Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds

We investigate a potential relationship between mirror symmetry for Calabi-Yau manifolds and the mirror duality between quasi-Fano varieties and Landau-Ginzburg models. More precisely, we show that if a Calabi-Yau admits a so-called Tyurin degeneration to a union of two Fano varieties, then one should be able to construct a mirror to that Calabi-Yau by gluing together the Landau-Ginzburg models of those two Fano varieties. We provide evidence for this correspondence in a number of different settings, including Batyrev-Borisov mirror symmetry for K3 surfaces and Calabi-Yau threefolds, Dolgachev-Nikulin mirror symmetry for K3 surfaces, and an explicit family of threefolds that are not realized as complete intersections in toric varieties.Comment: v2: Section 5 has been completely rewritten to accommodate results removed from Section 5 of arxiv:1501.04019. v3: Final version, to appear in String-Math 2015, forthcoming volume in the Proceedings of Symposia in Pure Mathematics serie

Families of lattice polarized K3 surfaces with monodromy

We extend the notion of lattice polarization for K3 surfaces to families over a (not necessarily simply connected) base, in a way that gives control over the action of monodromy on the algebraic cycles, and discuss the uses of this new theory in the study of families of K3 surfaces admitting fibrewise symplectic automorphisms. We then give an application of these ideas to the study of Calabi-Yau threefolds admitting fibrations by lattice polarized K3 surfaces

Calabi-Yau Threefolds Fibred by Mirror Quartic K3 Surfaces

We study threefolds fibred by mirror quartic K3 surfaces. We begin by showing that any family of such K3 surfaces is completely determined by a map from the base of the family to the moduli space of mirror quartic K3 surfaces. This is then used to give a complete explicit description of all Calabi-Yau threefolds fibred by mirror quartic K3 surfaces. We conclude by studying the properties of such Calabi-Yau threefolds, including their Hodge numbers and deformation theory.Comment: v2: Significant changes at the request of the referee. Section 3 has been rearranged to accommodate a revised proof of Proposition 3.5 (formerly 3.2). Section 5 has been removed completely, it will instead appear as part of Section 5 in arxiv:1601.0811

Transient Heat Partition Factor for a Sliding Railcar Wheel

During a wheel slide the frictional heat generated at the contact interface causes intense heating of the adjacent wheel material. If this material exceeds the austenitising temperature and then cools quickly enough, it can transform into martensite, which may ultimately crack and cause wheel failure. A knowledge of the distribution of the heat partitioned into the wheel and the rail and the resulting temperature fields is critical to developing designs to minimize these deleterious effects. A number of theoretical solutions have appeared in the literature to model the thermal aspects of this phenomenon. The objective of this investigation was to examine the limitations of these solutions by comparing them to the results of a finite element analysis that does not incorporate many of the simplifying assumptions on which these solutions are based. It was found that these simplified solutions can produce unrealistic results under some circumstances

The Hodge--Poincar\'e polynomial of the moduli spaces of stable vector bundles over an algebraic curve

Let X be a nonsingular complex projective variety that is acted on by a reductive group $G$ and such that $X^{ss} \neq X_{(0)}^{s}\neq \emptyset$. We give formulae for the Hodge--Poincar\'e series of the quotient $X_{(0)}^s/G$. We use these computations to obtain the corresponding formulae for the Hodge--Poincar\'e polynomial of the moduli space of properly stable vector bundles when the rank and the degree are not coprime. We compute explicitly the case in which the rank equals 2 and the degree is even.Comment: Final published version. arXiv admin note: text overlap with arXiv:math/0305346, arXiv:math/0305347 by other author

An approach to supervised learning of three valued Lukasiewicz logic in Hölldobler's core method

The core method [6] provides a way of translating logic programs into a multilayer perceptron computing least models of the programs. In [7] , a variant of the core method for three valued Lukasiewicz logic and its applicability to cognitive modelling were introduced. Building on these results, the present paper provides a modified core suitable for supervised learning, implements and executes supervised learning with the backpropagation algorithm and, finally, constructs a rule extraction method in order to close the neural-symbolic cycle

Learning Lukasiewicz logic

The integration between connectionist learning and logic-based reasoning is a longstanding foundational question in artificial intelligence, cognitive systems, and computer science in general. Research into neural-symbolic integration aims to tackle this challenge, developing approaches bridging the gap between sub-symbolic and symbolic representation and computation. In this line of work the core method has been suggested as a way of translating logic programs into a multilayer perceptron computing least models of the programs. In particular, a variant of the core method for three valued Łukasiewicz logic has proven to be applicable to cognitive modelling among others in the context of Byrne’s suppression task. Building on the underlying formal results and the corresponding computational framework, the present article provides a modified core method suitable for the supervised learning of Łukasiewicz logic (and of a closely-related variant thereof), implements and executes the corresponding supervised learning with the backpropagation algorithm and, finally, constructs a rule extraction method in order to close the neural-symbolic cycle. The resulting system is then evaluated in several empirical test cases, and recommendations for future developments are derived

Reversible cerebral ischemia in patients with pheochromocytoma

Cerebral ischemia and symptoms of stroke can occur as a rare manifestation in patients with pheochromocytoma. We describe a 45-year-old woman who was admitted because of a right-sided hemiparesis due to an ischemic lesion in the left hypothalamus. The clinical diagnosis of a pheochromocytoma was proven by highly elevated urinary catecholamines and confirmed histologically after operation. The successful removal of the tumor led to the almost complete recovery of the neurological deficiencies. It is of vital importance to know this atypical presentation of pheochromocytoma. The diagnosis of pheochromocytoma should be suspected in patients with focal cerebral symptoms, particularly in the presence of intermittent hypertension or other paroxysmal symptoms suggestive of pheochromocytom

Multiple scaling regimes in simple aging models

We investigate aging in glassy systems based on a simple model, where a point in configuration space performs thermally activated jumps between the minima of a random energy landscape. The model allows us to show explicitly a subaging behavior and multiple scaling regimes for the correlation function. Both the exponents characterizing the scaling of the different relaxation times with the waiting time and those characterizing the asymptotic decay of the scaling functions are obtained analytically by invoking a `partial equilibrium' concept.Comment: 4 pages, 3 figure