Lectures on Symmetric Tensor Categories

This is an expanded version of the notes by the second author of the lectures on symmetric tensor categories given by the first author at Ohio State University in March 2019 and later at ICRA-2020 in November 2020. We review some aspects of the current state of the theory of symmetric tensor categories and discuss their applications, including ones unavailable in the literature.Comment: 34 pages, latex; v2 discusses results of the new paper [CEO], and derives stronger corollaries in the appendi

Representation Stability and Finite Orthogonal Groups

In this paper, we prove stability results about orthogonal groups over finite commutative rings where 2 is a unit. Inspired by Putman and Sam (2017), we construct a category $\mathbf{OrI}(R)$ and prove a Noetherianity theorem for the category of $\mathbf{OrI}(R)$-modules. This implies an asymptotic structure theorem for orthogonal groups. In addition, we show general homological stability theorems for orthogonal groups, with both untwisted and twisted coefficients, partially generalizing a result of Charney (1987).Comment: 21 pages, 0 figure

An efficient method to avoid path lookup in file access auditing in IO path to improve file system IO performance

One of the biggest challenges in metadata management schemes that sit outside the filesystem layer is their ability to index meaningful path information of files that are being referenced in an external system like a database or in a metadata journal file. Path to a file is a critical requirement that allows both meaningful interpretation of the locality of the file and its metadata and also secondly allows for more efficient user mode services that can transform the file or its metadata. Additionally path information is very essential in compliance systems where audit logs need to tell what happened to a file and where it is located. However when the data path is being audited from layers such as protocols, it becomes harder to reconstruct the entire path information for all the files given that the protocol layers do not directly integrate with the underlying Filesystem. The protocol layers would then need to rely on system cache to get the path data and sometimes this may not be possible making it required for the protocol to actually do an expensive reverse path walk, reconstructing the path. This actually heavily degrades the performance of the system. In this paper we discuss a mechanism that allows us to record enough information about the file using the unique ID of itself and its parent in the protocol layer such that if and when required the path information can be reconstructed based on a reliable reverse lookup in a database or a file based journal system. The idea is to have enough information to reconstruct the path at a later time and outside the system where the information was initially originated from. The paper also talks of keeping this system consistent under all conditions

Chemical patterning for the highly specific and programmed assembly of nanostructures

We have developed a new chemical patterning technique based on standard lithography-based processes to assemble nanostructures on surfaces with extraordinarily high selectivity. This patterning process is used to create patterns of aminosilane molecular layers surrounded by highly inert poly (ethylene glycol) (PEG) molecules. While the aminosilane regions facilitate nanostructure assembly, the PEG coating prevents adsorption of molecules and nanostructures, thereby priming the semiconductor substrate for the highly localized and programmed assembly of nanostructures. We demonstrate the power and versatility of this manufacturing process by building multilayered structures of gold nanoparticles attached to molecules of DNA onto the aminosilane patterns, with zero nanocrystal adsorption onto the surrounding PEG regions. The highly specific surface chemistry developed here can be used in conjunction with standard microfabrication and emerging nanofabrication technology to seamlessly integrate various nanostructures with semiconductor electronics

Intelligent Intrusion Detection System Using Genetic Algorithm

Intrusion detection is an essential and important technique in research field. One of the main challengesin the security system of large-scale high-speed networks is the detection of suspicious anomalies in network traffic patterns due to different kinds of network attack. We give attacks normally identified by intrusion detection systems. Differentiation can be done in existing intrusion detection methods and systems based on the underlying computational methods used. Intrusion detection methods started appearing in the last few years. In this paper we propose an Intrusion detection method using Genetic Algorithm (GA). In this research contribution of each of above mentioned techniques will be systematically summarized and compared that will allows us to clearly define existing research challenges, and to highlight promising new research directions

From the Albert algebra to Kac's ten-dimensional Jordan superalgebra via tensor categories in characteristic 5

Kac's ten-dimensional simple Jordan superalgebra over a field of characteristic 5 is obtained from a process of semisimplification, via tensor categories, from the exceptional simple Jordan algebra (or Albert algebra), together with a suitable order 5 automorphism. This explains McCrimmon's 'bizarre result' asserting that, in characteristic 5, Kac's superalgebra is a sort of 'degree 3 Jordan superalgebra'. As an outcome, the exceptional simple Lie superalgebra el(5;5), specific of characteristic 5, is obtained from the simple Lie algebra of type $E_8$ and an order 5 automorphism. In the process, precise recipes to obtain superalgebras from algebras in the category of representations of the cyclic group $C_p$, over a field of characteristic $p>2$, are given.Comment: 22 page

USFD at KBP 2011: Entity Linking, Slot Filling and Temporal Bounding

This paper describes the University of Sheffield's entry in the 2011 TAC KBP entity linking and slot filling tasks. We chose to participate in the monolingual entity linking task, the monolingual slot filling task and the temporal slot filling tasks. We set out to build a framework for experimentation with knowledge base population. This framework was created, and applied to multiple KBP tasks. We demonstrated that our proposed framework is effective and suitable for collaborative development efforts, as well as useful in a teaching environment. Finally we present results that, while very modest, provide improvements an order of magnitude greater than our 2010 attempt.Comment: Proc. Text Analysis Conference (2011