A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Smartphone app counts grapes for accurate yield estimation.
For Portugal there are few or none works about the international trade of fruits between Portugal and the other countries. In this work it aims to analyze the more recent data for the Portuguese international trade of fruits. They were used data for the years from 2006 to 2010, available by the INE (Statistics Portugal…
Fruit fly brain network learns word embeddings using sparse binary codes.
Improved classifier for PU data using logistic regression.
A new method extracts features from time series data using iterated sums and improves classification accuracy.
The paper connects disentanglement to manifold charts and commutativity.
The study examines lower and upper bounds of Wasserstein distances for affine transformations of random vectors.
In classical fixed point and coincidence theory the notion of Nielsen numbers has proved to be extremely fruitful. We extend it to pairs (f_1,f_2) of maps between manifolds of arbitrary dimensions, using nonstabilized normal bordism theory as our main tool. This leads to estimates of the minimum numbers MCC(f_1,f_2) (a…
The paper derives Chen-Ricci inequalities for Riemannian submersions and maps.
Binary autoencoder with sparse hidden layer preserves information and zero reconstruction error.
Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. This branch of differential geometry is still so far from being exhausted; only a small portion of an exceedingly fruitful field has been cultivated, much more remains to be discover…
Expander graphs have been, during the last five decades, the subject of a most fruitful interaction between pure mathematics and computer science, with influence and applications going both ways (cf. [Lub94], [HLW06], [Lub12] and the references therein). In the last decade, a theory of "high dimensional expanders" has …
The pioneering work of Jones and Kauffman unveiled a fruitful relationship between statistical mechanics and knot theory. Recently, Jones introduced two subgroups and of the Thompson groups and , respectively, together with a procedure that associates an oriented link diagram to any element o…
Interdisciplinary study linking potential theory and elliptic PDEs.
The main subject of this expository paper is a connection between Gromov's filling volumes and a boundary rigidity problem of determining a Riemannian metric in a compact domain by its boundary distance function. A fruitful approach is to represent Riemannian metrics by minimal surfaces in a Banach space and to prove r…
BioHash improves similarity search performance using sparse high-dimensional hash codes.
Survey on GKM theory in low dimensions, highlighting combinatorics-geometry interplay.
The mushroom body is the key network for the representation of learned olfactory stimuli in Drosophila and insects. The sparse activity of Kenyon cells, the principal neurons in the mushroom body, plays a key role in the learned classification of different odours. In the specific case of the fruit fly, the sparseness o…
This paper introduces a new metric for deep learning networks based on their classification performance.
Binary classification models get more efficient predictive probabilities.
Adversarial examples are slight perturbations that are designed to fool artificial neural networks when fed as an input. In this work the usability of the Fisher information for the detection of such adversarial attacks is studied. We discuss various quantities whose computation scales well with the network size, study…
This paper is devoted to a coordinate-free approach to several classic geometries such as hyperbolic (real, complex, quaternionic), elliptic (spherical, Fubini-Study), and lorentzian (de Sitter, anti de Sitter) ones. These geometries carry a certain simple structure that is in some sense stronger than the riemannian st…
New combinatorial structures represent subgroups of surface groups, analogous to Stallings core graphs.
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian dynamical system in a manifold, one can consider it as geometric equipment of this manif…
Consider the sum of the first eigenspaces for the Laplacian on a Riemannian manifold. A basis for this space determines a map to Euclidean space and for sufficiently large the map is an embedding. In analogy with a fruitful idea of Kähler geometry, we define (Riemannian) Bergman metrics of degree to be thos…
The concept of absence of opportunities for free lunches is one of the pillars in the economic theory of financial markets. This natural assumption has proved very fruitful and has lead to great mathematical, as well as economical, insights in Quantitative Finance. Formulating rigorously the exact definition of absence…
Twistor methods provide a powerful tool in the study of harmonic maps and harmonic morphisms. Indeed, their use has enabled us to produce a variety of examples of harmonic morphisms defined on 4-dimensional manifolds, and a complete classification in some cases. In the first part of this work, we generalize those const…
We consider tackling a single-agent RL problem by distributing it to learners. These learners, called advisors, endeavour to solve the problem from a different focus. Their advice, taking the form of action values, is then communicated to an aggregator, which is in control of the system. We show that the local plan…
The study examines stability of Sobolev inequalities on manifolds with Ricci bounds.
We use two of the most fruitful methods for constructing isospectral manifolds, the Sunada method and the torus action method, to construct manifolds whose Dirichlet-to-Neumann operators are isospectral at all frequencies. The manifolds are also isospectral for the Robin boundary value problem for all choices of Robin …
Early stopping is a well known approach to reduce the time complexity for performing training and model selection of large scale learning machines. On the other hand, memory/space (rather than time) complexity is the main constraint in many applications, and randomized subsampling techniques have been proposed to tackl…
Most animals possess the ability to actuate a vast diversity of movements, ostensibly constrained only by morphology and physics. In practice, however, a frequent assumption in behavioral science is that most of an animal's activities can be described in terms of a small set of stereotyped motifs. Here we introduce a m…
Generative Adversarial Networks (GANs) are a well-known technique that is trained on samples (e.g. pictures of fruits) and which after training is able to generate realistic new samples. Conditional GANs (CGANs) additionally provide label information for subclasses (e.g. apple, orange, pear) which enables the GAN to le…
This is an expository article. It discusses an approach to hypoelliptic Fredholm index theory based on noncommutative methods (groupoids, C*-algebras, K-theory). The paper starts with an explicit index theorem for scalar second order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-bro…
The common view that our creativity is what makes us uniquely human suggests that incorporating research on human creativity into generative deep learning techniques might be a fruitful avenue for making their outputs more compelling and human-like. Using an original synthesis of Deep Dream-based convolutional neural n…
Probabilistic-driven classification techniques extend the role of traditional approaches that output labels (usually integer numbers) only. Such techniques are more fruitful when dealing with problems where one is not interested in recognition/identification only, but also into monitoring the behavior of consumers and/…
New proof of Lie-Tresse theorem with computational advantages.
Breiman discusses two statistical cultures, advocating for more research on 'before' and 'after' the black box.
Commentary on Rashomon Effect complicating model selection.
Essential to each other, growth and exploration are jointly observed in populations, be it alive such as animals and cells or inanimate such as goods and money. But their ability to move, crucial to cope with uncertainty and optimize returns, is tempered by the space/time properties of the environment. We investigate h…
In this paper, we introduce the notion of Reidemeister torsion for quasi-isomorphisms of based chain complexes over a field. We call a chain map a quasi-isomorphism if its induced homomorphism between homology is an isomorphism. Our notion of torsion generalizes the torsion of acyclic based chain complexes, and is a ch…
The classical theory of prolongation of G-structures was generalized by N. Tanaka to a wide class of geometric structures (Tanaka structures), which are defined on a non-holonomic distribution. Examples of Tanaka structures include subriemannian, subconformal, CR-structures, structures associated to second order differ…
VAR-GPs solve continual learning by updating posteriors sequentially.
In recent years, ideas from statistics and scientific computing have begun to interact in increasingly sophisticated and fruitful ways with ideas from computer science and the theory of algorithms to aid in the development of improved worst-case algorithms that are useful for large-scale scientific and Internet data an…
We present MILABOT: a deep reinforcement learning chatbot developed by the Montreal Institute for Learning Algorithms (MILA) for the Amazon Alexa Prize competition. MILABOT is capable of conversing with humans on popular small talk topics through both speech and text. The system consists of an ensemble of natural langu…
Ring-reservoir networks simplify graph embeddings efficiently.
The social media revolution has changed the way that brands interact with consumers. Instead of spending their advertising budget on interstate billboards, more and more companies are choosing to partner with so-called Internet "influencers" --- individuals who have gained a loyal following on online platforms for the …
The topological Tverberg conjecture was considered a central unsolved problem of topological combinatorics. The conjecture asserts that for any integers and any continuous map of the -dimensional simplex there are pairwise disjoint faces such that $f(σ_1)…