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Memristive Crossbars: ALU Design, Testing, and Fault Analysis for Neuromorphic Applications
No full textIn 1971, Professor Leon Chua introduced the notion of a memristor, the fourth fundamental passive circuit component alongside resistor, capacitor, and inductor. The resistance of this two-terminal device depends on the current through it; thereby a memristor is similar to a resistor with memory. In 2008, a group of researchers at HP Labs built the first memristor successfully and demonstrated its characteristic resistance-switching behaviour. Its unique properties and compatibility with CMOS technology has made it a powerful circuit element and has significantly influenced design paradigms. Recent developments have shown that memristors are promising for designing memory and logic subsystems, which can store multiple states of memory by utilizing the analog variation of resistance in the cells. By combining CMOS components with memristor cells, hybrid systems can be created where CMOS components can perform computation-in-memory (CIM), while memristor cells can store data in a non-volatile manner. Memristor-based crossbars (MBCs) realised as a 2D-array of memristors, have been particularly effective for performing certain types of computations, such as vector-matrix multiplication (VMM) and vector outer product, which are crucial in neuromorphic computing systems. Developing practical and reliable memristive crossbar-based systems for various applications still poses significant challenges which can hinder their performance and scalability. This thesis tackles several challenges head-on, offering innovative solutions that elevate their performance, reliability, and scalability. In this thesis, we introduce novel designs for an arithmetic logic unit (ALU) that utilize differential currents passing through a hybrid-memristor crossbar network. The ALU performs integer addition, subtraction, multiplication, and logical operations in the binary domain, using both analog and digital components. Next, we envisage a 2D memristor crossbar as a network and identify certain paths that are suitable for fault sensitization. In order to optimize testing time for full-size square and rectangular memristive crossbars, we propose a path-based technique guided by maximum matching in bipartite graphs. We also employ an integer linear programming (ILP) formulation to solve the problem for a general crossbar. Finally, we present a thorough analysis of the impact of various hard faults of memristive crossbars on accuracy of different neuromorphic architectures for different datasets This study is critical as comprehending the effects of such faults and variations can enhance the reliability and efficacy of fault-tolerant memristor based neuromorphic computing systems with resource constraints. Overall, this thesis contributes to advancing memristor-based computing systems by addressing efficient ALU design, test time optimization, and analyzing the impact of faults on neuromorphic architectures. The findings provide valuable insights to improve the reliability and performance of future fault-tolerant memristor-based systems across a wide range of applications
Projective modules and complete intersection ideals over affine algebras
No full textAbstract not availabl
Some Contributions to Multiple Hypotheses Testing under Dependence
No full textLarge-scale multiple testing problems in various scientific disciplines often study correlated variables simultaneously. However, the existing literature lacks a study of the performances of FWER controlling procedures under dependence. This thesis concentrates mainly on FWER and generalized FWER controlling procedures under a correlated Gaussian sequence model framework. We establish upper bounds on Bonferroni FWER in the equicorrelated and non-negatively correlated non-asymptotic setup. We also derive similar upper bounds for the generalized FWER of the Lehmann-Romano procedure and propose an improved k-FWER controlling procedure. Towards this, we establish an inequality related to the probability that at least k out of n events occur, which extends and sharpens the classical ones. We have found that, under the non-negatively correlated setup, many classical procedures make zero rejections asymptotically as the number of hypotheses diverges. Specifically, we have shown that, under this setup, the Bonferroni and the Holm methods have zero FWER and power asymptotically. We have also established similar asymptotic zero results for the Hochberg and Hommel procedures under the equicorrelated setup. Finally, we consider the classical means-testing problem in an equicorrelated Gaussian and sequential framework. We focus on sequential test procedures that control the type I and type II familywise error probabilities at pre-specified levels. We establish that our proposed rules have the optimal expected sample sizes under every possible signal configuration asymptotically, as the two error probabilities vanish at arbitrary rates. The results in this thesis illuminate that dependence might be a blessing or a curse, subject to the type of dependence or the underlying paradigm. Several popular and widely used procedures fail to hold the FWER at a positive level asymptotically under positively correlated Gaussian frameworks. On the contrary, the expected sample size of the asymptotically optimal sequential multiple testing rule is a decreasing function in the common correlation under the equicorrelated framework. Thus, correlation plays a dual role in the classical fixed-sample size and the sequential paradigms
A control chart for monitoring images using jump location curves
No full textImage monitoring is a relatively new research area in statistics and machine learning that has wide applications in various fields including medical diagnostics and subsequently disease monitoring, satellite imaging, security systems, and so forth. In the literature, a vast majority of the methods use image intensity changes to detect out of control images. However, this approach is often unreasonable in many real-life applications where a change in contrast between the background and foreground of an image should not indicate an out of control image as long as the boundaries of the image objects remain unchanged. In this article, we propose a Shewhart-type control chart to monitor grayscale images using detected edges of the images. The central idea is to monitor the Hausdorff distance between the point-set of detected edge pixels in each image from the corresponding point-set of the estimated true in-control image. The proposed monitoring procedure should be easy to execute many real-life applications. Numerical studies show that it performs well in various types of situations in comparison with a number of competing methods
A logarithmic lower bound for the second Bohr radius
No full textThe purpose of this note is to obtain an improved lower bound for the multidimensional Bohr radius introduced by L. Aizenberg (2000, Proceedings of the American Mathematical Society 128, 1147-1155), by means of a rather simple argument
A new paratypothoracin aetosaur (Archosauria: Pseudosuchia) from the Upper Triassic Dharmaram Formation of India and its biostratigraphic implications
No full textThe Upper Triassic lower Dharmaram Formation of India has yielded a highly diverse archosaur-dominated fauna that included a paratypothoracin aetosaur Venkatasuchus armatum, a plateosaurian sauropodomorph Jaklapallisaurus asymmetrica, a neotheropod, and a Mystriosuchinae phytosaur. In this current contribution, we describe a new paratypothoracin aetosaur taxon, Kuttysuchus minori gen. et sp. nov., from the same horizon based on several isolated paramedian osteoderms recovered from a single fossil locality. These osteoderms are characterized by a weakly raised anterior bar with a short pointed anteromedial edge, deeply incised dorsal surface ornamentation composed of strongly radial pattern of ridges and grooves with a low density of pits surrounding a pointed pyramidal dorsal eminence placed near the posterior margin and a weakly developed ventral strut or transverse thickening. These features show similarity of the specimens to that of both Paratypothorax and Stagonolepis olenkae and strongly differentiate Kuttysuchus from the other paratypothoracin Venkatasuchus known from the same stratigraphic unit. Our phylogenetic analysis recovered Kuttysuchus as an early-diverging taxon within the clade Paratypothoracini. The rich record of paratypothoracin aetosaurs, along with that of a mystriosuchine phytosaur positively suggests a mid-to-late Norian age, though the age could be extended to the Rhaetian as suggested by previous studies. The current study considerably enhances knowledge of aetosaur diversity during the Late Triassic, particularly on Gondwana, and raises the potential of recovering a rich Gondwanan record of Paratypothoracini in future
A note on iterated maps of the unit sphere
No full textLet C(Sm) denote the set of continuous maps from the unit sphere Sm in the Euclidean space Rm+1 into itself endowed with the supremum norm. We prove that the set {fn:f∈C(Sm)andn≥2} of iterated maps is not dense in C(Sm). This, in particular, proves that the periodic points of the iteration operator of order n are not dense in C(Sm) for all n≥2, providing an alternative proof of the result that these operators are not Devaney chaotic on C(Sm) proved in Veerapazham et al. (Proc Am Math Soc 149(1):217–229, 2021)
A note on outer quantum automorphisms of finite dimensional von Neumann algebras
No full textThis is part of an ongoing project of formulating notion(s) of quantum group of outer automorphisms of a C∗ or von Neumann algebra. Motivated by the fact that the group of outer automorphism of a II1 factor can be viewed as a subgroup of the group of group-like or invertible objects in the category of Hilbert bimodules of finite ranks, we explore a natural class of objects in the bimodule category of a finite dimensional (i.e. direct sum of matrix algebras) von Neumann algebra A which may come from the (co-action) of a discrete quantum group. In particular, we prove that any discrete quantum group giving an outer quantum symmetry on A in a sense defined by us must be a finite dimensional quantum group. We relate the analysis of such quantum groups or the corresponding fusion rings with certain combinatorial objects involving matrices with nonnegative integer entries and do some explicit computations in a few simple examples
Appraisal of Heavy Metal Risk Hazards of Eisenia fetida-Mediated Steel Slag Vermicompost on Oryza sativa L.: Insights from Agro-Scale Inspection and Machine Learning Analytics
No full textThe steel industry drives world economic growth, yet it generates heavy metal-rich steel slag, which jeopardizes the environment. The utilization of vermi-technology is essential for the sustainable transformation of toxic steel waste slag (SW) into organic amendments, although field-scale use of vermiprocessed SW remains unexplored. To bridge the gap, this study evaluated the efficacy of vermiprocessed SW as an organic supplement for rice field cultivation, focusing on heavy metal (HM) bioavailability, human health risk, and yield in comparison to raw slag and NPK fertilizer. The results indicated a considerable decrease in the bioavailable fraction of heavy metals in T4 (1:1 SW vermicompost 50% + 50% fertilizer). In treatments, T9 (100% SW) and T10 (50% SW + 50% fertilizer) (FIAM) free ion activity modeling confirmed grain absorption of HMs, and the FIAM HQ values indicated the health risk for the direct application of steel slag waste on the field. The risk factor evaluation of HMs’ presence in treatments T9 and T10 established the possible cancer risk for living beings. Similarly, machine learning models like SOBOL sensitivity analysis and artificial neural networks revealed potential threats associated with HMs on different treatments, respectively. The correlation coefficient revealed the negative effects of bioavailable HMs on various soil microbial and enzymatic properties. Moreover, the abundant yield of rice was attributed to the combination treatment (1:1 50% + NPK 50%), which paved the way for an alternative agronomic approach based on the utilization of vermicomposted steel waste slag
Arithmetic Density and Congruences of t-Core Partitions
No full textA partition of n is called a t-core partition if none of its hook number is divisible by t. In 2019, Hirschhorn and Sellers (Bull Aust Math Soc 1:51–55, 2019) obtained a parity result for 3-core partition function a3(n) . Recently, Meher and Jindal (Arithmetic density and new congruences for 3-core 590 Partitions, 2023) proved density results for a3(n) , wherein we proved that a3(n) is almost always divisible by arbitrary power of 2 and 3. In this article, we prove that for a non-negative integer α, a3αm(n) is almost always divisible by arbitrary power of 2 and 3. Further, we prove that at(n) is almost always divisible by arbitrary power of pij, where j is a fixed positive integer and t=p1a1p2a2…pmam with primes pi≥ 5. Furthermore, by employing Radu and Seller’s approach, we obtain an algorithm and we give alternate proofs of several congruences modulo 3 and 5 for ap(n) , where p is prime number. Our results also generalizes the results in Radu and Sellers (Acta Arith 146:43–52, 2011)