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.
Study knot diagrams on a sphere without vertical lines, focusing on minimal crossings.
We analyze the effect of adding, removing, and moving basepoints on link Floer homology. We prove that adding or removing basepoints via a procedure called quasi-stabilization is a natural operation on a certain version of link Floer homology, which we call . We consider the effect on the full link Flo…
While invasively recorded brain activity is known to provide detailed information on motor commands, it is an open question at what level of detail information about positions of body parts can be decoded from non-invasively acquired signals. In this work it is shown that index finger positions can be differentiated fr…
The von Neumann graph entropy (VNGE) facilitates measurement of information divergence and distance between graphs in a graph sequence. It has been successfully applied to various learning tasks driven by network-based data. While effective, VNGE is computationally demanding as it requires the full eigenspectrum of the…
Link concordance equals homotopy for high-dimensional spheres.
Study surfaces in 4-manifolds using banded unlink diagrams.
Developed Taylor series for muscle-finger system analysis.
We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it recovers the usual Darcy's law for flow in flat, rectangular cells, with correctio…
In this paper, we present neuro-robotics models with a deep artificial neural network capable of generating finger counting positions and number estimation. We first train the model in an unsupervised manner where each layer is treated as a Restricted Boltzmann Machine or an autoencoder. Such a model is further trained…
We use reinforcement learning (RL) to learn dexterous in-hand manipulation policies which can perform vision-based object reorientation on a physical Shadow Dexterous Hand. The training is performed in a simulated environment in which we randomize many of the physical properties of the system like friction coefficients…
Population migration is valuable information which leads to proper decision in urban-planning strategy, massive investment, and many other fields. For instance, inter-city migration is a posterior evidence to see if the government's constrain of population works, and inter-community immigration might be a prior evidenc…
For humans, the process of grasping an object relies heavily on rich tactile feedback. Most recent robotic grasping work, however, has been based only on visual input, and thus cannot easily benefit from feedback after initiating contact. In this paper, we investigate how a robot can learn to use tactile information to…
A successful grasp requires careful balancing of the contact forces. Deducing whether a particular grasp will be successful from indirect measurements, such as vision, is therefore quite challenging, and direct sensing of contacts through touch sensing provides an appealing avenue toward more successful and consistent …
The study of dexterous manipulation has provided important insights in humans sensorimotor control as well as inspiration for manipulation strategies in robotic hands. Previous work focused on experimental environment with restrictions. Here we describe a method using the deformation and color distribution of the finge…
DIGIT is a low-cost tactile sensor for in-hand manipulation.
Deep learning is an established framework for learning hierarchical data representations. While compute power is in abundance, one of the main challenges in applying this framework to robotic grasping has been obtaining the amount of data needed to learn these representations, and structuring the data to the task at ha…
Designing of touchless user interface is gaining popularity in various contexts. Using such interfaces, users can interact with electronic devices even when the hands are dirty or non-conductive. Also, user with partial physical disability can interact with electronic devices using such systems. Research in this direct…
Grasping is a complex process involving knowledge of the object, the surroundings, and of oneself. While humans are able to integrate and process all of the sensory information required for performing this task, equipping machines with this capability is an extremely challenging endeavor. In this paper, we investigate …
Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of arXiv:1504.00371 corresponds to the case m=2, and our generalizations sheds additional light on …
This paper starts a systematic description of colored knot polynomials, beginning from the first non-(anti)symmetric representation R=[2,1]. The project involves several steps: (i) parametrization of big families of knots a la arXiv:1506.00339, (ii) evaluating Racah/mixing matrices for various numbers of strands in var…
Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of infinite-dimensional operator-valued kernels which are suitable for extending func…
Functional Magnetic Resonance Imaging (fMRI) relies on multi-step data processing pipelines to accurately determine brain activity; among them, the crucial step of spatial smoothing. These pipelines are commonly suboptimal, given the local optimisation strategy they use, treating each step in isolation. With the advent…
Let X be a finite 2-complex with unfree fundamental group. We prove lower bounds for the area of a metric on X, in terms of the square of the least length of a noncontractible loop in X. We thus establish a uniform systolic inequality for all unfree 2-complexes. Our inequality improves the constant in M. Gromov's inequ…
A new knot move preserves pass-move equivalence and differs in count.
It is well known that any two diagrams representing the same oriented link are related by a finite sequence of Reidemeister moves O1, O2 and O3. Depending on orientations of fragments involved in the moves, one may distinguish 4 different versions of each of the O1 and O2 moves, and 8 versions of the O3 move. We introd…
In this paper, we introduce an equivalence relation on the set of local moves and classify local moves, called the extended -moves, up to the equivalence. Moreover, by inducing a binary relation on the set of equivalence classes of local moves, we show that an extended -move realizes the crossing change or the …
Minimal sets of moves for isotopic knots and trivalent graphs identified.
The H(n)-move simplifies virtual and welded knots and links.
We prove that the classical set of moves for standard spines of 3-manifolds (i.e. the MP-move and the V-move) does not suffice to relate to each other any two standard skeleta of a 3-manifold with marked boundary. We also describe a condition on the 3-manifold with marked boundary that tells whether the generalised set…
The (ordinary) unknotting-number of 1-dimensional knots, which is defined by using the crossing-change, is a very basic and important invariant. It is very natural to consider the `unknotting-number' associated with other local-moves on n-dimensional knots, where n is a natural number. In this paper we prove the follow…
Classifies virtual links up to a specific move.
New rational band moves simplify knot classification.
We prove that the crossing changes, Delta moves, and sharp moves are unknotting operations on welded knots.
New methods for delta-moves on algebraically split links identified.
In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger stretch tensor in a Gaussian process. We then consider an improvement on this a…
Minimal moves for surfaces in 4D discovered, linking planar and spatial moves.
Study virtualized Delta, Sharp, and Pass moves for oriented virtual knots and links.
Minimal generating sets of Reidemeister moves identified and classified.
We start a systematic analysis of links up to 5-move equivalence. Our motivation is to develop tools which later can be used to study skein modules based on the skein relation being deformation of a 5-move (in an analogous way as the Kauffman skein module is a deformation of a 2-move, i.e. a crossing change). Our main …
New diagonal move simplifies knots and links efficiently.
New moves help untangle complex knots.
Minimal moves for surfaces in 4D identified.
New virtualized Δ-move simplifies virtual knots and links.
Algorithm for recognizing and performing Reidemeister moves in Gauss diagrams.
Minimal sets of moves for rotational Reidemeister diagrams are identified.
4-move kills Alexander polynomial
Tactile sensors provide useful contact data during the interaction with an object which can be used to accurately learn to determine the stability of a grasp. Most of the works in the literature represented tactile readings as plain feature vectors or matrix-like tactile images, using them to train machine learning mod…
Complete classification of links up to specific moves.