22 research outputs found
Hyman Bass and Ubiquity: Gorenstein Rings
No full textThis paper is based on a talk given by the author in October, 1997 at a conference in Columbia University in celebration of Hyman Bass's 65th birthday. The paper details some of the history of Gorenstein rings and their uses
Studies on Depth and Torsion in Tensor Products of Modules
No full textThis dissertation represents an in-depth exploration of two distinct yet interconnected research topics within commutative algebra: one centered around a conjecture of Huneke and R. Wiegand and the other concerns a depth inequality of Auslander. It consists of the following three papers as well as the author\u27s work under the direction of Professor Olgur Celikbas: Remarks on a conjecture of Huneke and Wiegand and the vanishing of (co)homology, Journal of Mathematical Society of Japan Advance Publication. (joint work with Olgur Celikbas, Hiroki Matsui, and Arash Sadeghi). An extension of a depth inequality of Auslander, Taiwanese Journal of Mathematics, volume 1, no. 1, pages 1-24 (2022). (joint work with Olgur Celikbas and Hiroki Matsui). On the depth and reflexivity of tensor products, Journal of Algebra, volume 606, pages 916-932 (2022). (joint work with Olgur Celikbas and Hiroki Matsui).
The first research topic of this thesis centers around the Huneke-Wiegand Conjecture, which has been a long-standing problem. Building upon the foundational work of Huneke and R. Wiegand, and O. Celikbas, we provide affirmative results for this conjecture in specific cases. In particular, we establish results for 2-periodic modules over local domains. Following the publication of the first paper, the author extended the affirmative result for the conjecture of Huneke and Wiegand to 2-periodic modules over local rings, as well as 4-periodic modules over Gorenstein rings. This thesis also provides a condition for which the conjecture holds for any periodic module. Our goal is to offer a comprehensive understanding of the Huneke-Wiegand Conjecture and potentially uncover new insights into the nature of this conjecture.
The second research topic focuses on a characteristic property of Tor-rigid modules, that is, each regular sequence of a module is also a regular sequence of its underlying ring. This characteristic is equivalent to a depth inequality, which is known as the Auslander\u27s Inequality. By thoroughly examining this inequality, we proceed to extend it in two distinct forms: a natural extension and a syzygy extension. These extensions allow us to explore the conditions under which the extended inequalities hold, thereby providing new insights into the Auslander\u27s Inequality and its far-reaching implications. Moreover, this thesis goes beyond the theoretical exploration. It includes a practical application of the extended inequalities. By employing these extended inequalities, we are able to address a specific problem related to the Auslander Inequality, presenting an innovative solution and further highlighting the practical significance of our research findings
Lectures on Local Cohomology
No full textThis article is based on five lectures the author gave during the summer school, Interactions between Homotopy Theory and Algebra, from July 26–August 6, 2004, held at the University of Chicago, organized by Lucho Avramov, Dan Christensen, Bill Dwyer, Mike Mandell, and Brooke Shipley. These notes introduce basic concepts concerning local cohomology, and use them to build a proof of a theorem Grothendieck concerning the connectedness of the spectrum of certain rings. Several applications are given, including a theorem of Fulton and Hansen concerning the connectedness of intersections of algebraic varieties. In an appendix written by Amelia Taylor, an another application is given to prove a theorem of Kalkbrenner and Sturmfels abou
Placebo and nocebo effects in gambling disorder pharmacological trials: a meta-analysis
No full textBackground: placebo and nocebo effects are widely reported across psychiatric conditions, yet have seldom been examined in the context of gambling disorder. Through meta-analysis, we examined placebo effects, their moderating factors, and nocebo effects, from available randomised, controlled pharmacological clinical trials in gambling disorder.Methods: we searched, up to 19 February 2024, a broad range of databases, for double-blind randomised controlled trials (RCTs) of medications for gambling disorder. Outcomes were gambling symptom severity and quality of life (for efficacy), and drop outs due to medication side effects in the placebo arms.Results:We included 16 RCTs (n = 833) in the meta-analysis. The overall effect size for gambling severity reduction in the placebo arms was 1.18 (95%CI 0.91–1.46) and for quality of life improvement was 0.63 (0.42-0.83). Medication class, study sponsorship, trial duration, baseline severity of gambling and publication year significantly moderated effect sizes for at least some of these outcome measures. Author conflict of interest, placebo run-in, gender split, severity scale choice, age of participants or unbalanced randomisation did not moderate effect sizes. Nocebo effects leading to drop out from the trial were observed in 6% of participants in trials involving antipsychotics, while this was less for other medication types.Conclusion: placebo effects in trials of pharmacological treatment of gambling disorder are large, and there are several moderators of this effect. Nocebo effects were measureable and may be influenced by medication class being studied. Practical implications of these new findings for the field are discussed, along with recommendations for future clinical trials.<br/
Placebo and nocebo effects in gambling disorder pharmacological trials: A meta-analysis
No full textBackground: Placebo and nocebo effects are widely reported across psychiatric conditions, yet have seldom been examined in the context of gambling disorder. Through meta-analysis, we examined placebo effects, their moderating factors, and nocebo effects, from available randomised, controlled pharmacological clinical trials in gambling disorder. Methods: We searched, up to 19 February 2024, a broad range of databases, for double-blind randomised controlled trials (RCTs) of medications for gambling disorder. Outcomes were gambling symptom severity and quality of life (for efficacy), and drop outs due to medication side effects in the placebo arms. Results: We included 16 RCTs (n = 833) in the meta-analysis. The overall effect size for gambling severity reduction in the placebo arms was 1.18 (95%CI 0.91-1.46) and for quality of life improvement was 0.63 (0.42-0.83). Medication class, study sponsorship, trial duration, baseline severity of gambling and publication year significantly moderated effect sizes for at least some of these outcome measures. Author conflict of interest, placebo run-in, gender split, severity scale choice, age of participants or unbalanced randomisation did not moderate effect sizes. Nocebo effects leading to drop out from the trial were observed in 6% of participants in trials involving antipsychotics, while this was less for other medication types. Conclusion: Placebo effects in trials of pharmacological treatment of gambling disorder are large, and there are several moderators of this effect. Nocebo effects were measureable and may be influenced by medication class being studied. Practical implications of these new findings for the field are discussed, along with recommendations for future clinical trials
: Development of a Tool to Author Interactive, Multimedia, Computer‐Based Patient Simulations
No full textRisk factor analysis for fast track protocol failure
No full textBackground: The introduction of fast-track treatment procedures following cardiac surgery has significantly shortened hospitalisation times in intensive care units (ICU). Readmission to intensive care units is generally considered a negative quality criterion. The aim of this retrospective study is to statistically analyse risk factors and predictors for re-admission to the ICU after a fast-track patient management program.
Methods: 229 operated patients (67 ± 11 years, 75% male, BMI 27 ± 3, 6/2010-5/2011) with use of extracorporeal circulation (70 ± 31 min aortic crossclamping, CABG 62%) were selected for a preoperative fast-track procedure (transfer on the day of surgery to an intermediate care (IMC) unit, stable circulatory conditions, extubated). A uni- and multivariate analysis were performed to identify independent predictors for re-admission to the ICU.
Results: Over the 11-month study period, 36% of all preoperatively declared fast-track patients could not be transferred to an IMC unit on the day of surgery (n = 77) or had to be readmitted to the ICU after the first postoperative day (n = 4). Readmission or ICU stay signifies a dramatic worsening of the patient outcome (mortality 0/10%, mean hospital stay 10.3 ± 2.5/16.5 ± 16.3, mean transfusion rate 1.4 ± 1,7/5.3 ± 9.1). Predicators for failure of the fast-track procedure are a preoperative ASA class > 3, NYHA class > III and an operation time >267 min ± 74. The significant risk factors for a major postoperative event (= low cardiac output and/or mortality and/or renal failure and/or re-thoracotomy and/or septic shock and/or wound healing disturbances and/or stroke) are a poor EF (OR 2.7 CI 95% 0.98-7.6) and the described ICU readmission (OR 0.14 CI95% 0.05-0.36).
Conclusion: Re-admission to the ICU or failure to transfer patients to the IMC is associated with a high loss of patient outcome. The ASA > 3, NYHA class > 3 and operation time >267 minutes are independent predictors of fast track protocol failure
CASE STUDIES for Dentistry®: Development of a Tool to Author Interactive, Multimedia, Computer-Based Patient Simulations
No full textComputer-based patient simulations have been used to enhance the dental curriculum since the 1980s. This article describes the development of CASE STUDIES for Dentistry (CSD), a patient case simulation building template, developed at Virginia Commonwealth University, with which authors who have no programming expertise can create realistic, effective, interactive multimedia patient simulations by entering their own information and images into a straightforward, fill in the blanks interface. This program was written with Authorware, by Macromedia Inc. Design considerations included emphasis on information collection and analysis, synthesis of collected information, hypothesis proposal and testing, diagnosis, and treatment planning. The program consists of easily accessible interfaces for both authors and students. Authors build simulated patients using typed-in text and their own images. Faculty can build computer-based simulated patients so that students can immediately practice what they learn in class within a simulated doctor-patient relationship. CSD allows building simulations ranging from simple to complex patients in multiple disciplines. Robust feedback and other features allow students to learn both process and content in a self-directed, interactive environment
Gorenstein hilbert coefficients
No full textWe prove upper and lower bounds for all the coefficients in the Hilbert polynomial of a graded Gorenstein algebra S = R-I with a quasi-pure resolution over R. The bounds are in terms of the minimal and the maximal shifts in the resolution of R. These bounds are analogous to the bounds for the multiplicity found in [9] and are stronger than the bounds for the Cohen Macaulay algebras found in [5]. © 2013 Rocky Mountain Mathematics Consortium.Boij M, 2008, J LOND MATH SOC, V78, P85, DOI 10.1112-jlms-jdn013; Bruns W., 1993, CAMBR STUD ADV MATH, V39; PESKINE C, 1974, CR ACAD SCI A MATH, V278, P1421; Eisenbud D, 2009, J AM MATH SOC, V22, P859; El Khoury S., 2011, INT J ALG, V5, P679; Herzog J, 1998, T AM MATH SOC, V350, P2879, DOI 10.1090-S0002-9947-98-02096-0; Herzog J, 2009, P AM MATH SOC, V137, P487; HUNEKE C, 1985, CAN J MATH, V37, P1149, DOI 10.4153-CJM-1985-062-4; Srinivasan H, 1998, J ALGEBRA, V208, P425, DOI 10.1006-jabr.1998.74130
On the embedded primes of the Mayr-Meyer ideals
No full textThis paper investigates the doubly exponential ideal membership property of the Mayr-Meyer ideals. These ideals were first defined by Mayr and Meyer in [MM], where their doubly exponential behavior was first observed, and subsequently these ideals were further analyzed by Bayer and Stillman [BS], Demazure [D], Koh [K]. The analysis in this paper, as well in as [S1, S2], is from the point of view of the structure of the associated primes. The motivation came from a question raised by Bayer, Huneke and Stillman of whether the doubly exponential behavior is due to the number of minimal and/or associated primes, or to the nature of one of them. The complete answer for the case of the Mayr-Meyer ideals with the fewest possible number of variables (the case n = 1) is given in [S1]. For all other cases, it was proved in [S2] that the doubly exponential behavior is due to the embedded primes. [S2] also computed all the minimal components, the minimal primes, their heights, and the intersection of all the minimal components. This paper provides partial answers about the embedded primes. In the analysis a new family of ideals emerges which also has the doubly exponential ideal membership property. This new family and its associated primes are further analyzed in [S3]. The main tool used below for finding the associated primes of the Mayr-Meyer ideals are various short exact sequences, and the fact that the associated primes of the middle module in a short exact sequence is contained in the union of the associated primes of the The author thanks the NSF for partial support on grants DMS-0073140 and DMS997056
