arXiv research

We prove an explicit and sharp upper bound for the Castelnuovo-Mumford regularity of an FI-module V in terms of the degrees of its generators and relations. We use this to refine a result of Putman on the stability of homology of congruence subgroups, extending his theorem to previously excluded small characteristics a…

Deep learning predicts user identity, activity, and location from Wi-Fi signals.

New FI method accurately predicts feature importance.

Paper categorifies Vassiliev skein relation for Khovanov homology.

FI-modules were introduced by the first three authors in [CEF] to encode sequences of representations of symmetric groups. Over a field of characteristic 0, finite generation of an FI-module implies representation stability for the corresponding sequence of S_n-representations. In this paper we prove the Noetherian pro…

Representation stability is a theory describing a way in which a sequence of representations of different groups is related, and essentially contains a finite amount of information. Starting with Church-Ellenberg-Farb's theory of $FI$-modules describing sequences of representations of the symmetric groups, we now have …

The paper detects entrance positions using Wi-Fi and GPS signals.

This paper investigates the investment behaviour of a large unregulated financial institution (FI) with CARA risk preferences. It shows how the FI optimizes its trading to account for market illiquidity using an extension of the Almgren-Chriss market impact model of multiple risky assets. This expected utility optimiza…

This paper provides a guide to feature importance methods for better scientific inference.

New method for mixed data FI controls type I error and achieves high power.

Hi-fi priors enhance BNNs by learning flexible activations.

The paper sets lower bounds for sampling non-log-concave distributions using Fisher information.

Graph representation learning aims at transforming graph data into meaningful low-dimensional vectors to facilitate the employment of machine learning and data mining algorithms designed for general data. Most current graph representation learning approaches are transductive, which means that they require all the nodes…

The category $\mathrm{FI}_G$ was first defined and explored by Sam-Snowden. Here, we develop more of the machinery of $\mathrm{FI}_G$-modules and find numerous examples to apply it to, extending the work of Church-Ellenberg-Farb and Wilson. In particular we develop a notion of character polynomials for $\mathrm{FI}_G$-…

Due to their ubiquitous and pervasive nature, Wi-Fi networks have the potential to collect large-scale, low-cost, and disaggregate data on multimodal transportation. In this study, we develop a semi-supervised deep residual network (ResNet) framework to utilize Wi-Fi communications obtained from smartphones for the pur…

Signed pairwise interactions conflate uniqueness, redundancy, and synergy

Losaw improves FI scores by decorrelating features in ML models.

In this paper we apply the theory of finitely generated FI-modules developed by Church, Ellenberg and Farb to certain sequences of rational cohomology groups. Our main examples are the cohomology of the moduli space of n-pointed curves, the cohomology of the pure mapping class group of surfaces and some manifolds of hi…

Adaptive PINNs improve accuracy by adding points where solutions are uncertain.

Wi-Fi signals-based person identification attracts increasing attention in the booming Internet-of-Things era mainly due to its pervasiveness and passiveness. Most previous work applies gaits extracted from WiFi distortions caused by the person walking to achieve the identification. However, to extract useful gait, a p…

A method for concept-based learning using probabilistic inference and expert rules.

We utilize Wi-Fi communications from smartphones to predict their mobility mode, i.e. walking, biking and driving. Wi-Fi sensors were deployed at four strategic locations in a closed loop on streets in downtown Toronto. Deep neural network (Multilayer Perceptron) along with three decision tree based classifiers (Decisi…

The study predicts solar flare productivity using magnetic data from SDO/HMI.

An FI-module $V$ over a commutative ring $\bf{k}$ encodes a sequence $(V_n)_{n \geq 0}$ of representations of the symmetric groups $(\mathfrak{S}_n)_{n \geq 0}$ over $\bf{k}$. In this paper, we show that for a "finitely generated" FI-module $V$ over a field of characteristic $p$, the cohomology groups $H^t(\mathfrak{S}…

In this paper, we propose hybrid building/floor classification and floor-level two-dimensional location coordinates regression using a single-input and multi-output (SIMO) deep neural network (DNN) for large-scale indoor localization based on Wi-Fi fingerprinting. The proposed scheme exploits the different nature of th…

This is a sequel to the paper [Cas]. Here, we extend the methods of Farb-Wolfson using the theory of FI_G-modules to obtain stability of equivariant Galois representations of the etale cohomology of orbit configuration spaces. We establish subexponential bounds on the growth of unstable cohomology, and then use the Gro…

New method handles missing data in multimodal brain imaging.

New method corrects bias in feature importance measures of GBM.

In this paper we introduce and develop the theory of FI-modules. We apply this theory to obtain new theorems about: - the cohomology of the configuration space of n distinct ordered points on an arbitrary (connected, oriented) manifold - the diagonal coinvariant algebra on r sets of n variables - the cohomology and tau…

A new risk measure (FRM) for EM FI returns helps investors protect against volatility and policy instability.

One of the key technologies for future large-scale location-aware services covering a complex of multi-story buildings --- e.g., a big shopping mall and a university campus --- is a scalable indoor localization technique. In this paper, we report the current status of our investigation on the use of deep neural network…

The paper introduces a cobordism for Khovanov homology crossing change and categorifies Vassiliev skein relations.

Improves FI-PINNs by combining re-sampling and subset simulation for better failure probability estimation.

It is known that finitely generated FI-modules over a field of characteristic 0 are Noetherian. We generalize this result to the abstract setting of an infinite EI category satisfying certain combinatorial conditions.

Inspired by the immense success of deep learning, graph neural networks (GNNs) are widely used to learn powerful node representations and have demonstrated promising performance on different graph learning tasks. However, most real-world graphs often come with high-dimensional and sparse node features, rendering the le…

FIS-GAN uses importance sampling in GANs to speed up training.

Church-Ellenberg-Farb used the language of FI-modules to prove that the cohomology of certain sequences of hyperplane arrangements with S_n-actions satisfies representation stability. Here we lift their results to the level of the arrangements themselves, and define when a collection of arrangements is "finitely genera…

Representation stability is a phenomenon whereby the structure of certain sequences $X_n$ of spaces can be seen to stabilize when viewed through the lens of representation theory. In this paper I describe this phenomenon and sketch a framework, the theory of FI-modules, that explains the mechanism behind it.

This paper proves some results on negative gradient dynamics of Morse functions on Hilbert manifolds. It contains the compactness of flow lines, manifold structures of certain compacti- fied moduli spaces, orientation formulas, and CW structures of the underlying manifolds.

The groups $Γ_{n,s}$ are defined in terms of homotopy equivalences of certain graphs, and are natural generalisations of $\mbox{Out}(F_n)$ and $\mbox{Aut}(F_n)$. They have appeared frequently in the study of free group automorphisms, for example in proofs of homological stability in [8,9] and in the proof that Out$(F_n…

Study identifies key parameters and input dimensions making LLMs and VLMs brittle.

Frequent Itemsets (FIs) mining is a fundamental primitive in data mining. It requires to identify all itemsets appearing in at least a fraction $θ$ of a transactional dataset $\mathcal{D}$. Often though, the ultimate goal of mining $\mathcal{D}$ is not an analysis of the dataset \emph{per se}, but the understanding of …

For k >= 1, let Torelli_g^1(k) be the k-th term in the Johnson filtration of the mapping class group of a genus g surface with one boundary component. We prove that for all k, there exists some G_k >= 0 such that Torelli_g^1(k) is generated by elements which are supported on subsurfaces whose genus is at most G_k. We a…

TensorFI injects faults in TensorFlow programs to assess their reliability.

In this paper, we present a new location fingerprinting database comprised of Wi-Fi received signal strength (RSS) and geomagnetic field intensity measured with multiple devices at a multi-floor building in Xi'an Jiatong-Liverpool University, Suzhou, China. We also provide preliminary results of localization and trajec…

For a topological space $X$, we introduce a criterion for the $\rm FI$ module $H^i({\rm Conf}_n(X))$ to be finitely generated and give several applications. For instance, if $C$ is a finite connected $CW$ complex, then $X = C \times \mathbb{R}^2$ satisfies the criterion. Our main tool is a spectral sequence that we der…

In this paper, we study local solutions F=(F1,..,Fn) of a general functional equation of the form F1(U1(x,y))+....+Fn(Un(x,y))=0. A such equation will be called an ``abelian functional equation'' (Afe). We will restrict ourselves to the case when the inner functions Ui's are real rational functions. First we prove that…

Detects synchronized behavior in streaming data.