Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight 2. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and we study Faltings heights of arithmetic Hirzebruch-Zagier divisors.

Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

Verifying Harder's Conjecture for Classical and Siegel Modular Forms

A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form. Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.

Évaluation du régulateur sur une courbe modulaire et valeurs particulières

Bloch et Beilinson ont proposé plusieurs conjectures sur les liens entre les applications régulateurs du groupe de K-théorie algébrique associée à une courbe modulaire et des valeurs spéciales de fonction L. Fixons N, un entier naturel et considérons le sous-groupe de congruence $\Gamma_0(N)$. Le présent mémoire démontre une formule explicite entre le régulateur de la courbe modulaire $X_0(N)$ appliqué à une forme primitive et une valeur spéciale de la fonction L associée.

Frobenius polynomials for Calabi-Yau equations

Sei $\pi:X\rightarrow S$ eine \"uber $\Z$ definierte Familie von Calabi-Yau Varietaten der Dimension drei. Es existiere ein unter dem Gauss-Manin Zusammenhang invarianter Untermodul $M\subset H^3_{DR}(X/S)$ von Rang vier, sodass der Picard-Fuchs Operator $P$ auf $M$ ein sogenannter {\em Calabi-Yau } Operator von Ordnung vier ist. Sei $k$ ein endlicher K\"orper der Charaktetristik $p$, und sei $\pi_0:X_0\rightarrow S_0$ die Reduktion von $\pi$ \uber $k$. F\ur die gew\ohnlichen (ordinary) Fasern $X_{t_0}$ der Familie leiten wir eine explizite Formel zur Berechnung des charakteristischen Polynoms des Frobeniusendomorphismus, des {\em Frobeniuspolynoms}, auf dem korrespondierenden Untermodul $M_{cris}\subset H^3_{cris}(X_{t_0})$ her. Sei nun $f_0(z)$ die Potenzreihenl\osung der Differentialgleichung $Pf=0$ in einer Umgebung der Null. Da eine reziproke Nullstelle des Frobeniuspolynoms in einem Teichm\uller-Punkt $t$ durch $f_0(z)/f_0(z^p)|_{z=t}$ gegeben ist, ist ein entscheidender Schritt in der Berechnung des Frobeniuspolynoms die Konstruktion einer $p-$adischen analytischen Fortsetzung des Quotienten $f_0(z)/f_0(z^p)$ auf den Rand des $p-$adischen Einheitskreises. Kann man die Koeffizienten von $f_0$ mithilfe der konstanten Terme in den Potenzen eines Laurent-Polynoms, dessen Newton-Polyeder den Ursprung als einzigen inneren Gitterpunkt enth\alt, ausdr\ucken,so beweisen wir gewisse Kongruenz-Eigenschaften unter den Koeffizienten von $f_0$. Diese sind entscheidend bei der Konstruktion der analytischen Fortsetzung. Enth\alt die Faser $X_{t_0}$ einen gew\ohnlichen Doppelpunkt, so erwarten wir im Grenz\ubergang, dass das Frobeniuspolynom in zwei Faktoren von Grad eins und einen Faktor von Grad zwei zerf\allt. Der Faktor von Grad zwei ist dabei durch einen Koeffizienten $a_p$ eindeutig bestimmt. Durchl\auft nun $p$ die Menge aller Primzahlen, so erwarten wir aufgrund des Modularit\atssatzes, dass es eine Modulform von Gewicht vier gibt, deren Koeffizienten durch die Koeffizienten $a_p$ gegeben sind. Diese Erwartung hat sich durch unsere umfangreichen Rechnungen best\atigt. Dar\uberhinaus leiten wir weitere Formeln zur Bestimmung des Frobeniuspolynoms her, in welchen auch die nicht-holomorphen L\osungen der Gleichung $Pf=0$ in einer Umgebung der Null eine Rolle spielen.

Deforming semistable Galois representations

Let V be a p-adic representation of Gal(Q̄/Q). One of the ideas of Wiles’s proof of FLT is that, if V is the representation associated to a suitable autromorphic form (a modular form in his case) and if V′ is another p-adic representation of Gal(Q̄/Q) “closed enough” to V, then V′ is also associated to an automorphic form. In this paper we discuss which kind of local condition at p one should require on V and V′ in order to be able to extend this part of Wiles’s methods.

A modular magnetic anastomotic device for minimally invasive digestive anastomosis: proof of concept and preliminary data in the pig model.

BACKGROUND: The aim of our study was to assess the feasibility of minimally invasive digestive anastomosis using a modular flexible magnetic anastomotic device made up of a set of two flexible chains of magnetic elements. The assembly possesses a non-deployed linear configuration which allows it to be introduced through a dedicated small-sized applicator into the bowel where it takes the deployed form. A centering suture allows the mating between the two parts to be controlled in order to include the viscerotomy between the two magnetic rings and the connected viscera. METHODS AND PROCEDURES: Eight pigs were involved in a 2-week survival experimental study. In five colorectal anastomoses, the proximal device was inserted by a percutaneous endoscopic technique, and the colon was divided below the magnet. The distal magnet was delivered transanally to connect with the proximal magnet. In three jejunojejunostomies, the first magnetic chain was injected in its linear configuration through a small enterotomy. Once delivered, the device self-assembled into a ring shape. A second magnet was injected more distally through the same port. The centering sutures were tied together extracorporeally and, using a knot pusher, magnets were connected. Ex vivo strain testing to determine the compression force delivered by the magnetic device, burst pressure of the anastomosis, and histology were performed. RESULTS: Mean operative time including endoscopy was 69.2 ± 21.9 min, and average time to full patency was 5 days for colorectal anastomosis. Operative times for jejunojejunostomies were 125, 80, and 35 min, respectively. The postoperative period was uneventful. Burst pressure of all anastomoses was ≥ 110 mmHg. Mean strain force to detach the devices was 6.1 ± 0.98 and 12.88 ± 1.34 N in colorectal and jejunojejunal connections, respectively. Pathology showed a mild-to-moderate inflammation score. CONCLUSIONS: The modular magnetic system showed enormous potential to create minimally invasive digestive anastomoses, and may represent an alternative to stapled anastomoses, being easy to deliver, effective, and low cost.

Comparative modular analysis of gene expression in vertebrate organs.

ABSTRACT: BACKGROUND: The degree of conservation of gene expression between homologous organs largely remains an open question. Several recent studies reported some evidence in favor of such conservation. Most studies compute organs' similarity across all orthologous genes, whereas the expression level of many genes are not informative about organ specificity. RESULTS: Here, we use a modularization algorithm to overcome this limitation through the identification of inter-species co-modules of organs and genes. We identify such co-modules using mouse and human microarray expression data. They are functionally coherent both in terms of genes and of organs from both organisms. We show that a large proportion of genes belonging to the same co-module are orthologous between mouse and human. Moreover, their zebrafish orthologs also tend to be expressed in the corresponding homologous organs. Notable exceptions to the general pattern of conservation are the testis and the olfactory bulb. Interestingly, some co-modules consist of single organs, while others combine several functionally related organs. For instance, amygdala, cerebral cortex, hypothalamus and spinal cord form a clearly discernible unit of expression, both in mouse and human. CONCLUSIONS: Our study provides a new framework for comparative analysis which will be applicable also to other sets of large-scale phenotypic data collected across different species.

Population Variation and Genetic Control of Modular Chromatin Architecture in Humans.

Chromatin state variation at gene regulatory elements is abundant across individuals, yet we understand little about the genetic basis of this variability. Here, we profiled several histone modifications, the transcription factor (TF) PU.1, RNA polymerase II, and gene expression in lymphoblastoid cell lines from 47 whole-genome sequenced individuals. We observed that distinct cis-regulatory elements exhibit coordinated chromatin variation across individuals in the form of variable chromatin modules (VCMs) at sub-Mb scale. VCMs were associated with thousands of genes and preferentially cluster within chromosomal contact domains. We mapped strong proximal and weak, yet more ubiquitous, distal-acting chromatin quantitative trait loci (cQTL) that frequently explain this variation. cQTLs were associated with molecular activity at clusters of cis-regulatory elements and mapped preferentially within TF-bound regions. We propose that local, sequence-independent chromatin variation emerges as a result of genetic perturbations in cooperative interactions between cis-regulatory elements that are located within the same genomic domain.

Are we modular lying cues detectors ? The answer is "yes sometimes"

We quickly form first impressions about newly encountered people guiding our subsequent behaviour (approach, avoidance). Such instant judgments might be innate and automatic, being performed unconsciously and independently to other cognitive processes. Lying detection might be subject to such a modular process. Unfortunately, numerous studies highlighted problems with lying detection paradigms such as high error rates and learning effects. Additionally, humans should be motivated doing both detecting others' lies and dis- guising own lies. Disguising own lies might even be more challenging than detecting other people's lies. Thus, when trying to disguise cheating behaviour, liars might display a mixture of disguising (fake) trust cues and uncontrolled lying cues making the interpretation of the expression difficult (perceivers are guessing). In two consecutive online studies, we tested whether seeing an increasing amount (range 0-4) of lying cues (LC) and non-lying cues (NLC) on a standard face results in enhanced guessing behaviour (studies 1 and 2) and that enhanced guessing is accompanied by slower responding (study 2). Results showed that pronounced guessing and slowest responding occurred for faces with an intermediate number and not with the highest number of LC and NLC. In particular, LC were more impor- tant than NLC to uncertain lying decisions. Thus, only a few LC may interfere with automatic processing of lying detection (irrespective of NLC), probably because too little lying cue information is yet available.

Modular framework for outlier detection

Outlier detection is an important form of data analysis because outliers in several cases contain the interesting and important pieces of information. In the recent years, many different outlier detection algorithms have been devised for finding different kinds of outliers in varying contexts and environments. Some effort has been put to study how to effectively combine different outlier detection methods. The combination of outlier detection algorithms as an ensemble was studied in this thesis by designing a modular framework for outlier detection, which combines arbitrary outlier detection techniques. This work resulted in an example implementation of the framework. Outlier detection capability of the ensemble method was validated using datasets and methods found in outlier detection research. The framework achieved better results than the individual outlier algorithms. Future research includes how to handle large datasets effectively and the possibilities for real-time outlier monitoring.

Fundamentos epistemológicos da teoria modular da mente de Jerry A. Fodor

Este artigo é uma apresentação dos fundamentos da teoria modular desenvolvida por Jerry A. Fodor e uma reflexão sobre seus principais desafios. A noção de modularidade da mente de Fodor, por um lado, procura superar as insuficiências metodológicas e epistemológicas do associacionismo e do localizacionismo a respeito das explicações da estrutura e do funcionamento mental; por outro lado, é uma oposição à postura culturalista de Vygotsky, para o qual as funções superiores da mente, como a cognição, são produtos artificiais, culturais. A psicologia cognitiva de Chomsky converteu esse produto "artificial" em "natural", postulando a existência de módulos inatos para desempenhar funções cognitivas específicos. Com base nessa ideia de Chomsky, Fodor procura explicar a mente como um conjunto de módulos. No entanto, sua principal contribuição para as ciências cognitivas é a apresentação da arquitetura mental em dois níveis e a afirmação da existência de módulos centrais responsáveis pelas atividades cognitivas superiores, como criatividade, reflexão ou imaginação.

Investigating a dynamic modular framework for subjective well-being

According to Diener (1984), the three primary components of subjective well-being (SWB) are high life satisfaction (LS), frequent positive affect (P A), and infrequent negative affect (NA). The present dissertation extends previous research and theorizing on SWB by testing an innovative framework developed by Shmotkin (2005) in which SWB is conceptualized as an agentic process that promotes and maintains positive functioning. Two key components ofShmotkin's framework were explored in a longitudinal study of university students. In Part 1, SWB was examined as an integrated system of components organized within individuals. Using cluster analysis, five distinct configurations of LS, P A, and NA were identified at each wave. Individuals' SWB configurations were moderately stable over time, with the highest and lowest stabilities observed among participants characterized by "high SWB" and "low SWB" configurations, respectively. Changes in SWB configurations in the direction of a high SWB pattern, and stability among participants already characterized by high SWB, coincided with better than expected mental, physical, and interpersonal functioning over time. More positive levels of functioning and improvements in functioning over time discriminated among SWB configurations. However, prospective effects of SWB configurations on subsequent functioning were not observed. In Part 2, subjective temporal perspective "trajectories" were examined based on individuals' ratings of their past, present, and anticipated future LS. Upward subjective LS trajectories were normative at each wave. Cross-sectional analyses revealed consistent associations between upward subjective trajectories and lower levels of LS, as well as less positive mental, physical, and interpersonal functioning. Upward subjective LS trajectories were biased both with respect to underestimation of past LS and overestimation of future LS, demonstrating their illusional nature. Further, whereas more negative retrospective bias was associated with greater current distress and dysfunction, more positive prospective bias was associated with less positive functioning in the future. Prospective relations, however, were not consistently observed. Thus, steep upward subjective LS trajectory appeared to be a form of wishful-thinking, rather than an adaptive form of selfenhancement. Major limitations and important directions for future research are considered. Implications for Shmotkin's (2005) framework, and for research on SWB more generally, also are discussed

Development and illustrative outputs of the Community Integrated Assessment System (CIAS), a multi-institutional modular integrated assessment approach for modelling climate change.

This paper describes the development and first results of the “Community Integrated Assessment System” (CIAS), a unique multi-institutional modular and flexible integrated assessment system for modelling climate change. Key to this development is the supporting software infrastructure, SoftIAM. Through it, CIAS is distributed between the community of institutions which has each contributed modules to the CIAS system. At the heart of SoftIAM is the Bespoke Framework Generator (BFG) which enables flexibility in the assembly and composition of individual modules from a pool to form coupled models within CIAS, and flexibility in their deployment onto the available software and hardware resources. Such flexibility greatly enhances modellers’ ability to re-configure the CIAS coupled models to answer different questions, thus tracking evolving policy needs. It also allows rigorous testing of the robustness of IA modelling results to the use of different component modules representing the same processes (for example, the economy). Such processes are often modelled in very different ways, using different paradigms, at the participating institutions. An illustrative application to the study of the relationship between the economy and the earth’s climate system is provided.

Jmax-pruning: a facility for the information theoretic pruning of modular classification rules

The Prism family of algorithms induces modular classification rules in contrast to the Top Down Induction of Decision Trees (TDIDT) approach which induces classification rules in the intermediate form of a tree structure. Both approaches achieve a comparable classification accuracy. However in some cases Prism outperforms TDIDT. For both approaches pre-pruning facilities have been developed in order to prevent the induced classifiers from overfitting on noisy datasets, by cutting rule terms or whole rules or by truncating decision trees according to certain metrics. There have been many pre-pruning mechanisms developed for the TDIDT approach, but for the Prism family the only existing pre-pruning facility is J-pruning. J-pruning not only works on Prism algorithms but also on TDIDT. Although it has been shown that J-pruning produces good results, this work points out that J-pruning does not use its full potential. The original J-pruning facility is examined and the use of a new pre-pruning facility, called Jmax-pruning, is proposed and evaluated empirically. A possible pre-pruning facility for TDIDT based on Jmax-pruning is also discussed.