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1. Stable multivariate generalizations of matching polynomials

Author

Amini, Nima

Subjects
Mathematics - Combinatorics, 05C31, 30C15, 05E99
Abstract

The first part of this note concerns stable averages of multivariate matching polynomials. In proving the existence of infinite families of bipartite Ramanujan $d$-coverings, Hall, Puder and Sawin introduced the $d$-matching polynomial of a graph $G$, defined as the uniform average of matching polynomials over the set of $d$-sheeted covering graphs of $G$. We prove that a natural multivariate version of the $d$-matching polynomial is stable, consequently giving a short direct proof of the real-rootedness of the $d$-matching polynomial. Our theorem also includes graphs with loops, thus answering a question of said authors. Furthermore we define a weaker notion of matchings for hypergraphs and prove that a family of natural polynomials associated to such matchings are stable. In particular this provides a hypergraphic generalization of the classical Heilmann-Lieb theorem., Comment: 15 pages, 4 figures

Published
2019

2. The Cone of Cyclic Sieving Phenomena

Author

Alexandersson, Per and Amini, Nima

Subjects
Mathematics - Combinatorics, Mathematics - Representation Theory
Abstract

We study cyclic sieving phenomena (CSP) on combinatorial objects from an abstract point of view by considering a rational polyhedral cone determined by the linear equations that define such phenomena. Each lattice point in the cone corresponds to a non-negative integer matrix which jointly records the statistic and cyclic order distribution associated with the set of objects realizing the CSP. In particular we consider a universal subcone onto which every CSP matrix linearly projects such that the projection realizes a CSP with the same cyclic orbit structure, but via a universal statistic that has even distribution on the orbits. Reiner et.al. showed that every cyclic action give rise to a unique polynomial (mod $q^n-1$) complementing the action to a CSP. We give a necessary and sufficient criterion for the converse to hold. This characterization allows one to determine if a combinatorial set with a statistic give rise (in principle) to a CSP without having a combinatorial realization of the cyclic action. We apply the criterion to conjecture a new CSP involving stretched Schur polynomials and prove our conjecture for certain rectangular tableaux. Finally we study some geometric properties of the CSP cone. We explicitly determine its half-space description and in the prime order case we determine its extreme rays.

Published
2018
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4. Equidistributions of Mahonian statistics over pattern avoiding permutations

Author

Amini, Nima

Subjects
Mathematics - Combinatorics, 05A05 (Primary) 05A15, 05A19 (Secondary)
Abstract

A Mahonian d-function is a Mahonian statistic that can be expressed as a linear combination of vincular pattern statistics of length at most d. Babson and Steingrimsson classified all Mahonian 3-functions up to trivial bijections and identified many of them with well-known Mahonian statistics in the literature. We prove a host of Mahonian 3-function equidistributions over pattern avoiding sets of permutations. Tools used include block decomposition, Dyck paths and generating functions., Comment: 31 pages, 4 figures, 2 tables

Published
2017

5. Spectrahedrality of hyperbolicity cones of multivariate matching polynomials

Author

Amini, Nima

Subjects
Mathematics - Combinatorics, Mathematics - Optimization and Control
Abstract

The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Br\"and\'en). Finally we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman., Comment: 23 pages

Published
2016

6. Recurrent retroauricular cystic nodules: lichen planus follicularis tumidus

Author

Chau, Thinh, Amini, Nima, Eisen, Daniel B., and Fung, Maxwell A.

Subjects
lichen planus follicularis tumidus, lichen planus, retroauricular cystic nodules, interface dermatitis, dermatopathology
Abstract

Lichen planus follicularis tumidus (LPFT) is a rare subtype of lichen planus (LP) that has been most commonly described in middle-aged women. LPFT clinically manifests as recurrent cystic follicular nodules that preferentially involve the retroauricular area; concurrent classic LP lesions on the extremities and mucosal surfaces may also be present. Histologically, LPFT demonstrates epithelial-lined follicular cysts filled with orthokeratotic keratin surrounded by a dense lichenoid infiltrate. We present a case of a 67-year-old man with clinical and histopathologic findings consistent with LPFT and discuss differential diagnostic considerations for entities resembling LPFT. Lastly, treatment options for LPFT are reviewed.

Published
2018

7. Non-representable hyperbolic matroids

Author

Amini, Nima and Brändén, Petter

Subjects
Mathematics - Combinatorics, Mathematics - Optimization and Control
Abstract

The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. Hyperbolic polynomials give rise to a class of (hyperbolic) matroids which properly contains the class of matroids representable over the complex numbers. This connection was used by the second author to construct counterexamples to algebraic (stronger) versions of the generalized Lax conjecture by considering a non-representable hyperbolic matroid. The V\'amos matroid and a generalization of it are, prior to this work, the only known instances of non-representable hyperbolic matroids. We prove that the Non-Pappus and Non-Desargues matroids are non-representable hyperbolic matroids by exploiting a connection between Euclidean Jordan algebras and projective geometries. We further identify a large class of hyperbolic matroids which contains the V\'amos matroid and the generalized V\'amos matroids recently studied by Burton, Vinzant and Youm. This proves a conjecture of Burton et al. We also prove that many of the matroids considered here are non-representable. The proof of hyperbolicity for the matroids in the class depends on proving nonnegativity of certain symmetric polynomials. In particular we generalize and strengthen several inequalities in the literature, such as the Laguerre-Tur\'an inequality and Jensen's inequality. Finally we explore consequences to algebraic versions of the generalized Lax conjecture.

Published
2015

10. Comparison of oral candidiasis characteristics in head-and-neck cancer patients before and during radiotherapy

Author

Dehghan, Parvin, primary, Golestannejad, Zahra, additional, Khozeimeh, Faezeh, additional, Najafizade, Nadia, additional, Tabesh, Adel, additional, Faghihian, Elham, additional, Maheronnaghsh, Mehrnoush, additional, Kheirkhah, Mahnaz, additional, Hosseini, SayedMohsen, additional, Sadeghalbanaei, Leila, additional, Jamshidi, Mina, additional, Chermahini, AhmadAmiri, additional, Saberi, Zahra, additional, Pakravan, Fahimeh, additional, Emamibafrani, Maryam, additional, Amini, Nima, additional, and Tadayon, Faezeh, additional

Published
2023
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11. Comparison of oral candidiasis characteristics in head-and-neck cancer patients before and during radiotherapy.

Author

Golestannejad, Zahra, Khozeimeh, Faezeh, Najafizade, Nadia, Tabesh, Adel, Faghihian, Elham, Maheronnaghsh, Mehrnoush, Kheirkhah, Mahnaz, Hosseini, Sayed Mohsen, Sadeghalbanaei, Leila, Jamshidi, Mina, Chermahini, Ahmad Amiri, Saberi, Zahra, Pakravan, Fahimeh, Dehghan, Parvin, Emamibafrani, Maryam, Amini, Nima, and Tadayon, Faezeh

Subjects
THRUSH (Mouth disease), STATISTICS, RESEARCH methodology, HEAD & neck cancer, EMPLOYEE recruitment, GENETIC polymorphisms, CANCER patients, BACTERIAL growth, MICROBIOLOGICAL techniques, CHI-squared test, POLYMERASE chain reaction
Abstract

Background: Patients undergoing head-and-neck radiotherapy are susceptible to Candida colonization and infection. This study aimed to identify oral Candida species type (ST), colony count (CC), and oropharyngeal candidiasis (OPC) in head-and-neck cancer patients, undergoing radiotherapy, before and 2 weeks after radiation. Materials and Methods: In this quasi-experimental study, head-and-neck cancer patients undergoing radiotherapy (up to 6000 cGy) were recruited. Samples were taken before and 2 weeks after radiation therapy (RT). CC was assigned using Sabouraud dextrose agar culture medium and morphological studies were performed to confirm OPC. For identification, polymerase chain reaction-restriction fragment length polymorphism was performed. Data were analyzed using Chi-square-test and kappa coefficient. P < 0.05 was considered statistically significant. Results: Twenty-one of 33 patients were Candida positive. The detected fungal species included Candida albicans (60%), Candida tropicalis (22%), Candida glabrata (9%), and other species (9%). Following RT, OPC and CC changed significantly (P = 0.003 and P = 0.001, respectively), whereas ST did not significantly change (P = 0.081). Two new species (Candida krusei and Candida parapsilosis) were detected after the intervention. The OPC, CC, and ST changes after RT were not significantly related to malignancy site or radiation dose (P > 0.05). Conclusion: The present study showed that OPC, CC, and ST were not related to the malignancy site. Following RT, OPC and CC changed significantly, while ST showed no significant change. The radiation dose and malignancy site had no effects on the OPC, CC, or ST alterations following RT. [ABSTRACT FROM AUTHOR]

Published
2023

18. Combinatorics and zeros of multivariate polynomials

Author

Amini, Nima

Subjects
Discrete Mathematics, Diskret matematik
Abstract

This thesis consists of five papers in algebraic and enumerative combinatorics. The objects at the heart of the thesis are combinatorial polynomials in one or more variables. We study their zeros, coefficients and special evaluations. Hyperbolic polynomials may be viewed as multivariate generalizations of real-rooted polynomials in one variable. To each hyperbolic polynomial one may associate a convex cone from which a matroid can be derived - a so called hyperbolic matroid. In Paper A we prove the existence of an infinite family of non-representable hyperbolic matroids parametrized by hypergraphs. We further use special members of our family to investigate consequences to a central conjecture around hyperbolic polynomials, namely the generalized Lax conjecture. Along the way we strengthen and generalize several symmetric function inequalities in the literature, such as the Laguerre-Tur\'an inequality and an inequality due to Jensen. In Paper B we affirm the generalized Lax conjecture for two related classes of combinatorial polynomials: multivariate matching polynomials over arbitrary graphs and multivariate independence polynomials over simplicial graphs. In Paper C we prove that the multivariate $d$-matching polynomial is hyperbolic for arbitrary multigraphs, in particular answering a question by Hall, Puder and Sawin. We also provide a hypergraphic generalization of a classical theorem by Heilmann and Lieb regarding the real-rootedness of the matching polynomial of a graph. In Paper D we establish a number of equidistributions between Mahonian statistics which are given by conic combinations of vincular pattern functions of length at most three, over permutations avoiding a single classical pattern of length three. In Paper E we find necessary and sufficient conditions for a candidate polynomial to be complemented to a cyclic sieving phenomenon (without regards to combinatorial context). We further take a geometric perspective on the phenomenon by associating a convex rational polyhedral cone which has integer lattice points in correspondence with cyclic sieving phenomena. We find the half-space description of this cone and investigate its properties. QC 20190510

Published
2019

20. The cone of cyclic sieving phenomena

Author

Amini, Nima, Alexandersson, Per, Amini, Nima, and Alexandersson, Per

Abstract

We study cyclic sieving phenomena (CSP) on combinatorial objects from an abstract point of view by considering a rational polyhedral cone determined by the linear equations that define such phenomena. Each lattice point in the cone corresponds to a non-negative integer matrix which jointly records the statistic and cyclic order distribution associated with the set of objects realizing the CSP. In particular we consider a universal subcone onto which every CSP matrix linearly projects such that the projection realizes a CSP with the same cyclic orbit structure, but via a universal statistic that has even distribution on the orbits. Reiner et.al. showed that every cyclic action gives rise to a unique polynomial (mod q^n-1) complementing the action to a CSP. We give a necessary and sufficient criterion for the converse to hold. This characterization allows one to determine if a combinatorial set with a statistic gives rise (in principle) to a CSP without having a combinatorial realization of the cyclic action. We apply the criterion to conjecture a new CSP involving stretched Schur polynomials and prove our conjecture for certain rectangular tableaux. Finally we study some geometric properties of the CSP cone. We explicitly determine its half-space description and in the prime order case we determine its extreme rays., QC 20190510

Published
2019
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21. Alleviating the negative side effects of ramp metering: development of a supplementary ramp metering algorithm

Author

Amini, Nima

Subjects
User acceptance, Algorithm design, Traffic control, Long term impact, Efficiency, Equity, Delays, Ramp metering, Disbenefits
Abstract

Ramp meters reduce the total travel-time when aggregated across all freeway users. However, the distribution of this benefit is highly skewed, with some freeway users experiencing an increase in travel time. The bias in benefit distribution can have negative side-effects such as user dissatisfaction, encouraging trips from outer-rim suburbs, and exacerbating urban sprawl. These side-effects can restrict road authorities in realising the full potential of ramp meters and are in conflict with demand management strategies of expanding cities. The root cause of this issue is the variation in ramp metering delay across the on-ramps, which real-world ramp metering algorithms do not consider for the primary control decisions. In this research, ramp metering delay is considered as a form of congestion-toll that is paid at the on-ramps. A model based algorithm is developed that dynamically controls the ramp metering delay at each on-ramp according to the level of congestion it is predicted to cause. Predictive ramp metering can be inefficient given the stochastic nature of bottleneck capacities; therefore, the proposed algorithm is deployed as a supplementary algorithm that extends the functionality of existing reactive control methods. As a by-product a framework for evaluation and development of coordinated ramp metering algorithms is introduced, in addition to a practical method for measuring and controlling ramp metering delays. Examination of the proposed supplementary algorithm in combination with the well-known HERO algorithm indicates that the benefit distribution bias is significantly reduced, whilst the total travel time can be reduced because the controllability of the system is increased. This method aligns the short-term control problem with long-term planning concepts such as demand management and equity, which is expected to provide road authorities with greater leverage to realise the full potential of the ramp metering system.

Published
2018
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23. Spectrahedrality of hyperbolicity cones of multivariate matching polynomials

Author

Amini, Nima and Amini, Nima

Abstract

The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Brändén). Finally we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman., QC 20190510Delarbete till avhandling, ej dubblett med DiVA 1360105Not duplicate with DiVA 1360105

Published
2018

24. Equidistributions of mahonian statistics over pattern avoiding permutations

Author

Amini, Nima and Amini, Nima

Abstract

A Mahonian d-function is a Mahonian statistic that can be expressed as a linear combination of vincular pattern functions of length at most d. Babson and Ste- ingrímsson classified all Mahonian 3-functions up to trivial bijections and identified many of them with well-known Mahonian statistics in the literature. We prove a host of Mahonian 3-function equidistributions over permutations in Sn avoiding a single classical pattern in S3. Tools used include block decomposition, Dyck paths and generating functions., QC 20180205

Published
2018
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25. Alleviating the negative side effects of ramp metering: development of a supplementary ramp metering algorithm

Author

Waller, Travis, Civil & Environmental Engineering, Faculty of Engineering, UNSW, Gardner, Lauren, Civil & Environmental Engineering, Faculty of Engineering, UNSW, Amini, Nima, Civil & Environmental Engineering, Faculty of Engineering, UNSW, Waller, Travis, Civil & Environmental Engineering, Faculty of Engineering, UNSW, Gardner, Lauren, Civil & Environmental Engineering, Faculty of Engineering, UNSW, and Amini, Nima, Civil & Environmental Engineering, Faculty of Engineering, UNSW

Abstract

Ramp meters reduce the total travel-time when aggregated across all freeway users. However, the distribution of this benefit is highly skewed, with some freeway users experiencing an increase in travel time. The bias in benefit distribution can have negative side-effects such as user dissatisfaction, encouraging trips from outer-rim suburbs, and exacerbating urban sprawl. These side-effects can restrict road authorities in realising the full potential of ramp meters and are in conflict with demand management strategies of expanding cities. The root cause of this issue is the variation in ramp metering delay across the on-ramps, which real-world ramp metering algorithms do not consider for the primary control decisions. In this research, ramp metering delay is considered as a form of congestion-toll that is paid at the on-ramps. A model based algorithm is developed that dynamically controls the ramp metering delay at each on-ramp according to the level of congestion it is predicted to cause. Predictive ramp metering can be inefficient given the stochastic nature of bottleneck capacities; therefore, the proposed algorithm is deployed as a supplementary algorithm that extends the functionality of existing reactive control methods. As a by-product a framework for evaluation and development of coordinated ramp metering algorithms is introduced, in addition to a practical method for measuring and controlling ramp metering delays. Examination of the proposed supplementary algorithm in combination with the well-known HERO algorithm indicates that the benefit distribution bias is significantly reduced, whilst the total travel time can be reduced because the controllability of the system is increased. This method aligns the short-term control problem with long-term planning concepts such as demand management and equity, which is expected to provide road authorities with greater leverage to realise the full potential of the ramp metering system.

Published
2018

29. Non-representable hyperbolic matroids

Author

Amini, Nima, Bränden, Petter, Amini, Nima, and Bränden, Petter

Abstract

The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positivesemidefinite matrices. Hyperbolic polynomials give rise to a class of (hyperbolic) matroids which properly containsthe class of matroids representable over the complex numbers. This connection was used by the first author toconstruct counterexamples to algebraic (stronger) versions of the generalized Lax conjecture by considering a nonrepresentable hyperbolic matroid. The Vamos matroid and a generalization of it are to this day the only known ´instances of non-representable hyperbolic matroids. We prove that the Non-Pappus and Non-Desargues matroids arenon-representable hyperbolic matroids by exploiting a connection, due to Jordan, between Euclidean Jordan algebrasand projective geometries. We further identify a large class of hyperbolic matroids that are parametrized by uniformhypergraphs and prove that many of them are non-representable. Finally we explore consequences to algebraicversions of the generalized Lax conjecture., QC 20200616

Published
2016

41. Long‑term Outcomes of Ahmed Glaucoma Valve Implantation in Refractory Glaucoma at Farabi Eye Hospital, Tehran, Iran.

Author

Zarei, Reza, Amini, Heidar, Daneshvar, Ramin, Nabi, Fahimeh Naderi, Moghimi, Sasan, Fakhraee, Ghasem, Eslami, Yadollah, Mohammadi, Masoud, and Amini, Nima

Subjects
GLAUCOMA treatment, HEALTH outcome assessment, OPHTHALMIC & aural hospitals, EYE care, INTRAOCULAR pressure
Abstract

Purpose: To describe long‑term outcomes and complications of Ahmed glaucoma valve (AGV) implantation in subjects with refractory glaucoma at Farabi Eye Hospital, Tehran, Iran. Materials and Methods: This retrospective cohort study evaluated patient records of all subjects with refractory glaucoma who had undergone AGV implantation up to January 2013. The main outcome measure was the surgical success rate. Complete success was defined as intraocular pressure (IOP) <22 mmHg, without anti‑glaucoma medications or additional surgery. Qualified success was IOP <22 mmHg regardless of number of anti‑glaucoma medications. In all cases, loss of vision (no light perception) was considered an independent indicator of failure. Data were also collected on intraoperative and postoperative complications. Results: Twenty‑eight eyes were included in the study. With a mean follow‑up of 48.2 ± 31.7 months (median: 40.50 months; range: 3–124 months), the IOP decreased from a mean preoperative value of 30.8 ± 5.6 mmHg to 20.0 ± 6.4 mmHg at last visit. The number of medications decreased from 3.7 ± 0.4 preoperatively to 2.5 ± 1.1 postoperatively. Cumulative qualified success was achieved in 69% of eyes. Mean time to failure according to qualified success criteria was 92.3 ± 9.4 months. Postoperative complications were recorded in 16 (57.1%) eyes. The most common complication was focal endothelial corneal decompensation at the site of tube‑cornea touch. Conclusion: AGV implantation with adjunctive topical anti‑glaucoma drops controlled IOP in approximately 70% of eyes with refractory glaucoma with a median of 40.5 months of follow‑up. However, complication rates were higher. [ABSTRACT FROM AUTHOR]

Published
2016
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43. Early-onset Pseudoexfoliation Syndrome following Multiple Intraocular Procedures.

Author

Amini, Heydar, Daneshvar, Ramin, Eslami, Yadollah, Moghimi, Sasan, and Amini, Nima

Abstract

Purpose: To present early-onset ocular manifestations of pseudoexfoliation syndrome in young patients who had undergone multiple intraocular procedures. Methods: This is an observational case series, introducing four cases with histories of multiple intraocular procedures for glaucoma. Results: All reported cases demonstrated typical manifestations of pseudoexfoliation unilaterally in the eye that had undergone multiple surgeries. The diagnosis of pseudoexfoliation was made prior to the age of 50 in all subjects and the earliest manifestation was at the age of 18 in a case with primary congenital glaucoma Conclusion: The role of multiple surgical procedures, in addition to genetic predisposition, should be further investigated as a possible inciting factor predisposing to pseudoexfoliation in younger individuals. [ABSTRACT FROM AUTHOR]

Published
2012

44. Office-based Slit-lamp Needle Revision with Adjunctive Mitomycin-C for Late Failed or Encapsulated Filtering Blebs.

Author

Amini, Heidar, Esmaili, Alireza, Zarei, Reza, Amini, Nima, and Daneshvar, Ramin

Subjects
SLIT lamp microscopy, MITOMYCIN C, BLISTERS, GLAUCOMA, INTRAOCULAR pressure, PATIENTS, THERAPEUTICS
Abstract

Purpose: The purpose of this study was to assess the results of bleb needling in glaucomatous patients with late failed filtering blebs. Materials and Methods: A retrospective case series of 27 eyes of 27 patients was considered. All patients underwent needle bleb revision with adjuvant mitomycin-C performed at the slit lamp, during an office visit. Complete success was defined as postneedling intraocular pressure (IOP) ≤ 21 mmHg without any antiglaucoma medications and qualified success was IOP ≤ 21 mmHg with topical antiglaucoma medications. Results: There were 12 eyes with encapsulated blebs and 15 eyes with flat blebs. The mean interval between index filtering surgery and bleb revision was 32.74 ± 15.36 months. Mean IOP was 25.07 ± 4.80 mmHg before surgery and 19.66 ± 4.97 mmHg at last postoperative follow-up. The mean follow-up was 20.31 ± 15.63 months. Complete and qualified successes were 7.4% and 51.9%, respectively. Cumulative rates of success at 1, 2, 3, and 4 years were 76%, 65%, 49%, and 37%, respectively. The mean number of antiglaucoma medications was reduced from 3.15 ± 0.36 preoperatively to 2.33 ± 1.21 postoperatively (P<0.001). Conclusion: Slit-lamp needle revision in office is a simple and effective method for treating late encapsulated or flat filtering blebs without significant complications even for late bleb failure. [ABSTRACT FROM AUTHOR]

Published
2012
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45. Central Corneal Thickness in Iranian Congenital Glaucoma Patients.

Author

Amini, Heidar, Fakhraie, Ghasem, Abolmaali, Sara, Amini, Nima, and Daneshvar, Ramin

Subjects
TONOMETRY, INTRAOCULAR pressure, CONGENITAL glaucoma, BLINDNESS in children, EYE diseases, STRABISMUS
Abstract

Purpose: To compare central corneal thickness (CCT) in subjects with controlled primary congenital glaucoma (PCG) and nonglaucomatous subjects and to investigate the correlation between CCT and intraocular pressure (IOP) in the study population. Materials and Methods: Twenty-three consecutive PCG cases with controlled IOP and no clinical evidence of corneal edema comprised the Study Group. There was an interval of at least 2 months between last intraocular surgery and inclusion in the study. Twenty-one subjects with strabismus or lacrimal drainage insufficiency who did not have glaucoma or any history of intraocular surgery or ocular trauma comprised the control group. The Control Group was age and sex-matched. Data from ultrasonic pachymetry and applanation tonometry were analyzed for differences between groups. Correlation of the study parameters was investigated. A P-value less than 0.05 was statistically significant. Results: Data from both eyes of subjects in the Study Group and Control Group were included in the original analysis. Mean CCT was statistically significantly higher in the Study Group compared to the Control Group (589.42 ± 53.44 μm vs. 556.14 ± 30.51 μm, respectively; P=0.001). There was a significant correlation between CCT and IOP (r=0.63; P<0.0001). Similar statistically significant outcomes were observed when only one eye per subject was used in a reanalysis of the data for the Study and Control Groups. Conclusion: Patients with PCG who had controlled IOP have statistically significantly thicker corneas than nonglaucomatous age and sex-matched subjects The thicker cornea could significantly alter IOP measurement with applanation tonometry. Pachymetry should be considered an essential part of the evaluation for PCG. [ABSTRACT FROM AUTHOR]

Published
2012
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46. Ahmed Glaucoma Valve with Adjunctive Amniotic Membrane for Refractory Glaucoma.

Author

Amini, Heydar, Kiarudi, Mohammad Yaser, Moghimi, Sasan, Fakhraie, Ghasem, and Amini, Nima

Abstract

Purpose: To evaluate the efficacy and safety of Ahmed Glaucoma Valve (AGV) implantation with adjunctive use of preserved amniotic membrane for surgical management of refractory glaucoma. Methods: Seven patients (5 female subjects) with refractory glaucoma were included in the study. An AGV (model FP7) was implanted in the usual manner and was covered with two layers of cryopreserved human amniotic membrane. Intraocular pressure (IOP) and number of glaucoma medications before and after surgery, and complications were evaluated. Results: Mean duration of follow-up was 16.8±4.6 months. Mean preoperative IOP was 31.7±4.4 mmHg which was reduced to 17.7±6.1 mmHg at final follow-up (P=0.01, Wilcoxon U test). Although the number of topical medications was also reduced (mean decrease of 0.85 drops), this decrease was not significant (P=0.10, Wilcoxon U test). None of the eyes developed encapsulation after surgery; only one case was complicated by posterior migration of the implant resulting in failure. Conclusion: Glaucoma shunt surgery using the AGV with adjunctive amniotic membrane seems to be a safe and effective procedure which may reduce the risk of bleb encapsulation in refractory glaucomas. [ABSTRACT FROM AUTHOR]

Published
2010

47. Stable multivariate generalizations of matching polynomials

Author

Amini, Nima and Amini, Nima

Abstract

The first part of this note concerns stable averages of multivariate matching polynomials. In proving the existence of infinite families of bipartite Ramanujan d-coverings, Hall, Puder and Sawin introduced the d-matching polynomial of a graph G, defined as the uniform average of matching polynomials over the set of d-sheeted covering graphs of G. We prove that a natural multivariate version of the d-matching polynomial is stable, consequently giving a short direct proof of the real-rootedness of the d-matching polynomial. Our theorem also includes graphs with loops, thus answering a question of said authors. Furthermore we define a weaker notion of matchings for hypergraphs and prove that a family of natural polynomials associated to such matchings are stable. In particular this provides a hypergraphic generalization of the classical Heilmann-Lieb theorem., QC 20190510

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