arXiv subjects

Anurag Singh

Publications and source records attributed to Anurag Singh.

At least 37 records · Page 2Linked to original sources

arXiv2024

Malaria Cell Detection Using Deep Neural Networks

Malaria remains one of the most pressing public health concerns globally, causing significant morbidity and mortality, especially in sub-Saharan Africa. Rapid and accurate diagnosis is crucial for effective treatment and disease management. Traditional diagnostic methods, such as microscopic examination of blood smears, are labor-intensive and require significant expertise, which may not be readily available in resource-limited settings. This project aims to automate the detection of malaria-infected cells using a deep learning approach. We employed a convolutional neural network (CNN) based on the ResNet50 architecture, leveraging transfer learning to enhance performance. The Malaria Cell Images Dataset from Kaggle, containing 27,558 images categorized into infected and uninfected cells, was used for training and evaluation. Our model demonstrated high accuracy, precision, and recall, indicating its potential as a reliable tool for assisting in malaria diagnosis. Additionally, a web application was developed using Streamlit to allow users to upload cell images and receive predictions about malaria infection, making the technology accessible and user-friendly. This paper provides a comprehensive overview of the methodology, experiments, and results, highlighting the effectiveness of deep learning in medical image analysis.

eess.IV↗

arXiv2024

Domain Generalisation via Imprecise Learning

Out-of-distribution (OOD) generalisation is challenging because it involves not only learning from empirical data, but also deciding among various notions of generalisation, e.g., optimising the average-case risk, worst-case risk, or interpolations thereof. While this choice should in principle be made by the model operator like medical doctors, this information might not always be available at training time. The institutional separation between machine learners and model operators leads to arbitrary commitments to specific generalisation strategies by machine learners due to these deployment uncertainties. We introduce the Imprecise Domain Generalisation framework to mitigate this, featuring an imprecise risk optimisation that allows learners to stay imprecise by optimising against a continuous spectrum of generalisation strategies during training, and a model framework that allows operators to specify their generalisation preference at deployment. Supported by both theoretical and empirical evidence, our work showcases the benefits of integrating imprecision into domain generalisation.

cs.LG↗

arXiv2024

Exploring the Influence of Graph Operations on Zero Forcing Sets

Zero forcing in graphs is a coloring process where a colored vertex can force its unique uncolored neighbor to be colored. A zero forcing set is a set of initially colored vertices capable of eventually coloring all vertices of the graph. In this paper, we focus on the numbers $z(G; i)$, which is the number of zero forcing sets of size $i$ of the graph $G$. These numbers were initially studied by Boyer et al. where they conjectured that for any graph $G$ on $n$ vertices, $z(G; i) \leq z(P_n; i)$ for all $i \geq 1$ where $P_n$ is the path graph on $n$ vertices. The main aim of this paper is to show that several classes of graphs, including outerplanar graphs and threshold graphs, satisfy this conjecture. We do this by studying various graph operations and examining how they affect the number of zero forcing sets.

math.CO↗

arXiv2024

Bounds for the collapsibility number of a simplicial complex and non-cover complexes of hypergraphs

The collapsibility number of simplicial complexes was introduced by Wegner in order to understand the intersection patterns of convex sets. This number also plays an important role in a variety of Helly type results. We show that the non-cover complex of a hypergraph $\mathcal{H}$ is $|V(\mathcal{H)}|- γ_i(\mathcal{H})-1$-collapsible, where $γ_i(\mathcal{H})$ is the generalization of independence domination number of a graph to hypergraph. This extends the result of Choi, Kim and Park from graphs to hypergraphs. Moreover, the upper bound in terms of strong independence domination number given by Kim and Kim for the Leray number of the non-cover complex of a hypergraph can be obtained as a special case of our result. In general, there can be a large gap between the collapsibility number of a complex and its well-known upper bounds. In this article, we construct a sequence of upper bounds $\mathcal{M}_k(X)$ for the collapsibility number of a simplicial complex $X$, which lie in this gap. We also show that the bound given by $\mathcal{M}_k$ is tight if the underlying complex is $k$-vertex decomposable.

math.CO↗

arXiv2024

Functionality Optimization for Singlet Fission Rate Screening in the Full-Dimensional Molecular and Intermolecular Coordinate Space

In computational chemistry, accurately predicting molecular configurations that exhibit specific properties remains a critical challenge. Its intricacies become especially evident in the study of molecular aggregates, where the light-induced functionality is tied to highly structure-dependent electronic couplings between molecules. Here, we present an efficient strategy for the targeted screening of the structural space employing a "functionality optimization" technique, in which a chosen descriptor, constrained by the ground state energy expression, is optimized. The chosen algorithmic differentiation (AD) framework allows to automatically obtain gradients without its tedious implementation. We demonstrate the effectiveness of the approach by identifying Perylene Bisiimide (PBI) dimer motifs with enhanced SF rate. Our findings reveal that certain structural modifications of the PBI monomer, such as helical twisting and bending, as well as slipped-rotated packing arrangements, can significantly increase the SF rate.

physics.comp-ph↗

arXiv2024

NewsCaption: Named-Entity aware Captioning for Out-of-Context Media

With the increasing influence of social media, online misinformation has grown to become a societal issue. The motivation for our work comes from the threat caused by cheapfakes, where an unaltered image is described using a news caption in a new but false-context. The main challenge in detecting such out-of-context multimedia is the unavailability of large-scale datasets. Several detection methods employ randomly selected captions to generate out-of-context training inputs. However, these randomly matched captions are not truly representative of out-of-context scenarios due to inconsistencies between the image description and the matched caption. We aim to address these limitations by introducing a novel task of out-of-context caption generation. In this work, we propose a new method that generates a realistic out-of-context caption given visual and textual context. We also demonstrate that the semantics of the generated captions can be controlled using the textual context. We also evaluate our method against several baselines and our method improves over the image captioning baseline by 6.2% BLUE-4, 2.96% CiDEr, 11.5% ROUGE, and 7.3% METEOR

cs.MM↗

arXiv2024

Fröberg's Theorem, vertex splittability and higher independence complexes

A celebrated theorem of Fröberg gives a complete combinatorial classification of quadratic square-free monomial ideals with a linear resolution. A generalization of this theorem to higher degree square-free monomial ideals is an active area of research. The existence of a linear resolution of such ideals often depends on the field over which the polynomial ring is defined. Hence, it is too much to expect that in the higher degree case a linear resolution can be identified purely using a combinatorial feature of an associated combinatorial structure. However, some classes of ideals having linear resolutions have been identified using combinatorial structures. In the present paper, we use the notion of $r$-independence to construct an $r$-uniform hypergraph from the given graph. We then show that when the underlying graph is co-chordal, the corresponding edge ideal is vertex splittable, a condition stronger than having a linear resolution. We use this result to explicitly compute graded Betti numbers for various graph classes. Finally, we give a different proof for the existence of a linear resolution using the topological notion of $r$-collapsibility.

math.AC↗

arXiv2023

Formation Pathways of the Spin-Correlated, Spatially Separated $^{1}$(T...T) State in the Singlet Fission Process of Perylene Diimide Stacks

For the theoretical screening of Singlet Fission (SF) rates in molecular aggregates, commonly dimer model systems are employed. However, there is experimental evidence, that the SF process proceeds from the $^{1}$(TT) state via an triplet-triplet energy transfer process to a further intermediate: a $^{1}$(T...T) state with two non-adjacent, spin-correlated triplets, which cannot be captured by the dimer models. In this work, we extend Michl's diabatic frontier orbital model to trimer systems, for which we automatically generate the diabatic two and three-center couplings using symbolic algebra. We apply this method to study the packing dependence of the $^{1}$(T...T) formation in the perylene diimide (PDI) trimer stack. We find that efficient triplet-triplet energy transfer is facilitated by structural motifs for which also significant excimer character can be observed. Furthermore, the coupling shows a local maximum for the structural motif that has been assigned to efficient $^{1}$(TT) population. Employing second order perturbation theory, we study the interference of the individual electronic pathways that arise in the PDI trimer system, allowing us to reproduce the packing dependence of the SF rates derived from the Redfield simulations in the work by Mirjani et. al. (Phys. Chem. C 2014, 118, 26, 14192-14199).

physics.chem-ph↗

arXiv2023

Čech complexes of hypercube graphs

A Čech complex of a finite simple graph $G$ is a nerve complex of balls in the graph, with one ball centered at each vertex. More precisely, let the Čech complex $\mathcal{N}(G,r)$ be the nerve of all closed balls of radius $\frac{r}{2}$ centered at vertices of $G$, where these balls are drawn in the geometric realization of the graph $G$ (equipped with the shortest path metric). The simplicial complex $\mathcal{N}(G,r)$ is equal to the graph $G$ when $r=1$, and homotopy equivalent to the graph $G$ when $r$ is smaller than half the length of the shortest loop in $G$. For higher values of $r$, the topology of $\mathcal{N}(G,r)$ is not well-understood. We consider the $n$-dimensional hypercube graphs $\mathbb{I}_n$ with $2^n$ vertices. Our main results are as follows. First, when $r=2$, we show that the Čech complex $\mathcal{N}(\mathbb{I}_n,2)$ is homotopy equivalent to a wedge of 2-spheres for all $n\ge 1$, and we count the number of 2-spheres appearing in this wedge sum. Second, when $r=3$, we show that $\mathcal{N}(\mathbb{I}_n,3)$ is homotopy equivalent to a simplicial complex of dimension at most 4, and that for $n\ge 4$ the reduced homology of $\mathcal{N}(\mathbb{I}_n, 3)$ is nonzero in dimensions 3 and 4, and zero in all other dimensions. Finally, we show that for all $n\ge 1$ and $r\ge 0$, the inclusion $\mathcal{N}(\mathbb{I}_n, r)\hookrightarrow \mathcal{N}(\mathbb{I}_n, r+2)$ is null-homotopic, providing a bound on the length of bars in the persistent homology of Čech complexes of hypercube graphs.

math.CO↗

arXiv2023

Dyck paths, binary words, and Grassmannian permutations avoiding an increasing pattern

A permutation is called Grassmannian if it has at most one descent. The study of pattern avoidance in such permutations was initiated by Gil and Tomasko in 2021. We continue this work by studying Grassmannian permutations that avoid an increasing pattern. In particular, we count the Grassmannian permutations of size $m$ avoiding the identity permutation of size $k$, thus solving a conjecture made by Weiner. We also refine our counts to special classes such as odd Grassmannian permutations and Grassmannian involutions. We prove most of our results by relating Grassmannian permutations to Dyck paths and binary words.

math.CO↗

arXiv2023

Homomorphism complexes, reconfiguration, and homotopy for directed graphs

The neighborhood complex of a graph was introduced by Lovász to provide topological lower bounds on chromatic number. More general homomorphism complexes of graphs were further studied by Babson and Kozlov. Such `Hom complexes' are also related to mixings of graph colorings and other reconfiguration problems, as well as a notion of discrete homotopy for graphs. Here we initiate the detailed study of Hom complexes for directed graphs (digraphs). For any pair of digraphs graphs $G$ and $H$, we consider the polyhedral complex $\text{Hom}(G,H)$ that parametrizes the directed graph homomorphisms $f: G \rightarrow H$. Hom complexes of digraphs have applications in the study of chains in graded posets and cellular resolutions of monomial ideals. We study examples of directed Hom complexes and relate their topological properties to certain graph operations including products, adjunctions, and foldings. We introduce a notion of a neighborhood complex for a digraph and prove that its homotopy type is recovered as the Hom complex of homomorphisms from a directed edge. We establish a number of results regarding the topology of directed neighborhood complexes, including the dependence on directed bipartite subgraphs, a digraph version of the Mycielski construction, as well as vanishing theorems for higher homology. The Hom complexes of digraphs provide a natural framework for reconfiguration of homomorphisms of digraphs. Inspired by notions of directed graph colorings we study the connectivity of $\text{Hom}(G,T_n)$ for $T_n$ a tournament. Finally, we use paths in the internal hom objects of digraphs to define various notions of homotopy, and discuss connections to the topology of Hom complexes.

math.CO↗

arXiv2023

Subsequence frequency in binary words

The numbers we study in this paper are of the form $B_{n, p}(k)$, which is the number of binary words of length $n$ that contain the word $p$ (as a subsequence) exactly $k$ times. Our motivation comes from the analogous study of pattern containment in permutations. In our first set of results, we obtain explicit expressions for $B_{n, p}(k)$ for small values of $k$. We then focus on words $p$ with at most $3$ runs and study the maximum number of occurrences of $p$ a word of length $n$ can have. We also study the internal zeros in the sequence $(B_{n, p}(k))_{k \geq 0}$ for fixed $n$ and discuss the unimodality and log-concavity of such sequences.

math.CO↗

arXiv2023

Chordal graphs, higher independence and vertex decomposable complexes

Given a simple undirected graph $G$ there is a simplicial complex $\mathrm{Ind}(G)$, called the independence complex, whose faces correspond to the independent sets of $G$. This is a well studied concept because it provides a fertile ground for interactions between commutative algebra, graph theory and algebraic topology. One of the line of research pursued by many authors is to determine the graph classes for which the associated independence complex is Cohen-Macaulay. For example, it is known that when $G$ is a chordal graph the complex $\mathrm{Ind}(G)$ is in fact vertex decomposable, the strongest condition in the Cohen-Macaulay ladder. In this article we consider a generalization of independence complex. Given $r\geq 1$, a subset of the vertex set is called $r$-independent if the connected components of the induced subgraph have cardinality at most $r$. The collection of all $r$-independent subsets of $G$ form a simplicial complex called the $r$-independence complex and is denoted by $\mathrm{Ind}_r(G)$. It is known that when $G$ is a chordal graph the complex $\mathrm{Ind}_r(G)$ has the homotopy type of a wedge of spheres. Hence it is natural to ask which of these complexes are shellable or even vertex decomposable. We prove, using Woodroofe's chordal hypergraph notion, that these complexes are always shellable when the underlying chordal graph is a tree. Further, using the notion of vertex splittable ideals we show that for caterpillar graphs the associated $r$-independence complex is vertex decomposable for all values of $r$. We also construct chordal graphs on $2r+2$ vertices such that their $r$-independence complexes are not sequentially Cohen-Macaulay for any $r \ge 2$.

math.CO↗

arXiv2022

Immunization Strategies Based on the Overlapping Nodes in Networks with Community Structure

Understanding how the network topology affects the spread of an epidemic is a main concern in order to develop efficient immunization strategies. While there is a great deal of work dealing with the macroscopic topological properties of the networks, few studies have been devoted to the influence of the community structure. Furthermore, while in many real-world networks communities may overlap, in these studies non-overlapping community structures are considered. In order to gain insight about the influence of the overlapping nodes in the epidemic process we conduct an empirical evaluation of basic deterministic immunization strategies based on the overlapping nodes. Using the classical SIR model on a real-world network with ground truth overlapping community structure we analyse how immunization based on the membership number of overlapping nodes (which is the number of communities the node belongs to) affect the largest connected component size. Comparison with random immunization strategies designed for networks with non-overlapping community structure show that overlapping nodes play a major role in the epidemic process.

cs.SI↗

arXiv2022

Pred&Guide: Labeled Target Class Prediction for Guiding Semi-Supervised Domain Adaptation

Semi-supervised domain adaptation aims to classify data belonging to a target domain by utilizing a related label-rich source domain and very few labeled examples of the target domain. Here, we propose a novel framework, Pred&Guide, which leverages the inconsistency between the predicted and the actual class labels of the few labeled target examples to effectively guide the domain adaptation in a semi-supervised setting. Pred&Guide consists of three stages, as follows (1) First, in order to treat all the target samples equally, we perform unsupervised domain adaptation coupled with self-training; (2) Second is the label prediction stage, where the current model is used to predict the labels of the few labeled target examples, and (3) Finally, the correctness of the label predictions are used to effectively weigh source examples class-wise to better guide the domain adaptation process. Extensive experiments show that the proposed Pred&Guide framework achieves state-of-the-art results for two large-scale benchmark datasets, namely Office-Home and DomainNet.

cs.CV↗

arXiv2022

The Borsuk-Ulam theorem for planar polygon spaces

The moduli space of planar polygons with generic side lengths is a closed, smooth manifold. Mapping a polygon to its reflected image across the $X$-axis defines a fixed-point-free involution on these moduli spaces, making them into free $\mathbb{Z}_2$-spaces. There are some important numerical parameters associated with free $\mathbb{Z}_2$-spaces, like index and coindex. In this paper, we compute these parameters for some moduli spaces of polygons. We also determine for which of these spaces a generalized version of the Borsuk-Ulam theorem hold. Moreover, we obtain a formula for the Stiefel-Whitney height in terms of the the genetic code, a combinatorial data associated with side lengths.

math.AT↗

arXiv2022

The topology of independence complexes of square grids

The independence complex of a graph G is a simplicial complex whose simplices are the independent sets in G. In the last couple of decades, the independence complexes of square grids (with various boundary conditions) have gained much attention because of their connections with the hard square model from statistical physics. In this article, we prove that if G is an $m\times n$ grid with open or cylindrical boundary condition then its independence complex is homotopy equivalent to a wedge of spheres. A part of this result settles a conjecture of Iriye.

math.CO↗

arXiv2022

Pattern avoidance of $[4,k]$-pairs in circular permutations

The study of pattern avoidance in linear permutations has been an active area of research for almost half a century now, starting with the work of Knuth in 1973. More recently, the question of pattern avoidance in circular permutations has gained significant attention. In 2002-03, Callan and Vella independently characterized circular permutations avoiding a single permutation of size $4$. Building on their results, Domagalski et al. studied circular pattern avoidance for multiple patterns of size $4$. In this article, our main aim is to study circular pattern avoidance of $[4,k]$-pairs, i.e., circular permutations avoiding one pattern of size 4 and another of size $k$. We do this by using well-studied combinatorial objects to represent circular permutations avoiding a single pattern of size $4$. In particular, we obtain upper bounds for the number of Wilf equivalence classes of $[4,k]$-pairs. Moreover, we prove that the obtained bound is tight when the pattern of size $4$ in consideration is $[1342]$. Using ideas from our general results, we also obtain a complete characterization of the avoidance classes for $[4,5]$-pairs.

math.CO↗