arXiv subjects

Md. Shamsuzzoha Bayzid

Publications and source records attributed to Md. Shamsuzzoha Bayzid.

6 recordsLinked to original sources

arXiv2026

On Threshold Pairwise Compatibility Graphs

Pairwise Compatibility Graphs (PCGs) form a tree-metric graph class that originated in phylogeny and has since attracted sustained interest in graph theory. Several natural generalizations have been proposed in order to overcome the expressive limitations of classical PCGs, including $k$-interval-PCGs, $k$-OR-PCGs, and $k$-AND-PCGs. In this paper, we introduce $(k,t)$-threshold-PCGs, a threshold-based framework that unifies these generalized notions: adjacency is determined by whether at least $t$ among $k$ underlying PCG predicates accept the vertex pair. We investigate the expressive power of this model from both constructive and asymptotic viewpoints. On the positive side, we show that every graph on $n$ vertices is a $(n,t)$-threshold-PCG for every $1 \le t \le n$. On the negative side, we prove that for every fixed pair $(k,t)$, the class of $(k,t)$-threshold-PCGs is asymptotically rare among all graphs. As a consequence, we obtain sharp separations from previously studied models, including a strict expressive gap relative to $k$-interval-PCGs. We also study explicit obstruction families through incidence graphs and derive additional structural consequences for the conjunction case, including the strictness of the $k$-AND-PCG hierarchy and the failure of closure under complement.

math.CO↗

arXiv2026

Pairwise Compatibility Representations of Multidimensional Grid Graphs

Pairwise compatibility graphs (PCGs) represent graph adjacency by an interval of leaf-to-leaf distances in a weighted tree. We study grid graphs under the PCG model and two natural extensions: multi-interval PCGs and OR-PCGs. First, we prove that every $d$-dimensional grid graph is a $(d-1)$-interval-PCG. The construction decomposes the grid into hyperplanes of constant coordinate sum and uses a large-base encoding so that distances between consecutive hyperplanes identify the coordinate direction of an edge. A pair of nearby code values is then merged into one interval, reducing the number of intervals from $d$ to $d-1$. Second, we prove that every $d$-dimensional grid is a $\lceil d/2\rceil$-OR-PCG by grouping coordinate directions into pairs; each paired-direction graph is a disjoint union of two-dimensional grid graphs and is therefore a PCG. Finally, an exact tree-metric satisfiability computation shows that $P_3\square P_3\square P_3$ is not a PCG. Consequently, the minimum number of intervals sufficient for all three-dimensional grid graphs is exactly two, resolving a previously posed open problem. The same obstruction shows that the OR-PCG bound is tight in dimension three and implies that every grid with at least three factors of order at least three is not a PCG.

math.CO↗

arXiv2026

DeCoDrift: Stabilizing Decoder Coupling in Closed-Loop Foundation Segmentation

Foundation segmentation models such as Segment Anything Model (SAM) are now routinely used in iterative pipelines, where each predicted mask is fed back as the next prompt. This practice turns segmentation into a closed-loop dynamical process, yet the decoder-level behavior of these systems remains largely unexamined. We show that this feedback loop can induce a previously overlooked failure mode, decoder coupling drift, in which the mask decoder's cross-attention progressively loses alignment with the target object, causing errors to accumulate across iterations. We study this phenomenon by instrumenting SAM's mask decoder and deriving ground-truth-free measures of prompt-image coupling, attention stability, and temporal consistency. On volumetric electron microscopy data, these decoder-internal signals reveal that standard iterative prompting systematically degrades attention alignment and temporal coherence relative to oracle-anchored feedback. We then formalize iterative prompting as a discrete-time dynamical system and show how proximal anchoring reduces error amplification in the feedback loop. Building on this analysis, we introduce DeCoDrift, a training-free inference-time stabilization framework that constrains prompt updates and preserves decoder coupling across iterations. Across extensive experiments, DeCoDrift consistently improves attention stability, temporal coherence, and segmentation quality over standard iterative prompting, without retraining or ground-truth supervision. More broadly, our results show that decoder-internal dynamics are not merely diagnostic: they provide actionable signals for stabilizing foundation segmentation models in closed-loop use.

cs.CV↗

arXiv2021

3D-FFS: Faster 3D object detection with Focused Frustum Search in sensor fusion based networks

In this work we propose 3D-FFS, a novel approach to make sensor fusion based 3D object detection networks significantly faster using a class of computationally inexpensive heuristics. Existing sensor fusion based networks generate 3D region proposals by leveraging inferences from 2D object detectors. However, as images have no depth information, these networks rely on extracting semantic features of points from the entire scene to locate the object. By leveraging aggregated intrinsic properties (e.g. point density) of point cloud data, 3D-FFS can substantially constrain the 3D search space and thereby significantly reduce training time, inference time and memory consumption without sacrificing accuracy. To demonstrate the efficacy of 3D-FFS, we have integrated it with Frustum ConvNet (F-ConvNet), a prominent sensor fusion based 3D object detection model. We assess the performance of 3D-FFS on the KITTI dataset. Compared to F-ConvNet, we achieve improvements in training and inference times by up to 62.80% and 58.96%, respectively, while reducing the memory usage by up to 58.53%. Additionally, we achieve 0.36%, 0.59% and 2.19% improvements in accuracy for the Car, Pedestrian and Cyclist classes, respectively. 3D-FFS shows a lot of promise in domains with limited computing power, such as autonomous vehicles, drones and robotics where LiDAR-Camera based sensor fusion perception systems are widely used.

cs.CV↗

arXiv2020

Align-gram : Rethinking the Skip-gram Model for Protein Sequence Analysis

Background: The inception of next generations sequencing technologies have exponentially increased the volume of biological sequence data. Protein sequences, being quoted as the `language of life', has been analyzed for a multitude of applications and inferences. Motivation: Owing to the rapid development of deep learning, in recent years there have been a number of breakthroughs in the domain of Natural Language Processing. Since these methods are capable of performing different tasks when trained with a sufficient amount of data, off-the-shelf models are used to perform various biological applications. In this study, we investigated the applicability of the popular Skip-gram model for protein sequence analysis and made an attempt to incorporate some biological insights into it. Results: We propose a novel $k$-mer embedding scheme, Align-gram, which is capable of mapping the similar $k$-mers close to each other in a vector space. Furthermore, we experiment with other sequence-based protein representations and observe that the embeddings derived from Align-gram aids modeling and training deep learning models better. Our experiments with a simple baseline LSTM model and a much complex CNN model of DeepGoPlus shows the potential of Align-gram in performing different types of deep learning applications for protein sequence analysis.

q-bio.QM↗

arXiv2015

Weighted Statistical Binning: enabling statistically consistent genome-scale phylogenetic analyses

Because biological processes can make different loci have different evolutionary histories, species tree estimation requires multiple loci from across the genome. While many processes can result in discord between gene trees and species trees, incomplete lineage sorting (ILS), modeled by the multi-species coalescent, is considered to be a dominant cause for gene tree heterogeneity. Coalescent-based methods have been developed to estimate species trees, many of which operate by combining estimated gene trees, and so are called summary methods. Because summary methods are generally fast, they have become very popular techniques for estimating species trees from multiple loci. However, recent studies have established that summary methods can have reduced accuracy in the presence of gene tree estimation error, and also that many biological datasets have substantial gene tree estimation error, so that summary methods may not be highly accurate on biologically realistic conditions. Mirarab et al. (Science 2014) presented the statistical binning technique to improve gene tree estimation in multi-locus analyses, and showed that it improved the accuracy of MP-EST, one of the most popular coalescent-based summary methods. Statistical binning, which uses a simple statistical test for combinability and then uses the larger sets of genes to re-calculate gene trees, has good empirical performance, but using statistical binning within a phylogenomics pipeline does not have the desirable property of being statistically consistent. We show that weighting the recalculated gene trees by the bin sizes makes statistical binning statistically consistent under the multispecies coalescent, and maintains the good empirical performance. Thus, "weighted statistical binning" enables highly accurate genome-scale species tree estimation, and is also statistical consistent under the multi-species coalescent model.

q-bio.QM↗