A note on Galois embeddings of abelian varieties

In this note we show that if an abelian variety possesses a Galois embedding into some projective space, then it must be isogenous to the self product of an elliptic curve. We prove moreover that the self product of an elliptic curve always has infinitely many Galois embeddings.Comment: Some typos fixed. To appear in Manuscripta Mathematic

Fixed points of endomorphisms of complex tori

We study the asymptotic behavior of the cardinality of the fixed point set of iterates of an endomorphism of a complex torus. We show that there are precisely three types of behavior of this function: it is either an exponentially growing function, a periodic function, or a product of both.Comment: Some typos corrected; the introduction was also revise

Hopfield Networks in Relevance and Redundancy Feature Selection Applied to Classification of Biomedical High-Resolution Micro-CT Images

We study filter–based feature selection methods for classification of biomedical images. For feature selection, we use two filters — a relevance filter which measures usefulness of individual features for target prediction, and a redundancy filter, which measures similarity between features. As selection method that combines relevance and redundancy we try out a Hopfield network. We experimentally compare selection methods, running unitary redundancy and relevance filters, against a greedy algorithm with redundancy thresholds [9], the min-redundancy max-relevance integration [8,23,36], and our Hopfield network selection. We conclude that on the whole, Hopfield selection was one of the most successful methods, outperforming min-redundancy max-relevance when\ud more features are selected

The Gauss map and secants of the Kummer variety

Fay's trisecant formula shows that the Kummer variety of the Jacobian of a smooth projective curve has a four dimensional family of trisecant lines. We study when these lines intersect the theta divisor of the Jacobian, and prove that the Gauss map of the theta divisor is constant on these points of intersection, when defined. We investigate the relation between the Gauss map and multisecant planes of the Kummer variety as well.Comment: Minor changes, to appear on the Bulletin of London Mathematical Societ

Smooth quotients of abelian surfaces by finite groups

Let $A$ be an abelian surface and let $G$ be a finite group of automorphisms of $A$ fixing the origin. Assume that the analytic representation of $G$ is irreducible. We give a classification of the pairs $(A,G)$ such that the quotient $A/G$ is smooth. In particular, we prove that $A=E^2$ with $E$ an elliptic curve and that $A/G\simeq\mathbb P^2$ in all cases. Moreover, for fixed $E$, there are only finitely many pairs $(E^2,G)$ up to isomorphism. This completes the classification of smooth quotients of abelian varieties by finite groups started by the first two authors.Comment: 15 pages. Comments are welcome. arXiv admin note: text overlap with arXiv:1801.0002

A decomposition of the Jacobian of a Humbert-Edge curve

A \textit{Humbert-Edge curve of type} $n$ is a non-degenerate smooth complete intersection of $n-1$ diagonal quadrics. Such a curve has an interesting geometry since it has a natural action of the group $(\mathbb{Z}/2\mathbb{Z})^n$. We present here a decomposition of its Jacobian variety as a product of Prym-Tyurin varieties, and we compute the kernel of the corresponding isogeny.Comment: 9 pages, comments welcome! To appear in Contemporary Mathematic

A Step towards Solving Olfactory Stimulus-Percept Problem

Odours are highly complex, relying on hundreds of receptors, and people are known to disagree in their linguistic descriptions of smells. It is partly due to these facts that, it is very hard to map the domain of odour molecules or their structure to that of perceptual representations, a problem that has been referred to as the Structure-Odour-Relationship. We collected a number of diverse open domain databases of odour molecules having unorganised perceptual descriptors, and developed a graphical method to find the similarity between perceptual descriptors; which is intuitive and can be used to identify perceptual classes. We then separately projected the physico-chemical and perceptual features of these molecules in a non-linear dimension and clustered the similar molecules. We found a significant overlap between the spatial positioning of the clustered molecules in the physico-chemical and perceptual spaces. We also developed a statistical method of predicting the perceptual qualities of a novel molecule using its physico-chemical properties with high receiver operating characteristics(ROC)

Effect of glenoid concavity loss on shoulder stability- a case report in a professional wrestler

Background Current glenoid defect measurement techniques only quantify bone loss in terms of defect diameter or surface. However, the glenoid depth plays an important role in shoulder stabilization by means of concavity compression. Case presentation We present a case of a professional wrestler who suffered from anterior shoulder instability after sustaining a bony Bankart lesion without loss of glenoid surface area but flattening of the concavity due to medialization of the fragment. The patient’s glenoid concavity was reconstructed arthroscopically by reduction and percutaneous screw fixation of the bony fragment along with a capsulo-ligamentous shift. Changes of the glenoid concavity with according alterations in the Bony Shoulder Stability Ratio (BSSR) were analyzed on pre-op, post-op, and follow-up CT scans. Postoperative CT scans revealed a deepened concavity (3.3 mm) and improved BSSR (46.1 %) compared to pre-op scans (0.7 mm; 11.3 %). Follow-up CT scans showed a slight remodeling of the glenoid concavity (3.2 mm) with steady BSSR (44.7 %). Conclusion This case shows that the passive stabilizing effect of the glenoid can be compromised by loss of concavity despite the absence of loss of articular surface. Therefore, addressing the concavity loss and resulting reduction of the BSSR is recommended in these cases. Bony Bankart repair was successful in restoring the BSSR of the patients shoulder as determined by mathematical calculations based on CT scans