacuum string graphs given by the Polyakov path integral. Invariance of the path integral under modular transformations gives a thermal duality invariant expression for the free energy of free closed strings at finite temperature. The free bosonic string gas exhibits a self-dual Kosterlitz-Thouless phase transition. The thermodynamic potentials of the gas of free bosonic closed strings are shown to exhibit an infinite hierarchy of thermal self-duality relations. Note Added (Sep 2005).Comment: 22pgs. Note Added (Sep 2005), clarifying conclusion

Impact of Protein Stability, Cellular Localization, and Abundance on Proteomic Detection of Tumor-Derived Proteins in Plasma

Tumor-derived, circulating proteins are potentially useful as biomarkers for detection of cancer, for monitoring of disease progression, regression and recurrence, and for assessment of therapeutic response. Here we interrogated how a protein's stability, cellular localization, and abundance affect its observability in blood by mass-spectrometry-based proteomics techniques. We performed proteomic profiling on tumors and plasma from two different xenograft mouse models. A statistical analysis of this data revealed protein properties indicative of the detection level in plasma. Though 20% of the proteins identified in plasma were tumor-derived, only 5% of the proteins observed in the tumor tissue were found in plasma. Both intracellular and extracellular tumor proteins were observed in plasma; however, after normalizing for tumor abundance, extracellular proteins were seven times more likely to be detected. Although proteins that were more abundant in the tumor were also more likely to be observed in plasma, the relationship was nonlinear: Doubling the spectral count increased detection rate by only 50%. Many secreted proteins, even those with relatively low spectral count, were observed in plasma, but few low abundance intracellular proteins were observed. Proteins predicted to be stable by dipeptide composition were significantly more likely to be identified in plasma than less stable proteins. The number of tryptic peptides in a protein was not significantly related to the chance of a protein being observed in plasma. Quantitative comparison of large versus small tumors revealed that the abundance of proteins in plasma as measured by spectral count was associated with the tumor size, but the relationship was not one-to-one; a 3-fold decrease in tumor size resulted in a 16-fold decrease in protein abundance in plasma. This study provides quantitative support for a tumor-derived marker prioritization strategy that favors secreted and stable proteins over all but the most abundant intracellular proteins