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Imran Ahmed

Publications and source records attributed to Imran Ahmed.

15 recordsLinked to original sources
arXiv2023

Cohen-Macaulayness of Total Simplicial Complexes

We first construct the total simplicial complex (TSC) of a finite simple graph $G$ in order to generalize the total graph $T(G)$. We show that $Δ_T(G)$ is not Cohen-Macaulay (CM) in general. For a connected graph $G$, we prove that the TSC is Buchsbaum. We demonstrate that the vanishing of first homology group of TSC associated to a connected graph $G$ is both a necessary and sufficient condition for it to be CM. We find the primary decomposition of the TSC associated to a family of friendship graphs $F_{5n+1}$ and prove it to be CM.

math.CO↗
arXiv2020

Single Storage Semi-Global Matching for Real Time Depth Processing

Depth-map is the key computation in computer vision and robotics. One of the most popular approach is via computation of disparity-map of images obtained from Stereo Camera. Semi Global Matching (SGM) method is a popular choice for good accuracy with reasonable computation time. To use such compute-intensive algorithms for real-time applications such as for autonomous aerial vehicles, blind Aid, etc. acceleration using GPU, FPGA is necessary. In this paper, we show the design and implementation of a stereo-vision system, which is based on FPGA-implementation of More Global Matching(MGM). MGM is a variant of SGM. We use 4 paths but store a single cumulative cost value for a corresponding pixel. Our stereo-vision prototype uses Zedboard containing an ARM-based Zynq-SoC, ZED-stereo-camera / ELP stereo-camera / Intel RealSense D435i, and VGA for visualization. The power consumption attributed to the custom FPGA-based acceleration of disparity map computation required for depth-map is just 0.72 watt. The update rate of the disparity map is realistic 10.5 fps.

cs.CV↗
arXiv2019

Multisensory cues facilitate coordination of stepping movements with a virtual reality avatar

The effectiveness of simple sensory cues for retraining gait have been demonstrated, yet the feasibility of humanoid avatars for entrainment have yet to be investigated. Here, we describe the development of a novel method of visually cued training, in the form of a virtual partner, and investigate its ability to provide movement guidance in the form of stepping. Real stepping movements were mapped onto an avatar using motion capture data. The trajectory of one of the avatar step cycles was then accelerated or decelerated by 15% to create a perturbation. Healthy participants were motion captured while instructed to step in time to the avatar's movements, as viewed through a virtual reality headset. Step onset times were used to measure the timing errors (asynchronies) between them. Participants completed either a visual-only condition, or auditory-visual with footstep sounds included. Participants' asynchronies exhibited slow drift in the Visual-Only condition, but became stable in the Auditory-Visual condition. Moreover, we observed a clear corrective response to the phase perturbation in both auditory-visual conditions. We conclude that an avatar's movements can be used to influence a person's own gait, but should include relevant auditory cues congruent with the movement to ensure a suitable accuracy is achieved.

cs.HC↗
arXiv2019

Weighted Homogeneous Polynomials with Isomorphic Milnor Algebras

We recall first some basic facts on weighted homogeneous functions and filtrations in the ring $A$ of formal power series. We introduce next their analogues for weighted homogeneous diffeomorphisms and vector fields. We show that the Milnor algebra is a complete invariant for the classification of weighted homogeneous polynomials with respect to right-equivalence, i.e. change of coordinates in the source and target by diffeomorphism.

math.AG↗
arXiv2019

Invariants of Relative Right and Contact Equivalences

We study holomorphic function germs under equivalence relations that preserve an analytic variety. We show that two quasihomogeneous polynomials, not necessarily with isolated singularities, having isomorphic relative Milnor algebras are relative right equivalent. Under the condition that the module of vector fields tangent to the variety is finitely generated, we also show that the relative Tjurina algebra is a complete invariant for the classification of arbitrary function germs with respect to the relative contact equivalence. This is the relative version of a well known result by Mather and Yau.

math.AG↗
arXiv2018

DeepWheat: Estimating Phenotypic Traits from Crop Images with Deep Learning

In this paper, we investigate estimating emergence and biomass traits from color images and elevation maps of wheat field plots. We employ a state-of-the-art deconvolutional network for segmentation and convolutional architectures, with residual and Inception-like layers, to estimate traits via high dimensional nonlinear regression. Evaluation was performed on two different species of wheat, grown in field plots for an experimental plant breeding study. Our framework achieves satisfactory performance with mean and standard deviation of absolute difference of 1.05 and 1.40 counts for emergence and 1.45 and 2.05 for biomass estimation. Our results for counting wheat plants from field images are better than the accuracy reported for the similar, but arguably less difficult, task of counting leaves from indoor images of rosette plants. Our results for biomass estimation, even with a very small dataset, improve upon all previously proposed approaches in the literature.

cs.CV↗
arXiv2017

Deep Reinforcement Learning for Sepsis Treatment

Sepsis is a leading cause of mortality in intensive care units and costs hospitals billions annually. Treating a septic patient is highly challenging, because individual patients respond very differently to medical interventions and there is no universally agreed-upon treatment for sepsis. In this work, we propose an approach to deduce treatment policies for septic patients by using continuous state-space models and deep reinforcement learning. Our model learns clinically interpretable treatment policies, similar in important aspects to the treatment policies of physicians. The learned policies could be used to aid intensive care clinicians in medical decision making and improve the likelihood of patient survival.

cs.AI↗
arXiv2017

Determinacy of Determinantal Varieties

A more general class than complete intersection singularities is the class of determinantal singularities. They are defined by the vanishing of all the minors of a certain size of a $m\times n$-matrix. In this note, we consider $\mathcal{G}$-finite determinacy of matrices defining a special class of determinantal varieties. They are called essentially isolated determinantal singularities (EIDS) and were defined by Ebeling and Gusein-Zade. In this note, we prove that matrices parametrized by generic homogeneous forms of degree $d$ define EIDS. It follows that $\mathcal{G}$-finite determinacy of matrices hold in general. As a consequence, EIDS of a given type $(m,n,t)$ holds in general.

math.AG↗
arXiv2017

Spanning Simplicial Complexes of Uni-Cyclic Multigraphs

A multigraph is a nonsimple graph which is permitted to have multiple edges, that is, edges that have the same end nodes. We introduce the concept of spanning simplicial complexes $Δ_s(\mathcal{G})$ of multigraphs $\mathcal{G}$, which provides a generalization of spanning simplicial complexes of associated simple graphs. We give first the characterization of all spanning trees of a uni-cyclic multigraph $\mathcal{U}_{n,m}^r$ with $n$ edges including $r$ multiple edges within and outside the cycle of length $m$. Then, we determine the facet ideal $I_\mathcal{F}(Δ_s(\mathcal{U}_{n,m}^r))$ of spanning simplicial complex $Δ_s(\mathcal{U}_{n,m}^r)$ and its primary decomposition. The Euler characteristic is a well-known topological and homotopic invariant to classify surfaces. Finally, we device a formula for Euler characteristic of spanning simplicial complex $Δ_s(\mathcal{U}_{n,m}^r)$.

math.AT↗
arXiv2017

Characterizations of Line Simplicial Complexes

Let $G$ be a finite simple graph. The line graph $L(G)$ represents the adjacencies between edges of $G$. We define first the line simplicial complex $Δ_L(G)$ of $G$ containing Gallai and anti-Gallai simplicial complexes $Δ_Γ(G)$ and $Δ_{Γ'}(G)$ (respectively) as spanning subcomplexes. The study of connectedness of simplicial complexes is interesting due to various combinatorial and topological aspects. In Theorem 3.3, we prove that the line simplicial complex $Δ_L(G)$ is connected if and only if $G$ is connected. In Theorem 3.4, we establish the relation between Euler characteristics of line and Gallai simplicial complexes. In Section 4, we discuss the shellability of line and anti-Gallai simplicial complexes associated to various classes of graphs.

math.AT↗
arXiv2017

Topological and Algebraic Characterizations of Gallai-Simplicial Complexes

We recall first Gallai-simplicial complex $Δ_Γ(G)$ associated to Gallai graph $Γ(G)$ of a planar graph $G$. The Euler characteristic is a very useful topological and homotopic invariant to classify surfaces. In Theorems 3.2 and 3.4, we compute Euler characteristics of Gallai-simplicial complexes associated to triangular ladder and prism graphs, respectively. Let $G$ be a finite simple graph on $n$ vertices of the form $n=3l+2$ or $3l+3$. In Theorem 4.4, we prove that $G$ will be $f$-Gallai graph for the following types of constructions of $G$. Type 1. When $n=3l+2$. $G=\mathbb{S}_{4l}$ is a graph consisting of two copies of star graphs $S_{2l}$ and $S'_{2l}$ with $l\geq 2$ having $l$ common vertices. Type 2. When $n=3l+3$. $G=\mathbb{S}_{4l+1}$ is a graph consisting of two star graphs $S_{2l}$ and $S_{2l+1}$ with $l\geq 2$ having $l$ common vertices.

math.AT↗
arXiv2017

An Android Cloud Storage Apps Forensic Taxonomy

Mobile phones have been playing a very significant role in our daily activities for the last decade. With the increase need for these devices, people are now more reliant on their smartphone applications for their daily tasks and many prefer to save their mobile data on a cloud platform to access them anywhere on any device. Cloud technology is the new way for better data storage, as it offers better security, more flexibility, and mobility. Many smartphones have been investigated as subjects, objects or tools of the crime. Many of these investigations include analysing data stored through cloud storage apps which contributes to importance of cloud apps forensics on mobile devices. In this paper, various cloud Android applications are analysed using the forensics tool XRY and a forensics taxonomy for investigation of these apps is suggested. The proposed taxonomy reflects residual artefacts retrievable from 31 different cloud applications. It is expected that the proposed taxonomy and the forensic findings in this paper will assist future forensic investigations involving cloud based storage applications.

cs.CR↗
arXiv2012

Invariants of Topological Relative Right Equivalences

The constancy of the Milnor number has several characterizations which were summarized by Greuel in 1986. This paper presents a study of these characterizations in the case of families of functions with isolated singularities defined on an analytic variety.

math.AG↗
arXiv2007

Polar Cremona Transformations and Monodromy of Polynomials

Consider the gradient map associated to any non-constant homogeneous polynomial $f\in \C[x_0,...,x_n]$ of degree $d$, defined by \[ϕ_f=grad(f): D(f)\to \CP^n, (x_0:...:x_n)\to (f_0(x):...:f_n(x))\] where $D(f)=\{x\in \CP^n; f(x)\neq 0\}$ is the principal open set associated to $f$ and $f_i=\frac{\partial f}{\partial x_i}$. This map corresponds to polar Cremona transformations. In Proposition \ref{p1} we give a new lower bound for the degree $d(f)$ of $ϕ_f$ under the assumption that the projective hypersurface $V:f=0 $ has only isolated singularities. When $d(f)=1$, Theorem \ref{t4} yields very strong conditions on the singularities of $V$.

math.AG↗