I need to do a PhD in Pure Mathematics and I am thinking of Topological Data Analysis. I want to use persistent homology and quiver representation to obtain topological features in data structures. Now, what kind of data structures can I use? Note that I need to come up with theorems and proofs, being a Pure Mathematics degree. It's not just about coding and coming up with persistence diagrams and barcodes.
2026-03-06 23:23:56.1772839436
Topological Invariance in Data Structures
93 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GENERAL-TOPOLOGY
- Is every non-locally compact metric space totally disconnected?
- Let X be a topological space and let A be a subset of X
- Continuity, preimage of an open set of $\mathbb R^2$
- Question on minimizing the infimum distance of a point from a non compact set
- Is hedgehog of countable spininess separable space?
- Nonclosed set in $ \mathbb{R}^2 $
- I cannot understand that $\mathfrak{O} := \{\{\}, \{1\}, \{1, 2\}, \{3\}, \{1, 3\}, \{1, 2, 3\}\}$ is a topology on the set $\{1, 2, 3\}$.
- If for every continuous function $\phi$, the function $\phi \circ f$ is continuous, then $f$ is continuous.
- Defining a homotopy on an annulus
- Triangle inequality for metric space where the metric is angles between vectors
Related Questions in ALGEBRAIC-TOPOLOGY
- How to compute homology group of $S^1 \times S^n$
- the degree of a map from $S^2$ to $S^2$
- Show $f$ and $g$ are both homeomorphism mapping of $T^2$ but $f$ is not homotopy equivalent with $g.$
- Chain homotopy on linear chains: confusion from Hatcher's book
- Compute Thom and Euler class
- Are these cycles boundaries?
- a problem related with path lifting property
- Bott and Tu exercise 6.5 - Reducing the structure group of a vector bundle to $O(n)$
- Cohomology groups of a torus minus a finite number of disjoint open disks
- CW-structure on $S^n$ and orientations
Related Questions in QUIVER
- idempotent in quiver theory
- Is this functor a left adjoint?
- Significance of adjoint relationship with Ext instead of Hom
- Mistake in the proof of Theorem 2.24 of Quiver Representations by Ralf Schiffler?
- From a lower triangular matrix to its quiver representation
- Indecomposable representation of an acyclic quiver on 3 vertices
- Full projective resolutions for path algebras in GAP
- Can this puzzle be solved using the representation theory of quivers?
- Usage and Realization of a Quiver Representation.
- Problem with hom-spaces and their dimensions in GAP
Related Questions in DATA-STRUCTURE
- Prove Statement with Asymptotic Notation
- Given two arrays A1,A2, return if for a given X , there is a pair of ai∈Ai such that a1+a2=X ((n log()))
- proof 0 (f (n)) = 0 (g(n)) if and only if f (n) E 0 (g(n)) and g(n) E O (f (n))
- What is a suitable index to express similarity in two observations of the same set of variables containing ratios?
- Set in an algebra of a data structure
- matrix columns represented by binary search tree
- How to formulate the mth value of this question directly,
- Would this suffice in a visual type theory to define an abstract List type?
- How do you define in particular a linked list in abstract type theory? Or would you even do that?
- Find K Closest pairs in a spatial database (Without specific query object)
Related Questions in TOPOLOGICAL-DATA-ANALYSIS
- Persistence Homology on a grid Distance measure
- Computing natural pseudo distance.
- Understanding the last step in computing persistent homology
- matrix columns represented by binary search tree
- TDA- Persistence Diagram and Barcodes using image data (and TDA R package)
- Are the results from persistent homology complete?
- Original source of the persistence algorithm?
- bottle neck distance: distance to diagonal points
- computing wasserstein distance vs. bottleneck distance between persistence diagrams
- Topological Data Analysis
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Have you tried looking at Steve Oudet's publications? (See his website.)
Note that he has written one book and coauthored another that could be of interest to you:
Steve Oudot. Persistence Theory: From Quiver Representations to Data Analysis. AMS Mathematical Surveys and Monographs, volume 209, 2015.
F. Chazal, V. de Silva, M. Glisse, S. Oudot. The Structure and Stability of Persistence Modules. Springer Briefs in Mathematics, 2016.