A note on sequences and y-regularity of Rees algebra

Given a graded ring $A$ and a homogeneous ideal $I$, the ideal is said to be of linear type if the Rees algebra of $I$ is isomorphic to the symmetric algebra of $I$. We examine the relations between different notions of sequences already known in literature which form ideals of linear type. We observe how the vanishing of $y$-regularity of the Rees algebra of an ideal is connected to the ideal being generated by some specific sequences. As an application of this, we discuss Koszulness and Cohen-Macaulayness of the diagonal subalgebras of Rees algebras of ideals generated by some of these sequences. We also mention Macaulay2 algorithms to check if an ideal is generated by a $d$-sequence, c-sequence, weak relative-regular sequence and for computing bi-regularities.Comment: Comments and suggestions are welcome. In version 2, subsection 2.1 has been adde

Rees algebra of Maximal Order Pfaffians and its diagonal subalgebras

Given a skew-symmetric matrix $X$, the Pfaffian of $X$ is defined as the square root of the determinant of $X$. In this article, we give the explicit defining equations of Rees algebra of Pfaffian ideal $I$ generated by maximal order Pfaffians of generic skew-symmetric matrices. We further prove that all diagonal subalgebras of the corresponding Rees algebra of $I$ are Koszul. We also look at the Rees algebra of Pfaffian ideals of linear type associated to certain sparse skew-symmetric matrices. In particular, we consider the tridiagonal matrices and identify the corresponding Pfaffian ideal to be of Gr\"obner linear type and as the vertex cover ideal of an unmixed bipartite graph. As an application of our results, we conclude that all their powers have linear resolutions.Comment: Comments and suggestions are welcom

FUZZY EXTREME LEARNING MACHINE ALGORITHM FOR MATRIX CONVERTER

This paper is focused on Fuzzy Extreme Learning Machine (ELM) algorithm based field oriented control system for induction motor fed by Matrix Converter drive. The use of fuzzy ELM algorithm based ANN Controllers in the FOC system reduces the computation time. The controller is used to compute the appropriate set of switching voltage vectors for matrix converter to achieve the maximum efficiency for any value of operating torque and motor speed. In this paper, the Matrix Converter with field oriented control system is designed using MATLAB/SIMULINK toolbox. Initially, fuzzy logic controllers are used as current and torque controllers. ELM controller is designed to replace space vector modulation circuit in the conventional field oriented control system. The three inputs to the Fuzzy ELM controller are V a * , V b * and V c * and the outputs of the ELM controller are voltage vectors for appropriate switching of matrix converter. The performance of the induction motor is tested for various reference speed and torque values. The speed and torque curves of the induction motor shows that the use of ELM controller reduces the ripples in torque and reduces the response time in the speed curve due to the fast response time of the ELM Controlle

Stock structure analysis of Splendid ponyfish Eubleekeria splendens (Cuvier, 1829) along Indian coast using truss network system

434-443Eubleekeria splendens (Cuvier, 1829) also called Splendid ponyfish, is commercially important and has wide distribution along the Indian coast. The species shows dominance along the south-west and south-east coast but there is no detailed information on the stock structure available from Indian waters. Therefore the present study focused on understanding the stock structure based on putative spawning stock. Fish samples were collected from five locations: Three from the west and two from the east coast. Twenty-four morphometric variables were measured using a box-truss network method. Principal component analysis delineated the population into east and west coast stocks. With respect to locations, each sampling unit formed separate clusters, thus representing isolated stocks. The samples from Mangaluru produced a single clustering with Kozhikode samples indicating that the morphological profiles of these two populations are homogeneous. Multiple comparisons on the factor scores indicated two independent stocks on the east coast, whereas the fishery on the west coast is replenished by a single stock on south-west coast but a separate stock on the north-west coast. Thus, information on the spatial structure of phenotypic stock makes it mandatory to understand the biology and dynamics of these isolated stocks of E. splendens separately and thereby a traditional stock assessment should be performed to estimate current resource status stock-wise in terms of biological reference points

Identification and Characterization of AES-135, a Hydroxamic Acid-Based HDAC Inhibitor That Prolongs Survival in an Orthotopic Mouse Model of Pancreatic Cancer

Pancreatic ductal adenocarcinoma (PDAC) is an aggressive, incurable cancer with a 20% 1 year survival rate. While standard-of-care therapy can prolong life in a small fraction of cases, PDAC is inherently resistant to current treatments, and novel therapies are urgently required. Histone deacetylase (HDAC) inhibitors are effective in killing pancreatic cancer cells in in vitro PDAC studies, and although there are a few clinical studies investigating combination therapy including HDAC inhibitors, no HDAC drug or combination therapy with an HDAC drug has been approved for the treatment of PDAC. We developed an inhibitor of HDACs, AES-135, that exhibits nanomolar inhibitory activity against HDAC3, HDAC6, and HDAC11 in biochemical assays. In a three-dimensional coculture model, AES-135 kills low-passage patient-derived tumor spheroids selectively over surrounding cancer-associated fibroblasts and has excellent pharmacokinetic properties in vivo. In an orthotopic murine model of pancreatic cancer, AES-135 prolongs survival significantly, therefore representing a candidate for further preclinical testing

An HLA-G/SPAG9/STAT3 axis promotes brain metastases

Brain metastases (BM) are the most common brain neoplasm in adults. Current BM therapies still offer limited efficacy and reduced survival outcomes, emphasizing the need for a better understanding of the disease. Herein, we analyzed the transcriptional profile of brain metastasis initiating cells (BMICs) at two distinct stages of the brain metastatic cascade-the "premetastatic" or early stage when they first colonize the brain and the established macrometastatic stage. RNA sequencing was used to obtain the transcriptional profiles of premetastatic and macrometastatic (non-premetastatic) lung, breast, and melanoma BMICs. We identified that lung, breast, and melanoma premetastatic BMICs share a common transcriptomic signature that is distinct from their non-premetastatic counterparts. Importantly, we show that premetastatic BMICs exhibit increased expression of HLA-G, which we further demonstrate functions in an HLA-G/SPAG9/STAT3 axis to promote the establishment of brain metastatic lesions. Our findings suggest that unraveling the molecular landscape of premetastatic BMICs allows for the identification of clinically relevant targets that can possibly inform the development of preventive and/or more efficacious BM therapies