相关论文: Local Equivalence of Metrics for Multiparameter Pe…

In addition to inherent computational challenges, the absence of a canonical method for quantifying `persistence' in multi-parameter persistent homology remains a hurdle in its application. One of the best known quantifications of…

We compare different periodic point invariants for families of maps parameterized over a compact manifold. Malkiewich and Ponto showed that, in the case of a single map, the Fuller trace is equivalent to the collection of Reidmeister traces…

The use of topological persistence in contemporary data analysis has provided considerable impetus for investigations into the geometric and functional-analytic structure of the space of persistence modules. In this paper, we isolate a…

Persistence modules are representations of products of totally ordered sets in the category of vector spaces. They appear naturally in the representation theory of algebras, but in recent years they have also found applications in other…

Lifted Reed-Solomon and multiplicity codes are classes of codes, constructed from specific sets of $m$-variate polynomials. These codes allow for the design of high-rate codes that can recover every codeword or information symbol from many…

A new variant of bit interleaved coded modulation (BICM) is proposed. In the new scheme, called Parallel BICM, L identical binary codes are used in parallel using a mapper, a newly proposed finite-length interleaver and a binary dither…

In this paper, diversity analysis of bit-interleaved coded multiple beamforming (BICMB) is extended to the case of general spatial interleavers, removing a condition on their previously known design criteria and quantifying the resulting…

Certain classes of multiparameter persistence modules may be encoded as signed barcodes, represented as points in a polyhedral subset of Euclidean space, we refer to as signed persistence diagrams. These signed persistence diagrams exist in…

We show that fiberwise stable vector bundles are preserved by relative Fourier-Mukai transforms between elliptic threefolds with relative Picard number one. Using these bundles we define new invariants of elliptic fibrations, and we relate…

This paper presents a new explicit construction for locally repairable codes (LRCs) for distributed storage systems which possess all-symbols locality and maximal possible minimum distance, or equivalently, can tolerate the maximal number…

Multiparameter persistent homology has been largely neglected as an input to machine learning algorithms. We consider the use of lattice-based convolutional neural network layers as a tool for the analysis of features arising from…

The Harder-Narasimhan type of a quiver representation is a discrete invariant parameterised by a real-valued function (called a central charge) defined on the vertices of the quiver. In this paper, we investigate the strength and…

A standard multimode optical fiber can be used as a general purpose spectrometer after calibrating the wavelength dependent speckle patterns produced by interference between the guided modes of the fiber. A transmission matrix was used to…

While persistent homology has taken strides towards becoming a wide-spread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and…

Fiber-reinforced ceramic-matrix composites are advanced materials resistant to high temperatures, with application to aerospace engineering. Their analysis depends on the detection of embedded fibers, with semi-supervised techniques usually…

We define notions of differentiability for maps from and to the space of persistence barcodes. Inspired by the theory of diffeological spaces, the proposed framework uses lifts to the space of ordered barcodes, from which derivatives can be…

Lifted Reed-Solomon codes, a subclass of lifted affine-invariant codes, have been shown to be of high rate while preserving locality properties similar to generalized Reed-Muller codes, which they contain as subcodes. This work introduces a…

A recent work by Lesnick and Wright proposed a visualisation of $2$D persistence modules by using their restrictions onto lines, giving a family of $1$D persistence modules. We give a constructive proof that any $1$D persistence module with…

We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…

We study a new bi-Lipschitz invariant \lambda(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor…