text:
We recommend using the latest version of IE11, Edge, Chrome, Firefox or Safari.

## CDAC Students Featured in Top Story in APS News Heading link

We’re delighted to see the work of two CDAC students: Bethany Chidester and Hannah Bausch featured ‘above the fold’ in the current issue of APS News. Notably their two studies, both conducted at Z, were the featured highlights of SHOCK22 in Annaheim in the article.

Bethany is a former CDAC student from the University of Chicago (and before that CDAC undergraduate summer intern), now a Director’s Fellow at LANL, and Hannah is currently a CDAC graduate student at Northwestern.

=================================================================

## CDAC Personnel Chair Sessions, Present Results at the Gordon Conference on Research at High Pressure Heading link

The 2022 Gordon Research Conference (GRC) on Research at High Pressure, entitled Exploring High Pressure Science at the Extremes Through Experiment and Computation was held on July 17-22 at New Hampshire’s Holderness School. CDAC students and postdoctoral researchers, as well as CDAC faculty and collaborators, were well represented at this event, which was held in-person for the first time since 2019. Established in 1955, this Gordon Conference is one of the longest running meetings in the Gordon Conferences portfolio.

The opening session, Challenges to Our Understanding of Dense Matter, featured a lecture by CDAC Partner Eva Zurek entitled “Predicted Light Element Superconductors Under Pressure.” CDAC Director Russell Hemley (University of Illinois Chicago) chaired the following session on Hydrogen-Rich Systems, and former CDAC postdoctoral researcher Amy (Lazicki) Jenei (Livermore National Laboratory) chaired the session Beyond Earth : Pressure as an Experimental Probe. CDAC collaborator and Beamline Scientist Guoyin Shen from HPCAT chaired the session on New Phenomena at High Density.

Graduate students affiliated with CDAC groups made a number of presentations at the poster session held on July 21, and UIC’s Anmol Lamichhane received one of the conferences’s Best Poster Awards.

The complete schedule is available at : https://www.grc.org/research-at-high-pressure-conference/2022/

On July 16-17, immediately preceding the GRC was the Gordon Research Seminar “Research at High Pressure” for graduate students and early career scientists. In the session Novel Chemistry and Syntheses, CDAC postdoctoral researcher Katie Hilleke (University at Buffalo) presented her work on “Chemical Pressure in the Structures of Superconducting Metal Hydrides : Stabilization and Design.”

The program for the Gordon Research Seminar is available at https://www.grc.org/research-at-high-pressure-grs-conference/2022

For more on the Gordon Research Conferences, go to https://www.grc.org/about/

=================================================================

Allison Pease, a CDAC graduate student from the research group of Academic Partner Susannah Dorfman at Michigan State University, is the 2022 recipient of the Edward H. Kraus Crystallographic Research Fund Grant from the Mineralogical Society of America. The Kraus award is based on a competitive proposal process and provides up to $5000 for research in the field of mineralogical crystallography. Proposals for research in the areas of mineralogy, crystal chemistry, petrology, mineral physics, biomineralization, and geochemistry are all eligible for funding, and studies may be pursued using crystallographic, spectroscopic, analytical or computational methods. The award may go to undergraduate or graduate students as well as beginning faculty and young researchers. The title of Allison’s proposal is “Structural Variation in Silicate Perovskites.” Other CDAC-supported graduate students receiving the Kraus award include Arianna Gleason (University of California-Berkeley, 2013) and Josh Townsend (Northwestern University, 2012). Current CDAC Academic Partner Steven Jacobsen (Northwestern University) also received the Kraus award as a graduate student at the University of Colorado-Boulder in 2001. Allison is a graduate of Augustana College in Rock Island, Illinois, and she also holds an M.S. degree from the University of Michigan. The entire CDAC community sends its best wishes to Allison in recognition of this outstanding achievement. Congratulations Allison! ================================================================= ## CHESS workshop: Computing, Machine Learning, and Data-Intensive Science at Synchrotron Facilities, July 26-27 Heading link Research at synchrotron light sources hold transformational promise to address some of the most pressing scientific questions in society. They provide the unique ability to probe matter from atomic to mesoscopic length scales; enable experiments at physically-relevant conditions with respect to parameters such as temperature, chemical environment, mechanical loading, and so on; and can probe phenomena over time-scales spanning many orders of magnitude. While these capabilities have enabled scientific breakthroughs across multiple fields, recent dramatic improvements in x-ray source brightness and advances in detector technology have led to an explosion in sophisticated measurement techniques and raw data volumes, presenting technological and computational challenges as well as scientific opportunities. To fully realize the promise of these facilities, we need new strategies for managing, interacting with, and extracting relevant physical information from increasingly large and complex datasets. This workshop will bring together experts in x-ray and domain science, machine learning, scientific computing, cyberinfrastructure, and data management to share knowledge and brainstorm ways to advance computational tools and infrastructure for data-intensive x-ray science. Workshop goals: • Inform future facility directions and initiatives • Identify opportunities for collaboration within and across disciplines • Identify community training and support needs Topical sessions: • On-the-fly data analysis • Machine learning • Computational- and data-intensive applications • Data curation • Workflows, visualization and systems for big data REGISTER NOW! JULY 26 & 27 JOIN NOW Passcode: CHESS ================================================================= ## Broader Impacts Beyond CDAC : Lectures on the Use of XTALOpt Heading link In June 2022, CDAC Academic Partner Eva Zurek (University at Buffalo) gave a 4hr hands-on workshop on using the XtalOpt evolutionary algorithm for crystal structure prediction to a group of graduate students and postdoctoral associates at the recent 56th Course at the International School of Crystallography: Crystallography Under Extreme Conditions: The Future is Very Bright and Compressed. The course, held in Erice, Sicily from June 3-11 also featured two lectures by Professor Zurek, one on state-of-the-art techniques for computational structure prediction, and another on how these techniques have been used to understand the structures and properties of hydrogen-rich materials at very high pressures. In 2022 Professor Zurek has also given three (virtual) seminars at primarily undergraduate institutions: St. Bonaventure University, California State University-San Bernardino, and California State Polytechnic University-Pomona, during which she described how crystal structure prediction is being used in materials design, and provided case studies of the successful application of these techniques. ================================================================= ## CDAC Collaborator Jorge Muñoz Receives Cottrell Scholar Award Heading link Jorge Muñoz, an assistant professor of physics at The University of Texas at El Paso, has been named a 2022 Cottrell Scholar by the Research Corporation for Science Advancement. Muñoz, who was a CDAC graduate student working with former CDAC Academic Partner Brent Fultz at the California Institute of Techology is one of 24 teacher-scholars in chemistry, physics, and astronomy to receive this highly prestigious award, which recognizes excellence in research and teaching as well as the recipient’s potential to become an academic leader. The award comes with a financial prize of$100,000.

=================================================================

The MST-8 Materials Science in Radiation and Dynamic Extremes Group in Materials Science and Technology Division at Los Alamos National Laboratory (LANL) has a summer internship opening (May-September, 2022) for a creative and resourceful Post Master’s student with background in Laue diffraction and high-pressure diamond anvil cell experiments for understanding structure property relationship in materials.

The in situ Laue diffraction at high pressure studies have the potential to probe materials deformation and microstructural changes in real-time. Although these methods are having a large impact on material science and on the understanding of materials at the mesoscale, one of the major challenges is real-time data analysis and automation. As a Post Master’s student the selected candidate will work with LANL mentors and collaborators at the Advanced Photon Source to develop workflow utilizing novel machine learning and deep learning techniques for enabling automated in situ data analysis and interpretation with minimum human intervention.

=================================================================

The 22nd Biennial APS Shock Compression of Condensed Matter Conference will be held in Anaheim, CA on July 11-15, 2022 at the Anaheim Marriott. We are planning an in-person meeting and are currently researching a hybrid option. Additional details will be provided as soon as we have them.
Abstract submission and hotel reservations are currently open! Abstract submissions close March 4, 2022 and can be submitted here: [https://PHYSICS.p%20lanion.com/Z?861248252]PHYSICS.p lanion.com/Z?861248252

Hotel reservations are open until June 17, 2022. Reservations are available at GSA per diem rate. If you’re planning to attend, please make your reservations early and use this link: book.passkey.com/e/50251972
It is very important to make reservations through the conference link to ensure we make our room block commitment.

Conference Website: engage.aps.org/gsccm/meetings/biennial-2022

=================================================================

Congratulations from the entire CDAC community go out to Academic Partner Eva Zurek from the University at Buffalo, who received the 2021 SUNY Chancellor’s Award for Excellence in Scholarship and Creative Activities.  Second from left in the accompanying photo, Professor Zurek is pictured with other Chancellor’s Award recipients.

The Chancellor’s Awards are conferred to acknowledge and provide recognition for consistently superior professional achievement and to encourage the pursuit of excellence. Chancellors Awards in the SUNY (State University of New York) group of universities are made in five categories: Faculty Service, Librarianship, Professional Service, Scholarship and Creative Activities, and Teaching.

Congratulations, Eva !

=================================================================

Sara Kadkhodaei, a CDAC affiliated faculty member at UIC and a co-PI with CDAC Partner Eva Zurek, CDAC Director Russell Hemley, and CDAC affilliated faculty member Michael Trenary on the DMREF award, “Machine Algorithm Prediction and Synthesis of Next-Generation Superhard Functional Materials” is a co-author on a new paper on the use of machine learning in materials science published recently in Nature Communications Materials.

The paper describes a method whereby the latent information that is inherently embedded in the structure of a crystalline material is used to create an image representation of a crystal structure based on its chemical attributes.  This image representation allows the use of a “convolutional encoder” that learns the features of chemical and structural features of materials that allow synthesis.  Materials are then classified into synthesizable materials and crystal anomalies.  The deep learning approach holds the promise of streamlining the synthesis of new materials with tailored properties by enabling the targeted search of parameter space, and replacing the time-consuming and inefficient trial-and-error method.

[Davariashtiyani, A., et al., Predicting synthesizability of crystalline materials via deep learning.  Nature Communications Materials 2, 115 (2021)]

=================================================================

## November 3, 2021

3:00 PM – 4:00 PM

Lawrence Livermore National Laboratory is a Department of Energy national laboratory dedicated to applying leading edge science and technology to address the most pressing challenges facing the nation and the world today, from pandemic disease to climate change to national security and beyond. This talk will explore the mission applications, science and technology foundations, and unique environment of LLNL and offer insight into building a career at the national labs. Dr. Budil holds a BS in Physics from UIC (1987), and holds a PhD in Engineering and Applied Science from UC Davis (1994).

=================================================================

The Sekazi K. Mtingwa Scholarship supports the increased participation of identities (African American/Black, Hispanic/Latinx,and Indigenous) that are historically underrepresented in the study and workforce of Accelerator Science and Engineering (AS&E). This merit-based award is named in honor of Professor Sekazi Mtingwa. Prof. Mtingwa, a pioneering accelerator physicist, received the 2017 Robert R. Wilson Prize for Achievement in the Physics of Particle Accelerators for his innovative work on the theory of intrabeam scattering. Throughout his illustrious career he has actively sought to broaden participation in the physical sciences.

=================================================================

Bismuth is nominally the heaviest element stable to radioactive decay;
accordingly, it possesses a significant amount of spin-orbit coupling. We are
harnessing this spin orbit coupling to perturb the properties of other atoms. Our
effort spans molecules and materials, with a key emphasis on reconstituting a
magnetic moment from its two constituent components – spin and orbital angular
momentum. Bismuth offers orbital angular momentum, while paramagnetic
transition metals provide spin. Here we are creating new transition metal bismuth
interactions and probing their magnetic properties. Research on Fe-Bi
compounds will be presented, with an emphasis on unusual magnetic and
spectroscopic approaches to probe these materials.

Livestreaming at 10:00 AM (CT) THURS., October 21, 2021

=================================================================

The next edition of the APS Topical Group on Shock Compression of Condensed Matter (GSCCM) virtual seminar series; information on the seminar and how to join are below.

Shock Physics is widely described as a multi-disciplinary area with strong connections to Physics, Chemistry, Materials Science, Computing and many Engineering disciplines. The depth of understanding of different material classes along with the ability to predict the dynamic and shock response of materials varies markedly. The behaviour of metals is widely reported, the level of detail is very deep, challenges exist but there is a strong and wide range of expertise. Polymers are increasingly understood and insights into the marked effects of temperature and strain rate are being developed into a range of predictive material models. Biological materials and systems are amongst the least studied or understood, there large areas still to be addressed.

You are invited to a Zoom webinar.
When: Sep 14, 2021 12:00 PM Eastern Time (US and Canada)
Topic: GSCCM Virtual Seminar by Dr. Bill Proud

=================================================================

Congratulations to Livermore’s Brad Wallin for his selection as LLNL Principal Associate Director for Weapons and Complex Integration (WCI):

=================================================================

## Dynamic Materials Science at High Brilliance X-ray Light Sources Heading link

Dr. Dana M. Dattelbaum
Los Alamos National Laboratory

Tuesday, August 10, 2021 at 12:00 PM Eastern Time

High brilliance x-ray light sources are undergoing a transformation both in the U.S. and abroad, with facilities such as the Linac Coherent Light Source (LCLS) and Advanced Photon Source (APS) undergoing upgrades. Within NNSA, the brilliance and pulse structure of many of these sources provide an opportunity to study materials dynamics under extreme conditions of high pressures, temperatures, and strain rates. In many instances, the data obtained from x-ray diffraction and scattering fill the “micron gap,” providing information on materials structures at the mesoscale, which are foundational to next generation materials physics models. Most of the measurements performed using time-resolved x-rays are setting new precedents in terms of the detailed physics and chemistry they have revealed; examples range from measurement of carbon clustering in high explosives to the dynamics of solid-solid and melt transformations in metals under shockwave compression. In this presentation, I will provide examples from Los Alamos’ portfolio in dynamic materials science at U.S. light sources, providing several examples of recent work on low-Z materials using x-ray scattering, diffraction, and imaging. Lastly, information on a recent tri-lab response to NNSA of recommendations for future investments at U.S. light sources will also be provided.

=================================================================

## Openings for UIC Postdoctoral Positions in Experimental High-Pressure Materials Sciences Heading link

=================================================================

Congratulations to CDAC Partner (and former CDAC student) Susannah Dorfman on her promotion from Assistant Professor to Associate Professor with tenure at Michigan State University! Linkedin

=================================================================

Please join us for the next edition of the APS Topical Group on Shock Compression of Condensed Matter (GSCCM) virtual seminar series; information on the seminar and how to join are below. We would like to solicit nominations for future seminars and anticipate having a mix of a single speaker or two speakers during an hour time slot. Please email your nominations to Tracy Vogler (tjvogle@sandia.gov). Information on upcoming and past speakers can be found on the APS website. Recordings of some past seminars will also be available there.

GSCCM Virtual Seminar Series Organizing Committee
Minta Akin, Dana Dlott, Dan Eakins, Christopher “Kit” Neel, Laura Smilowitz, and Tracy Vogler

Stressing So Much That Defects Don’t Matter
Professor Neil Bourne
The University of Manchester (U.K.)

Tuesday, June 8, 2021 at 12:00 PM Eastern Time
Wouldn’t it be marvellous to live in world where we knew that matter had a single strength so that response could be predicted precisely and damage could be avoided? In our daily lives, failures can occur in people, organisations or structures when stresses mount to a point that the weakest link fails and local collapse ensues. However, matter has a limiting strength beyond which varied behaviours at lower compression change to uniform flow in the regime beyond. This threshold also opens a state in which materials transform their electronic states, change conductivity and transparency and emit radiation. That response above this threshold is predictable, allows extreme engineering to precede with less risk of failure than in the defective world in which we live. We shall explore these behaviours and discuss applications for this framework going forward.

You are invited to a Zoom webinar.
When: June 8, 2021 12:00 PM Eastern Time (US and Canada)
Topic: GSCCM Seminar by Professor Neil Bourne
Passcode: 521974

=================================================================

## Accidental synthesis of a previously unknown quasicrystal in the first atomic bomb test Heading link

This article reports the discovery of a heretofore unknown icosahedral quasicrystal created by the detonation of the first nuclear device at Alamogordo, NM, on 16 July 1945 (the Trinity test). Like all quasicrystals, the new example violates crystallographic symmetry rules that apply to ordinary (periodic) crystals. It was found in a sample of red trinitite, a combination of glass fused from natural sand and anthropogenic copper from transmission lines used during the test. The new quasicrystal is the oldest extant anthropogenic quasicrystal known, whose place and moment of origin are known from the historic records of the Trinity test. The thermodynamic/shock conditions that formed it are roughly comparable to those that formed natural quasicrystals recently found in meteorites.

L. Bindi et al., PNAS June 1, 2021 118 (22) e2101350118; https://doi.org/10.1073/pnas.2101350118

=================================================================

## Atomic-scale mixing between MgO and water in the deep interiors of water-rich planets Heading link

Water-rich planets exist in our Solar System (Uranus and Neptune) and are found to be common in the extrasolar systems (some of the sub-Neptunes).  In conventional models of these planets a thick water-rich layer is underlain by a separate rocky interior. Here we report experimental results on two rock-forming minerals, olivine ((Mg,Fe)2SiO4) and ferropericlase ((Mg,Fe) O), in water at the pressure and temperature conditions expected for the water-rich planets. Our data indicate a selective leaching of MgO, which peaks between 20 and 40 GPa and above 1,500 K. For water-rich planets with 1–6 Earth masses (>50 wt% H2O), the chemical reaction at the deep water–rock interface would lead to high concentrations of MgO in the H2O layer. For Uranus and Neptune, the top ~3% of the H2O layer would have a large storage capacity for MgO. If an early dynamic process enables the rock–H2O reaction, the topmost H2O layer may be rich in MgO, possibly affecting the thermal history of the planet.

=================================================================

## High pressure Laue diffraction at High Pressure Collaborative Access Team (HPCAT) Heading link

Date: Monday, May 24, 2021 – 2pm (CDT)
Speaker: Dmitry Popov, (HPCAT-XSD, Argonne National Laboratory)
Title: High pressure Laue diffraction at High Pressure Collaborative Access Team (HPCAT)
Abstract:

Laue diffraction technique is a powerful tool to investigate mechanisms of pressure induced processes including phase transitions, deformation, recrystallization, chemical reactions and so on. Experimental setup specifically optimized for in-situ and en-operando Laue diffraction studies in diamond anvil cells (DACs) is available for user operation at 16BMB beamline. Data collection and analysis routines implemented with the setup will be presented in details along with some recent scientific examples.

HPCAT organizes a High Pressure Special Interest Group Meeting each month. The meeting is held in the Conference room at building 434

*Note – Meetings will be held in a virtual format until further notice.  If you’d like to be added to the announcement email list, send a request to fhumble@anl.gov

=================================================================

## Q&A: Lawrence Livermore director Kimberly Budil on the evolving nuclear weapons enterprise Heading link

Named as the director of Lawrence Livermore National Laboratory in March, Kimberly Budil now leads a workforce of approximately 7400 employees and manages an annual operating budget of about \$2.7 billion. She is the first woman to lead the California facility and the second to head a US nuclear weapons laboratory.

Budil previously served as Livermore’s principal associate director for weapons and complex integration. She came to the lab in 1987 as a graduate student in laser programs, and she has worked in the lab’s National Ignition Facility (NIF), global security, and physical and life sciences programs. She has been detailed twice to DOE and was vice president for national laboratories at the University of California, which comanages Lawrence Livermore, Los Alamos, and Lawrence Berkeley National Laboratories. She holds a PhD in engineering and applied science from the University of California, Davis, and a bachelor’s in physics from the University of Illinois at Chicago. Physics Today spoke with Budil last month.

=================================================================

## Classical chemical kinetics in shock physics: Rate constants, order and applications in initiation and detonation Heading link

Dear Colleagues,

Please join us for the next edition of the APS Topical Group on Shock Compression of Condensed Matter (GSCCM) virtual seminar series; information on the seminar and how to join are below. We would like to solicit nominations for future seminars and anticipate having a mix of a single speaker or two speakers during an hour time slot. Please email your nominations to Tracy Vogler (tjvogle@sandia.gov). Information on upcoming and past speakers can be found on the APS website; recordings of some past seminars will also be available there.

GSCCM Virtual Seminar Series Organizing Committee
Minta Akin, Dana Dlott, Dan Eakins, Christopher “Kit” Neel, Laura Smilowitz, and Tracy Vogler

Classical chemical kinetics in shock physics: Rate constants, order and applications in initiation and detonation
Dr. Bryan Henson
Los Alamos National Laboratory

Tuesday, May 18, 2021 at 12:00 PM Eastern Time

Work has been ongoing in our group to produce globalized chemistry models of thermal ignition for secondary explosives valid over the entire temperature range of energetic response from thermal ignition by direct heating to detonation. We have made considerable progress recently, resulting in both the first broadly accurate global chemistry models of this type and the possible identification of a crucial component of the chemical mechanism governing the initial decomposition of the crystalline solid. We show that this initial component is based on the condensed phase thermodynamics of the explosive. We further show that it is a common feature of several members of the class of secondary explosives, and may constitute a fundamental, defining aspect of the insensitivity of this family of explosives. In this talk we present models for 1,3,5,7-octahydro-1,3,5,7-tetranitro-tetrazocine (HMX), 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) and 1,3-propanediol-2,2-bis[(nitrooxy)methyl]-tetranitrate (PETN), defined over the temperature range spanning 150 to 2500 C. We will also present a number of applications of these models to problems of ignition, initiation and detonation in these materials.

Click below to join the webinar at the specified time and date or use Webinar ID: 992 5275 7985
Passcode: 571084
Join Webinar
———————————-
You are invited to a Zoom webinar.
When: May 18, 2021 12:00 PM Eastern Time (US and Canada)
Topic: GSCCM Seminar by Dr. Bryan Henson
Passcode: 571084
Or One tap mobile :
US: +13017158592,,99252757985# or +19294362866,,99252757985# Or Telephone:
Dial (for higher quality, dial a number based on your current location): US: +1 301 715 8592 or +1 929 436 2866 or +1 312 626 6799 or +1 346 248 7799 or +1 669 900 6833 or +1 253 215 8782
Webinar ID: 992 5275 7985
International numbers available.

## 60th Anniversary of the Discovery of 'Dense Silica': Stishovite Heading link

Sixty years ago today, April 19, 1961, Sergei Stishov — then a graduate student at Moscow State University — together with Svetlana Popova first identified silica in the rutile-type structure from x-ray diffraction in high-pressure experiments, testing the hypothesis proposed a decade earlier about the high-pressure behavior of the common mineral quartz.

Upon learning about the discovery, Edward Chao of the U.S. Geological Survey found that their reported x-ray diffraction pattern matched that of material he had collected on the shocked Coconino sandstone at Meteor Crater, Arizona. He and his colleagues quickly announced the finding and proposed that the mineral be named stishovite.

The discovery was a landmark in both high-pressure physics and studies of the Earth’s deep interior. The story — indeed the geopolitical back story — is recounted in a memoir that Stishov published in 1995.  Additional information and pictures, from the 50th Anniversary Celebration of the discovery in 2011, are here and here.

Academician Stishov is currently a Staff Member at the Lebedev Physical Institute of the Russian Academy of Sciences (RAS), and is the former Director of the Institute of High Pressure Physics of the RAS. He has held numerous visiting appointments in the U.S., including LANL starting in 1993, as well as Caltech, Berkeley, and Stony Brook.  Svetlana Popova, who passed away five years ago, was a long-time Staff Member at the Institute of High Pressure Physics.

## Neutrons -- Hard Diamonds, High Pressures, at the Spallation Neutron Source Heading link

March 1, 2021

Researchers at Oak Ridge National Laboratory’s Spallation Neutron Source have developed a diamond anvil pressure cell that will enable high-pressure science currently not possible at any other neutron source in the world.

Using the SNAP instrument, the team measured high-quality powder diffraction data on a material above 120 gigapascals, shattering the previously held record of 62 GPa for meaningful structural data.

What’s more, the tiny submillimeter-sized sample used in the experiment is likely the smallest neutron sample ever measured and yet is also one of the largest powder samples ever held at such a high static pressure.

While scientists have used X-ray powder diffraction at such pressures for decades, it was previously not possible using neutrons.

“This breakthrough enables new studies on the structures of high-pressure super-hydrides that exhibit room-temperature superconductivity. It even enables investigations into materials at earth-core pressure conditions,” said ORNL’s Bianca Haberl.

=========================================================================================


text:
## Stream: maths

### Topic: atlases

#### Patrick Massot (Jun 26 2018 at 10:03):

I decided to try to move forward in my differential topology project without waiting for experts to sort out the module type class issues. So let's say I'm ready to sorry the definition of a diffeomorphism between two open subsets of R^n. Then the definition to formalize is https://en.wikipedia.org/wiki/Differentiable_manifold#Atlases I have no idea how to attack this coercion mess. I'd like to understand the definition of the transitions maps, and understand they are maps between open subsets of R^n

#### Patrick Massot (Jun 26 2018 at 10:04):

Even restricting a function to a subset is non-trivial in Lean

#### Patrick Massot (Jun 26 2018 at 10:05):

and here I need that the restriction of a homeo to a subset is a homeo onto its image

#### Johan Commelin (Jun 26 2018 at 11:19):

Even restricting a function to a subset is non-trivial in Lean

Can't you compose with subtype.val? And then you need that subtype.val is an immersion, and C^k for every value of k.

#### Patrick Massot (Jun 26 2018 at 12:21):

I need to invert the restriction of an equiv to some subset

#### Chris Hughes (Jun 26 2018 at 13:40):

Is this any use?

import analysis.topology.continuity
variables {α : Type*} {β : Type*} [topological_space α] [topological_space β]
(A : set α) (f : {f : α ≃ β // continuous f})

def restriction : {g : A ≃ f '' A // continuous g} :=
⟨{  to_fun := (λ a, ⟨f a.1, a, a.2, rfl⟩),
inv_fun := λ b, ⟨(equiv.symm (f : α ≃ β)) b, let ⟨a, ha₁, (ha₂ : f a = b)⟩ := b.2 in
calc _ = a : by rw ← ha₂; exact equiv.inverse_apply_apply _ _
... ∈ A : ha₁⟩,
left_inv := λ ⟨_, _⟩, subtype.eq (f.1.3 _),
right_inv := λ ⟨_, _⟩, subtype.eq (f.1.4 _)  },
continuous_subtype_mk (λ x, ⟨x, x.2, rfl⟩)
(continuous.comp continuous_subtype_val f.2)⟩

Maybe

#### Patrick Massot (Jun 26 2018 at 13:43):

I'm exploring a lot of ways to try to make Lean understanding this definition or variations on this definition

#### Patrick Massot (Jun 26 2018 at 13:44):

I already knew there were plenty of variations on the definition of manifolds but I'm discovering many more

#### Patrick Massot (Jun 26 2018 at 13:52):

A variation on this kind of effort could be to adapt

protected noncomputable def image {α β} (f : α → β) (s : set α) (H : injective f) :
s ≃ (f '' s) :=
⟨λ ⟨x, h⟩, ⟨f x, mem_image_of_mem _ h⟩,
λ ⟨y, h⟩, ⟨classical.some h, (classical.some_spec h).1⟩,
λ ⟨x, h⟩, subtype.eq (H (classical.some_spec (mem_image_of_mem f h)).2),
λ ⟨y, h⟩, subtype.eq (classical.some_spec h).2⟩

from equiv.lean to a version where H would be inj_on f s, which seems like a much more relevant hypothesis anyway

#### Patrick Massot (Jun 26 2018 at 13:54):

But maybe I don't care. I don't know. There are so many ways to try to setup this thing...

#### Chris Hughes (Jun 26 2018 at 13:56):

You're losing computability with that def, though I'm not sure you care.

#### Patrick Massot (Jun 26 2018 at 13:57):

Ah, at least there is something I know: I don't care about computability.

#### Patrick Massot (Jun 26 2018 at 13:57):

Chris, this remark worries me. I think you may be spending too much time with Kenny.

#### Patrick Massot (Jun 26 2018 at 14:01):

I'm completely confused about https://github.com/leanprover/mathlib/blob/master/data/equiv.lean#L527 How do you access this definition? It seems to be in namespace set but is obviously not the same as set.range

#### Kenny Lau (Jun 26 2018 at 14:02):

the equiv namespace never ended :)

#### Kenny Lau (Jun 26 2018 at 14:02):

equiv.set.range

Oh, that's nasty

thanks Kenny

#### Patrick Massot (Jun 26 2018 at 14:04):

hum, I hear I urgently need to go to the main lecture hall in IHES

#### Patrick Massot (Jun 26 2018 at 14:04):

it seems the match started already

#### Sebastien Gouezel (Jun 26 2018 at 20:27):

Are you planning to implement only C^\infty manifolds over the reals, or manifolds with different classes of smoothness (say C^0, or C^1, or C^k, or analytic, or PL, or whatever you like, over R or C)? It seems to me that it would be better to implement various classes of smoothness in the same framework. For instance, one could axiomatize what one needs to have a "smoothness class" (families of maps which are all homeos between open subsets of a given topological space, stable under restriction and composition and inverses), and then one could define a manifold with respect to this smoothness class. Two advantages of this approach:
- this is more general, and useful
- you don't need to define R^n and smooth maps to start working with this definition (but of course, you will have no example at the beginning, except maybe for C^0 manifolds which would be the first example to work out)
Any thoughts?

#### Patrick Massot (Jun 26 2018 at 20:29):

Unfortunately I'm pretty far from being able to do that. The trouble is partially defined functions are everywhere. A chart is defined on part of the manifold, a transition function is defined on the image of part of the domain of a chart. I really struggle with this. How is this handled in Isabelle? Do you have smooth functions defined on open subsets of R^n and a convenient way to restrict a smooth function to an open subset?

#### Patrick Massot (Jun 26 2018 at 20:30):

But, to answer your question, I was indeed hoping to implement manifolds modeled on any pseudo-group

#### Patrick Massot (Jun 26 2018 at 20:31):

I also find it very interesting to see that, once again, the only source which seems to be suitable for formalization is Bourbaki.

#### Sebastien Gouezel (Jun 26 2018 at 20:35):

In Isabelle, I would model a smoothness class by a set of pairs (U, f) where U is an open subset of R^n and f is a map from R^nto itself such that its restriction to U is a homeomorphism. So, I would have a predicate homeomorphism_on U f saying that f is a homeomorphism on U, together with basic properties of homeomorphisms (say, if f is a homeomorphism on U and gis a homeomorphism on V and f(U) \subseteq V, then g o f is a homeomorphism on U). Then you don't ever need to restrict your functions to subsets, and you avoid a lot of trouble.

#### Sebastien Gouezel (Jun 26 2018 at 20:35):

and the smoothness on open subsets is also defined for total functions, using a predicate as above.

#### Patrick Massot (Jun 26 2018 at 20:40):

I thought about trying to get functions defined everywhere and asking for injectivity and smoothness only on subsets. But I fear it will be a nightmare when trying to prove things because every function would be defined by lambda x, if x in U then real_thing x else 42.

#### Patrick Massot (Jun 26 2018 at 20:41):

And also I don't like this has nothing to do with math

#### Patrick Massot (Jun 26 2018 at 20:41):

It's purely an artefact of the type theoretic foundations

#### Sebastien Gouezel (Jun 26 2018 at 20:51):

You would never have any if in your definitions. The composition of two homeomorphisms fon U and g on V is just g o f on U (and it only makes sense if f(U) \subseteq V, but this is also the case with the true definition). The restriction of a homeomorphism fon U to a smaller subset U' is still f . And so on. This may seem surprising at first sight, but in fact it is not so surprising: if you only do meaningful constructions, then the values of your function outside of its "domain of definition" should never play any role, so what happens there is never relevant, and it can behave in the way it wants.

#### Patrick Massot (Jun 26 2018 at 20:52):

I know it's the theory, I've seen it countless times with 0/0 and other crazy stuff. But you still need to define an arbitrary crazy value. For 0/0 you can choose 0, fine. What if the target is a manifold?

#### Sebastien Gouezel (Jun 26 2018 at 20:53):

It is just like the fact that the division is total on real numbers: surprising and annoying at the beginning, and then when you get used to it you realize you don't care at all what it does at zero because you're not stupid and you never apply it at 0 (and of course you always have to check that the denominator is nonzero -- here in the same way you would always have to check that the points you apply your function to are in the "domain of definition")

#### Patrick Massot (Jun 26 2018 at 20:55):

Do you have the same crazyness in Isabelle then?

#### Sebastien Gouezel (Jun 26 2018 at 20:55):

At least for the definition of a manifold in terms of an atlas of compatible charts, you would never need to specify a value, it is just some axioms you want to satisfy.
Probably, when you define a manifold structure on some object, yes, you will have to make some arbitrary and irrelevant choice at some point. But that would be very rare, I guess.

#### Patrick Massot (Jun 26 2018 at 20:56):

Yes, I want to define actual manifolds, like smooth affine varieties in R^n (say S^{n-1})

#### Sebastien Gouezel (Jun 26 2018 at 20:56):

The crazyness of what? Every function is total, yes. And it turns out to be a non-issue once you're used to it. (Takes some time to get used to it :)

thanks

#### Sebastien Gouezel (Jun 26 2018 at 20:58):

Think of S^{n-1}. Take the two natural stereographic charts: they are defined on the whole of R^{n-1}, so no issue of arbitrary choice when you define them. And then you just have to check the axiom that the composition of one chart and the inverse of the other one, restricted to the good sets, are smooth. No arbitrary choice again.

#### Sebastien Gouezel (Jun 26 2018 at 20:59):

Same think if you define Grassmannians, say: the natural local charts using linear maps are defined on the whole R^k. No arbitrary choice again.

#### Patrick Massot (Jun 26 2018 at 20:59):

This is not the definition I want to use. This one is only an exercise in understanding the internal plumbing that is the precise definition of a manifold. I want S^{n-1} defined by |x|² = 1

#### Patrick Massot (Jun 26 2018 at 20:59):

I want submanifolds of manifolds to be manifolds

#### Patrick Massot (Jun 26 2018 at 21:00):

But I'll try this total function road

#### Sebastien Gouezel (Jun 26 2018 at 21:00):

Then you want to use two theorems, that the preimage of a regular value by a map is a submanifold, and that a submanifold is a manifold. Again no choice :)

#### Patrick Massot (Jun 26 2018 at 21:01):

Are you sure the second one will require no choice? Maybe.

#### Sebastien Gouezel (Jun 26 2018 at 21:02):

The way answers are intermingled is really strange in such a chat. Anyway, to prove that a submanifold is a manifold, essentially you will first straighten your submanifold, and then restrict your charts to the submanifold. Then there should be no ifin the involved arguments.

#### Patrick Massot (Jun 26 2018 at 21:04):

I'll try all this tomorrow (what I tried today is on https://github.com/PatrickMassot/lean-differential-topology/blob/master/src/manifold.lean if you are curious (there may be stupid things there, I switched gears so many times...)

#### Patrick Massot (Jun 26 2018 at 21:05):

thank you very much for this conversation

good night!

#### Patrick Massot (Jun 27 2018 at 13:38):

I try to get used to totalization of functions. What do people think about:

universes u v
variables {α : Type u} [inhabited α] {β : Type v}

def inverse_on  {U : set α} {f : α → β} (H : inj_on f U) : β → α :=
λ b, if h : b ∈ f '' U then classical.some h else default α

lemma inverse_on_spec {U : set α} {f : α → β} (H : inj_on f U) :
inv_on (inverse_on H) f U (f '' U) :=
begin
split ; intros x h,
{ have H' := mem_image_of_mem f h,
cases classical.some_spec H' with h1 h2,
simp [inverse_on, H', H h1 h h2] },
{ cases classical.some_spec h with h1 h2,
simpa [inverse_on, h] using h2 }
end

Is it something I should be doing?

#### Reid Barton (Jun 27 2018 at 14:05):

I don't see why it should be necessary to work with total functions here, and this approach has its own disadvantages. I think the root problem is that you currently lack a sufficient Lean vocabulary to work with partial functions and partial bijections

#### Patrick Massot (Jun 27 2018 at 14:06):

What would be that vocabulary?

#### Reid Barton (Jun 27 2018 at 14:09):

For example, looking at the definition of pseudogroup, you could state most of these axioms immediately given:

• A type pequiv a b representing a bijection between a subset of the type a and a subset of the type b. Note that the subsets of a and b are not indices of the type pequiv a b.
• A "restricted composition" operation pequiv a b \to pequiv b c \to pequiv a c.
• A "restricted identity" of type pequiv a a for each s : set a, which is the identity bijection between s and itself. From this and the previous one, you can implement restriction of a pequiv to a subset of the domain or codomain.
• A way to extract from a pequiv a b the domain s as a set a, and a function subtype s \to b, which you can then check for continuity or smoothness or whatever.

#### Patrick Massot (Jun 27 2018 at 14:11):

What would be a "restricted composition" in a world where all functions are total? That's precisely the trouble.

#### Reid Barton (Jun 27 2018 at 14:11):

Also I forgot the "symmetry" pequiv a b \to pequiv b a.

#### Reid Barton (Jun 27 2018 at 14:12):

Well then you are asking about how to implement this interface, right?

#### Patrick Massot (Jun 27 2018 at 14:12):

Everything is about implementation in this discussion, I already know what is a manifold.

#### Reid Barton (Jun 27 2018 at 14:12):

Or are you asking about the meaning of the operation? It's just the one which, given partial bijections f and g, is defined on x when f(x) is defined and g(f(x)) is also defined

#### Patrick Massot (Jun 27 2018 at 14:13):

Indeed having the subsets as fields instead of parameters may be enough to do the trick

#### Patrick Massot (Jun 27 2018 at 14:15):

I guess this is closer in spirit to the option a type than totalizing functions

#### Reid Barton (Jun 27 2018 at 14:16):

You might also want to check out roption and the data.pfun module

#### Reid Barton (Jun 27 2018 at 14:17):

But the main point is that for a computer, everything is hard, even these utterly trivial notions like "bijection between a subset of a and a subset of b".

#### Reid Barton (Jun 27 2018 at 14:18):

It helps to decompose the problem into pieces, so you are not thinking about manifolds when trying to define the composition of partial bijections. Of course this concept is not foreign to mathematicians, but here the pieces are much smaller than we are used to.

#### Patrick Massot (Jun 27 2018 at 14:20):

Yes I noticed all this (but noticing doesn't make it easy to use Lean)

#### Reid Barton (Jun 27 2018 at 14:20):

Once you have settled on the right interface for pequiv, the choice of implementation is not so important

#### Patrick Massot (Jun 27 2018 at 14:20):

I'll look at roption and pfun

#### Reid Barton (Jun 27 2018 at 14:23):

Something that may not be obvious from the pfun module is that because roption is a monad, you get a composition operation (a -> roption b) -> (b -> roption c) -> (a -> roption c) for free

#### Reid Barton (Jun 27 2018 at 14:28):

Apparently it doesn't really have a name in Lean aside from  >=>

#### Patrick Massot (Jun 27 2018 at 14:29):

I hope I'll be able to avoid this kind of notations...

#### Reid Barton (Jun 27 2018 at 14:29):

Again, only a question of implementation

#### Reid Barton (Jun 27 2018 at 14:29):

Of course for pequiv, you can choose whichever notation you like

#### Reid Barton (Jun 27 2018 at 14:32):

By the way, even though you don't care about constructiveness, I think things will be easier in the long run if you keep the maps in both directions as data in a bijection

#### Patrick Massot (Jun 27 2018 at 14:33):

as in using equiv rather than bijective you mean?

#### Reid Barton (Jun 27 2018 at 14:33):

Otherwise, when defining the canonical manifold structure on R^n for example, I think the transition maps will turn out to be something like lam x, classical.choice (\ex y, y = x) rather than lam x, x

Exactly

#### Sebastien Gouezel (Jun 27 2018 at 14:43):

def inverse_on  (U : set α) (f : α → β) : β → α :=
λ b, if h : b ∈ f '' U then classical.some h else default α

and having the injectivity as an assumption in your lemma inverse_on_spec. So that inverse_on is really taking as argument a function, and not a proof: formulas with inverse_on U f should be much more understandable than inverse_on H where you don't remember what H is. (This is really an implementation detail, everything is clearly equivalent, but still aiming at readability is always good!)

#### Reid Barton (Jun 27 2018 at 14:44):

If you keep track of both directions, then you can always produce the inverse using bijective and "unique choice" whenever it would be less convenient to provide it manually. But if you throw away the inverse direction and only keep the Prop of bijectivity, you can only recover the inverse function up to propositional equality. Then you may be faced with proving some equality these reconstructed inverses, where if you had kept the original inverses the proof would just be rfl

#### Patrick Massot (Jun 27 2018 at 14:46):

Thanks to both of you, this is all very interesting. I'll keep on working on the totalization path until I can define manifolds modulo the definition of smooth maps (it looks like it will work). But then I'll try to redo everything using the pequiv idea, and compare.

#### Patrick Massot (Jun 27 2018 at 14:48):

The definition of inverse_on without injectivity assumption really looks weird

#### Patrick Massot (Jun 27 2018 at 14:49):

I don't care at all about constructivism, and I don't mind using the axiom of choice. But this really doesn't feel like defining a function.

#### Sebastien Gouezel (Jun 27 2018 at 14:52):

I like my functions to be total :) So inverse_on is also total with this definition.
More seriously, in some settings, just taking one (any) preimage will make sense. For instance if you are working in a coarse geometry setting and you know that the preimages of any point have bounded diameter. This is the way one inverts quasi-isometries.

#### Kevin Buzzard (Jun 27 2018 at 14:52):

The axiom of choice is a pain to use in practice, because you need to keep track of random proof terms. I had two types X and Y in bijection recently, with a computable map X -> Y and a noncomptable map Y -> X, and after failing to construct something of type equiv X Y directly because of proof terms giving me problems I just proved X->Y was a bijection and then invoked equiv.of_bijection. Working with the axiom of choice can be a pain. Basically if you invoke it twice then there's no guaranteeing you got the same answer twice, so you can only invoke it once and then you have to keep a very careful track of where you invoked it and what you got.

#### Sebastien Gouezel (Jun 27 2018 at 14:54):

The idea would be that you never ever come back to the definition of inverse_on, but only use the two lemmas saying that f (inverse_on U f y) = y if y \in f''(U), and that inverse_on U f( f x) = x if x \in U and f is injective on U.

#### Patrick Massot (Jun 27 2018 at 14:56):

My inverse_on_spec is the conjunction of these two statements

#### Sebastien Gouezel (Jun 27 2018 at 14:56):

Yes, but for one of them you don't need the injectivity.

#### Patrick Massot (Jun 27 2018 at 14:57):

Sure. But I needed injectivity in the definition for psychological confort.

:)

#### Sebastien Gouezel (Jun 27 2018 at 14:57):

Go for the minimal assumptions. It will simplify your proofs if there are less assumptions to check!

#### Patrick Massot (Jun 27 2018 at 15:52):

I noticed Mario sometimes goes for biconditional statements in this situation. It indeed feels weird.

#### Patrick Massot (Jun 27 2018 at 15:53):

I will need a more precise stub for smoothness if I want to prove that equivalence of atlases is an equivalence relation...

#### Johannes Hölzl (Jul 02 2018 at 07:57):

inverse_on is inv_fun_on in logic/function.lean. For surjective functions there is also surj_inv (there the range doesn't need to be inhabited).

#### Patrick Massot (Jul 02 2018 at 09:38):

Thanks! I completely failed to see that file. I still don't understand the criterion separating stuff in data/set/function.lean and logic/function.lean.

#### Mario Carneiro (Jul 02 2018 at 09:44):

I would say that the difference is the use of sets

#### Patrick Massot (Jul 02 2018 at 09:44):

There are sets everywhere in both

#### Mario Carneiro (Jul 02 2018 at 09:45):

logic.function does not import data.set.basic

#### Mario Carneiro (Jul 02 2018 at 09:45):

so the only set stuff is what is available in core

#### Patrick Massot (Jul 02 2018 at 09:46):

Would putting everything in the same file create dependency issues?

yes

#### Mario Carneiro (Jul 02 2018 at 09:47):

although it is likely that inv_fun_on can be moved to set safely

#### Mario Carneiro (Jul 02 2018 at 09:48):

I like to think of the logic directory as covering more or less the "pure type theory" part of lean, just functions and pis and such

Last updated: May 09 2021 at 10:11 UTC

format: plain


text:
# Why a long-dated option has delta > 0.5?

Each option book states that the delta, considered as the hedge ratio and not the probability to have the option exercised, is 50% for ATM options. Anyway, empirically speaking I see it is more than this as the maturity of the option is longer.

Can you please clarify this?

• ATM is usually never 50D. See here for an explanation. It is with higher vol as opposed to time there but if you look at the equation you can see it's the same explanation. Usually books should state ATM is close to 50d, not claim it is 50d. Aug 12 at 7:45
• Thanks @AKdemy, really helpful! Aug 12 at 11:13


text:
## anonymous one year ago 10√x5•x4•x2 simply

1. anonymous

@OregonDuck

2. DanJS

those are powers right

3. anonymous

yes

4. DanJS

$10\sqrt{x^5}* x^4 *x^2$

5. DanJS

is the 5 under the root or outside

6. anonymous

yes

7. DanJS

remember $\sqrt{x} = x ^{1/2}$

8. DanJS

also remember, a power raised to a power, you multiply them together... $[x^{a}]^b = x^{a*b}$

9. DanJS

and lastly, remember, multiplying a base raised to two powers, you ADD them $x^a * x^b = x^{a+b}$

10. DanJS

so, with those notes, can you start it

11. anonymous

i got x = 5

12. DanJS

you cant solve for x, it is not an equation, just make it look different, simpler

13. anonymous

x^ 10/11

14. DanJS

...ill show you step by step

15. DanJS

For the first root term $10\sqrt{x^5} = 10[x ^{5}]^{1/2} = 10x^{5*1/2} = 10x^{5/2}$

16. DanJS

Then when multiplying that by x^4 and x^2 you add the exponents $10x^{5/2}*x^4*x^2 = 10x^{5/2+4+2}$

17. DanJS

so i got $10x^{17/2}$

18. DanJS

you just have to remember the three or so basic exponent rules, then you can do all the probs


text:
# A compound formed by elements X and Y has a cubic structure in which X atoms are at the corner of the cube and also at alternate face centers. Y atoms are present at the body center and also at the alternate edge center of the cube.(e) If all the atoms are removed from one of the axis passing through the middle of the cube containing face center atoms, calculate (i) Zeff, (ii) total number of atoms in a cube, and (iii) formula of the compound.

(i) 2,(ii) 2,(iii) $XY_2$


text:
# All Questions

2k views

### How to find rows that have maximum value?

Suppose if I have following list { {10,b,30}, {100,a,40}, {1000,b,10}, {1000,b,70}, {100,b,20}, {10,b,70} } How to find rows that have max value in ...
695 views

### How to make traditional output for derivatives

Hello again after some pause. i have a problem how to present partial derivatives in traditional form, not as Mathematica gave it to me in its notation. So I want to present this ...
305 views

### Is it possible to use Begin and End inside a Manipulate?

May be someone can explain why I can't use Begin["context`"] and End[] inside a Manipulate ...
464 views

### Prefix operator with low precedence

The question is simple, but I will elaborate on the background as well for those interested in the idea: How to define a new operator with specified precedence value? Background Mathematica was ...
464 views

### Usage of Assuming for Integration

For some reason, when I enter the following integration in Mathematica Assuming[{k ∈ Integers}, Integrate[ Exp[ I k t], {t, -π, π}]] the result turns out to be ...
938 views

### Combined numerical minimization and maximization

I want to numerically calculate the maximum of a function defined by the minimization of another function, like the following: ...
946 views

### Mathematica won't give eigenvectors but Wolfram Alpha will? What am I doing wrong?

If I ask Mathematica to find the eigenvectors and eigenvalues of the matrix: ...
770 views

### How Can I use Solve/Reduce Output

Suppose I want x and y to be rationals Solve[ x^2 + y^2 == 1, {x, y}, Rationals] I am ...
470 views

### Retrieving the ImagePadding in absolute units

Consider the following graphic: g = Graphics[Circle[], Frame -> True, FrameLabel -> {"one", "two"}] Retrieving the ...
322 views

### Using Evaluate and Evaluated -> True in Plot

A few use cases: (1) This, as expected, returns (almost) immediately: f[x_?NumericQ] := Evaluate[(Pause[1]; x)] Plot[f[x], {x, 0, 1}] (2) This takes ...
845 views

### Why is ContourPlot not displaying this curve?

I am using the general form of a second-degree plane curve: $$Ax^2+2Bxy + Cy^2+2Dx + 2Ey + F = 0$$ I want to randomly generate plane curves of this form, so I am using ...
537 views

### How to extract the numerical value of a dynamical variable

I want to inspect interactively an image by selecting points by the mouse pointer. This is easily done by LocatorPane - here is a simplified example: ...
864 views

### Select/Delete with Sublist elements?

Probably easy and short question, I still didn't fully figure out how to easily select/delete sublists from a list. Example: tt = {{2, 4}, {4, 8}} I want to delete/select all the elements where ...
587 views

### Automatically load packages at startup

I'm a physics student and I try to simplify my day with Mathematica. Every time I use Mathematica I need Div[], Grad[], ...
982 views

### Using D to find a symbolic derivative

I need to do the following: Define a function Take the derivative of this function and have a look at the symoblic representation Substitute in some values With the bonus that I want to use the ...
272 views

### How can I compare a dynamic variable with a literal in Mathematica?

I'm doing a Mathematica Notebook and I want to make an alarm clock. Something like this: ...
311 views

### Help on evaluation control?

I want to plot series of slopes: x, 2x, 3x, 4x, 5x, 6x... I'm trying to do this: ...
5k views

### Resources for beautiful Mathematica Stylesheets

When the Wolfram Demonstrations were introduced and the Documentation-Center was redesigned, I remember it was the first time I thought someone had put some effort into creating a beautiful ...
10k views

### How to create word clouds?

Word clouds are rather useless fancy and visually appealing plots, where words are plotted with different sizes according to their frequency in a corpus. Many applications exist out there (Wordle, ...
12k views

### How to make an inkblot?

How to effectively create a polygon that looks like a realistic inkblot? So far, I could come up with this (borrowing from Ed Pegg Jr.'s Rorschach demonstration): ...
5k views

### How to peel the labels from marmalade jars using Mathematica?

How can I detect and peel the label from the jar below (POV, cylinder radius, jar contents are all unknown) to get something like this, which is the original label before it was stuck on the jar? ...
2k views

### How can I make an X-Y scatter plot with histograms next to the X-Y axes?

I just saw a nice plot there: How could I implement that in Mathematica — by which I mean the plot structure, not so much the styling.
1k views

This is my oldest question on SO. It still hasn't generated a useful answer there, so I thought I'd give it a try here. The question was: I don't seem to be able to find the method to generate the ...
805 views

### Compiling more functions that don't call MainEvaluate

I would like to use Compile with functions defined outside Compile. For example if I have the two basic functions F and G F[x_] := x + 2 G[x_] := x And I want ...
1k views

### How to visualize/edit a big matrix as a table?

Is it possible to visualize/edit a big matrix as a table ? I often end up exporting/copying big tables to Excel for seeing them, but I would prefer to stay in Mathematica and have a similar view as in ...
3k views

### Computing and plotting a spectrogram in Mathematica

How can I compute and plot the spectrogram of a signal/time series/data in Mathematica? I have a WAV file, sampled at 44100 samples/second and I want to generate a spectrogram of that data. Something ...
1k views

### Saving Mathematica kernel state?

If I save a notebook, I only save what I see. That is, if I close Mathematica and reopen the notebook later, all previous calculations are lost, except for those things I've output. Now I know that ...
5k views

### How to use Mathematica functions in Python programs?

I'd like to know how can I call Mathematica functions from Python. I appreciate a example, for example, using the Mathematica function Prime. I had search about MathLink but how to use it in Python ...
1k views

### Simpler input for the new unit support

I've been playing with the new unit support in Mathematica 9. It seems very useful, but the syntax is very verbose. Instead of typing: ...
1k views

### How to make a drop-shadow for Graphics3D objects

What's the best way to make a drop shadow for a 3D object? image = Graphics3D[Sphere[], Boxed -> False] I can get a blurry black outline of this: ...
733 views

### What is the complete list of valid Front End Tokens?

What is the complete list of valid Front End Tokens? Preferably, by version number.
669 views

### Programmatically move the cursor to a desired location on the screen

Is it possible to set/move the mouse pointer's location directly from Mathematica without using external tools like Run["xdotool mousemove x y"]?
2k views

### Extract current viewing parameters from a 3D view?

Is there a way to find out the current viewing parameters of a 3D view? What often happens is that I create a view, for example: ...
358 views

### How can I make threading more flexible?

Threading automatically with Listable functions requires the argument expressions to have the same length (or for one of them to be atomic). For nested lists the ...
1k views

### Point Renderings Slightly Off in Mathematica

The Mathematica code ...
958 views

### Faster alternatives for DayOfWeek

It has been noticed on several occasions that DayOfWeek function is rather slow when applied to a large list of dates, e.g. in this recent question. What faster ...
1k views

### Vertically aligning two separate plots

How do I vertically align plots so that the two plots are displayed in a way that lines up with respect to the axes? The code I have so far is: ...
729 views

### Transpose uneven lists

Is there a quick method to transpose uneven lists without conditionals? With: Drop[Table[q, {10}], #] & /@ Range[10] Thus the first list would have the ...
3k views

### How to create a heatmap from list of coordinates?

I have a list of coordinates in form {{x1,y1},{x2,y2},...} Is there a way in mma to builds density plots based on position ( ...
469 views

### Optimising 2D binning code

I have a set of (x,y,z) data, 45,000 to be precise and I want to bin the z values in 256 equidistant bins based on their (x,y) values. The final array should be a set of 256x256 array with each slot ...
5k views

### Is it possible to export the equations from Mathematica to MATLAB?

Is it possible to export the output expressions from Mathematica computations (e.g., equations) in valid MATLAB syntax?
2k views

### Given a Table of Plots with some parameter, how would I mark each of the plots with that parameter

I've got a two variable function that I'm plotting against one axis for a few different values of a parameter ...
2k views

### Plotting several functions

I'd like to plot a function of one real and one integer variable, but I don't want them all shown in the same 2-D plot - I'd like to see them as separate curves so I can see both 'axes', more like ...
6k views

### How to make Jacobian automatically in Mathematica

If we have two vectors, a and b, how can I make Jacobian matrix automatically in Mathematica?  a=\left( \begin{array}{c} \text{x1}^3+2\text{x2}^2 \\ 3\text{x1}^4+7\text{x2} \end{array} ...
321 views

### Custom functions by delegating options in a specific way and using core functions

I'd like to create a custom function that does essentially the same as a core function of mathematica but uses different default settings. Example: I want a Plot function that uses Mathematica's core ...
438 views

### How to automate a FrontEnd return?

I use some custom shortcut keys in KeyEventTranslations.tr. One is for the Delete All Output function: ...
1k views

### How to fit 3 data sets to a model of 4 differential equations?

I'm a biologist and a newbie in Mathematica. I want to fit three data sets to a model consisting of four differential equations and 10 parameters. I want to find the parameters best fitting to my ...
1k views

### How do I use Map for a function with two arguments?

I'm a newbie who tries to be a good boy, and use Map instead of writing out a list of functions. I have a table I want to Map ...


text:
# Cost-Utility Analysis of IEV Drug Regimen Versus ESHAP Drug Regimen for the Patients With Relapsed and Refractory Hodgkin and Non-Hodgkin’s Lymphoma in Iran

AUTHORS

Nahid Hatam 1 , Mehdi Dehghani 2 , Mostafa Habibian 3 , Abdosaleh Jafari 4 , *

1 School of Management and Information Sciences, Shiraz University of Medical Sciences, Shiraz, IR Iran

2 Hematology and Oncology Ward, Hematology Research Center, Shiraz University of Medical Sciences, Shiraz, IR Iran

3 Student Research Committee, Department of Health Economics, School of Management and Information Sciences, Shiraz University of Medical Sciences, Shiraz, IR Iran

4 Health Management and Economics Research Center, Iran University of Medical Sciences, Tehran, IR Iran

How to Cite: Hatam N, Dehghani M, Habibian M, Jafari A. Cost-Utility Analysis of IEV Drug Regimen Versus ESHAP Drug Regimen for the Patients With Relapsed and Refractory Hodgkin and Non-Hodgkin’s Lymphoma in Iran, Int J Cancer Manag. 2015 ; 8(5):e4061. doi: 10.17795/ijcp-4061.

ARTICLE INFORMATION

Iranian Journal of Cancer Prevention: 8 (5); e4061
Published Online: October 27, 2015
Article Type: Research Article
Accepted: October 7, 2015

# Crossmark

#### CHEKING

##### Abstract

Background: Chemotherapy for lymph nodes cancer is often composed of several drugs that are used in a treatment program.

Objectives: The aim of this study was to perform a cost-utility analysis of IEV regimen (ifosfamide, epirubicin and etoposide) versus ESHAP regimen (etoposide, methylprednisolone, high-dose cytarabine, and cisplatin) in patients with lymphoma in the south of Iran.

Patients and Methods: This was a cost-utility analysis done as a cross-sectional study in the south of Iran. Using decision tree, expected costs, quality -adjusted life years (QALYs) and the incremental cost-effectiveness ratio (ICER) were estimated. In addition, the robustness of results was examined by sensitivity analysis.

Results: The results of this study indicated that the total lymphoma patients were about 65 people that 27 patients received IEV regimen and 38 patients ESHAP (43 patients with Hodgkin’s and 22 with non-Hodgkin lymphoma). The results of decision tree showed that in the IEV arm, the expected cost was $20952.93 and the expected QALYs was 3.89 and in the ESHAP arm, the expected cost was$31691.74 and the expected QALYs was 3.86. Based on the results of the study, IEV regimen was cost-effective alternative to the ESHAP regimen.

Conclusions: According to the results of this study, it is recommended that oncologists use IEV instead of ESHAP in the treatment of patients with lymphoma and because of high costs of IEV drug costs, it is suggested that IEV drugs should be covered by insurance.

## Keywords

Hodgkin Lymphoma Non-Hodgkin’s Lymphoma Cost-Utility Analysis IEV ESHAP

Copyright © 2015, Iranian Journal of Cancer Prevention.This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/) which permits copy and redistribute the material just in noncommercial usages, provided the original work is properly cited.

### 1. Background

14 million cases of cancer are diagnosed annually and the number of cancer patients will reach 24 million people in the world by the year 2035 (1). In 2012, in the United States, the death rate from lymphoma, both among women and men, included 3% of all cases of death (2). In 2008, in Canada, 7,000 new cases were detected and 3,100 deaths occurred approximately (3). The non-Hodgkin’s lymphomas are the second cancer rising, both in terms of incidence and mortality, and its incidence has doubled since 1970 (4). Non-Hodgkin’s lymphomas are the most common hematologic malignancy among adults in the world (5) and the sixth type of malignant neoplasm in the United States (6). The incidence of Hodgkin’s lymphomas in the United States and England is 2.7 to 2.8 per 100,000, and 1,700 new cases are identified annually (7).

In Iran, cancer is the third leading cause of death after cardiovascular diseases and accidents. It is estimated that more than 70,000 new cases of cancer occur every year in the country (8). In 2009, the total number of cancer cases reported were 74,067 people, 55.58% in males and 44.42% in females. In the meantime, the age-standardized incidence rate of Lymphoma cancer is 4.57 among men in Fars province (9).

Due to the increase in life expectancy and lifestyle choices related to cancer, the burden of cancer is increasing in developing countries (10). The study of Khajedaluee et al. in Mashhad, Iranindicated that the most disability adjusted life years (DALY) were attributed to gastric, leukemia and lung cancers and the maximum DALY was related to breast cancer in women aged 30 - 44 years old (11). Murray et al. in a study concluded that stomach cancer, other neoplasms, liver cancer, and trachea, bronchus, and lung cancers caused more than 15 million DALYs (12). In one study in Australia in 2001, years life lost (YLL) constituted 78% of the overall DALYs associated with cancer (13).

Because cancer is considered a chronic disease, it impacts the lives of many people in all ages (14). National Institute for America’s Health, in 2010, estimated overall costs of cancer to be about 263.8 billion that includes direct costs ($102.2 billion), indirect costs due to illness, or loss of productivity due to illness ($20.9 billion) and indirect costs due to mortality or reduced productivity due to premature death ($140) (15). Therefore, one can say that after the damage, death and destruction of human, the most important aspect of cancer is the economic aspects and costs that are imposed on the lives of individuals and communities (16). Therefore, it is important to measure the quality of life and cost-effectiveness, and costs as well as quality should be measured in order to make decisions about utilization of resources (17). Many patients with lymphatic cancer received chemotherapy as part of their treatment. Chemotherapy for cancer of the lymph nodes is often composed of several drugs that are used in a treatment program. Although lymphomas are potentially curable with standard chemotherapy, many patients either relapse or never achieve remission unless they use high dose chemotherapy (18). One of these methods is ESHAP regimen, a combination of the chemotherapeutic drugs etoposide, methylprednisolone, high-dose cytarabine, and cisplatin (19), and it has been shown to be active against refractory or relapsed lymphoma (20). Another method is IEV, a combination of three drugs Ifosfamide, epirubicin, and etoposide (21). ### 2. Objectives Due to the various medical expenses in the use of these two methods and, consequently, different financial and economic burden on the health system and also the limited knowledge about the costs and their effectiveness, the researcher aimed to do a study to determine the cost-utility IEV versus ESHAP, which is used commonly in treatment of lymphoma in Iran. ### 3. Patients and Methods This study was a cost- utility analysis done as a cross-sectional study in Amir Hospital in Shiraz, in the south of Iran. The study was conducted on patients who were admitted in Amir Hospital for chemotherapy in 2013. According to hospital statistics, in this period, approximately lymphoma patients were about 65 people, 27 of whom had received IEV and 38 patients ESHAP. Therefore, sampling was not done and all patients were included in the study. All of them underwent one of the two methods: IEV and ESHAP. When using these two methods, courses were repeated every 21 days about 3 - 4 times (21). To determine the cost-utility of IEV versus ESHAP, the decision tree was used. These patients responded to chemotherapy in three forms: complete response, partial response, non-response, complete response (CR) was defined as the complete disappearance of signs and symptoms due to lymphoma and maintained for at least 6 weeks; partial response (PR) was defined as a reduction of at least 50% in the product of the two largest perpendicular diameters of all measurable lesions for a duration of at least 6 weeks. Progression of disease (PD) or non- response was used where there was unequivocal evidence of advancing disease, despite continuation of the treatment (22). First, using this model, the expected costs and QALY were calculated for both methods and the incremental cost-effectiveness ratio was measured; it was defined as the ratio of the difference between the expected cost and expected QALY. In this study, a decision tree model was used to examine the cost and effectiveness of IEV and ESHAP. The decision tree model is a graphic representation of the pathways of diagnosis and treatment of different diseases in which the probabilities, costs and consequences of pathways are shown. The decision tree was shown in Figure 1. Figure 1. Decision Tree of IEV Versus ESHAP Data for this study was divided into two parts: utility and costs. The costs were identified and measured from social perspective. These items include medical and non- medical direct costs and indirect costs. In this study, a data collection form was used to collect data. It consisted of two parts. The first part included demographic data of the patients and the second section contained information about the therapy and pharmaceutical costs, diagnostic and laboratory (lab, radiology, MRI, etc.), the cost of accommodation and traveling and related expenses during chemotherapy. It should be noted that indirect costs are calculated using the human capital approach and because the study period was one year, we did not use the discount rate. To assess the utility of two regimens, the European organization for research and treatment of cancer quality of life questionnaire-core30 (EORTC QLQ-C30) was used (23). This questionnaire consisted of performance scale (physical, role, emotional, cognitive and social), symptom scale (dyspnea, insomnia, appetite loss, constipation, diarrhea and financial difficulties, fatigue, nausea and vomiting, pain), and an overall health-status scale. In the questionnaire, raw scores are considered from 0 to 100 and the highest score represents a high level of functioning, excluding symptom scales in which high scores represent a high level of symptoms. In general, this questionnaire reports separate scores for each dimension. First, using the weighted scores of quality of life, we calculated the utility (between zero and one) finally; the QALY was measured by multiplying the amount of utility in the treatment period (6 months or half a year). The data was collected in this part of the study by interviewing the patient one month after the last chemotherapy because according to oncology experts, drug effect emerges one month after chemotherapy. We also used the contact number of patients, available in patient records, designated time and place of the interview. At the beginning of each interview, the overall goal of the project and interview was explained to each patient separately. The patients who were interested in participation answered questions fully informed and voluntarily. Next, the researcher collected cost data through data collection forms and data on utilities by using a questionnaire (EORTC QLQ-C30). In this section, these data (cost and utility) were simultaneously obtained from the patient. However, during the interview, the interviewer was unaware of the treatment protocol because the study was designed as a double blind study. This increases the accuracy of the interview. At this stage, only the patient record numbers were recorded on a demographic questionnaire. Then, the researchers recorded treatment protocol by referring to the patient records. To perform this analysis, Treeage 2011 and SPSS 16.0 specific software were used as well as descriptive statistical analysis. Also, the Mann-Whitney test was used to determine the significant differences in costs between the two groups. Also, 95% confidence intervals (CIs) were calculated using non-parametric bootstrapping approach for cost and QALY. By the decision tree, the expected costs and QALY were calculated and to increase the accuracy of the study, one-way deterministic sensitivity analysis (Tornado Diagram) and probabilistic sensitivity analysis were performed. ### 4. Results Based on the results of the present study, of the 65 patients studied, 66.1% were male, 67.7% were married, 60% were aged less than 40 years and all patients had insurance. Table 1 shows the mean QALY in patients, using two different regimens of IEV and ESHAP. According to the results, in the IEV, the QALY’s mean was 0.3676 (in Hodgkin lymphoma, 0.3712 and in non-Hodgkin lymphoma 0.362) and in the ESHAP; the QALY’s mean was 0.3029 (in Hodgkin lymphoma, 0.3065 and in non-Hodgkin lymphoma, 0.295). Table 1. QALY Value Based on the Type of Lymphoma Type of LymphomaType of Treatment ProtocolNumber of PatientsQALY a Hodgkin IEV170.3712 ± 0.0754 ESHAP260.3065 ± 0.0651 Non-Hodgkin IEV100.362 ± 0.0885 ESHAP120.295 ± 0.0602 Total IEV270.3676 ± 0.0789 ESHAP380.3029 ± 0.063 aData are presented as mean ± SD. According to Table 2, in both IEV and ESHAP, the mean of medical direct costs was the highest (1191.1 and 1819.57 dollars, respectively) and that of non-medical direct costs was minimum (237.06 and 208.39 dollars, respectively). As seen in Table 2, the mean of medical direct costs was significant in both IEV and ESHAP (P = 0.0001). But the means of non-medical direct costs, indirect costs and total cost difference were not significant statistically. As seen in Table 3, the mean cost of chemotherapy in the IEV was 488.94 dollars that is the highest type of medical direct costs. Also, in the ESHAP, the cost of chemotherapy was 866.92 dollars and it was the highest medical direct costs. Travel costs and indirect costs of the patients were respectively the highest type of non-medical direct costs and indirect costs in both (in the IEV, 149.52 and 562.2 dollars and in the ESHAP 104.75 and 351.65 dollars, respectively). Table 2. The Cost of Cancer Patients With Lymph Node Based on the Type of Costs Type of Treatment ProtocolCosts MeanIEVESHAPP-Value Medical direct costs1191.1 ± 610.741819.57 ± 789.730.0001 Non-medical direct costs237.06 ± 207.42208.39 ± 179.70.545 Indirect costs598.24 ± 584.25456.83 ± 666.090.249 Total2026.42 ± 916.912484.79 ±1060.270.123 Table 3. The Cost Components of IEV and Eshap in Lymphatic Cancer as Included in the Analysisa StrategyIEVESHAP Medical direct costs1191.1 ± 610.741819.57 ± 789.73 Medication488.94 ± 338.57866.92 ± 354.91 Hospitalization127.84 ± 30.25261.35 ± 94.32 Sonography20.63 ± 35.3420.39 ± 34.09 Radiology53.37 ± 42.3872.4 ± 54.05 MRI10.46 ± 25.1216.36 ± 34.88 Surgical cost160.73 ± 399.53113.14 ± 164.96 Laboratory tests143.09 ± 76.89231.6 ± 210.90 CT-sCAN71.47 ± 81.3977.76 ± 80.56 Visits22.57 ± 24.2326.28 ± 21.61 Other91.95 ± 389.42133.33 ± 420.12 Non-medical direct costs237.06 ± 207.42208.39 ± 179.7 Traveling149.52 ± 142.95104.75 ± 98.56 Lodging48.89 ± 77.2455.56 ± 102.37 Phone25.19 ± 23.7823.42 ± 14.32 Auxiliary equipment4.78 ± 23.301.8 ± 7.31 Special diet8.67 ± 14.5022.84 ± 34.52 Indirect costs598.24 ± 584.25456.83 ± 666.09 Time spent by the patient562.2 ± 606.49351.65 ± 655.41 Time spent by the patient’s accompany36.03 ± 52.98105.17 ± 280.48 Total2026.42 ± 916.912484.79 ±1060.27 aData are presented as mean ± SD. The results of decision tree in Figure 1 showed that in the IEV arm, the expected cost was 20952.93 dollars and the expected QALYs were 3.89 and in the ESHAP arm, the expected cost was 31691.74 dollars and the expected QALYs were 3.86. Therefore, IEV is dominant compared to ESHAP (less costly and more effective). #### 4.1. Sensitivity Analysis Given that any economic evaluation study accompanies uncertainty, in this study the effects of uncertainty were examined using one-way and probabilistic sensitivity analysis. In the one-way sensitivity analysis, the value of each variable increased by 20%; in order to create the tornado diagram (24). According to the tornado diagram in Figure 2, changes in most of the input parameters had a few effects on the outcome. The incremental cost-effectiveness ratio (ICER) had high sensitivity to QALY of patients who did not respond to ESHAP and had low sensitivity to the cost of patients who did not respond to IEV. Figure 2. Results of One-Way Sensitivity Analysis (Tornado Diagram) Figure 3 indicated the results of probabilistic sensitivity analysis using Monte Carlo simulation of incremental costs and QALYs IEV versus ESHAP. For each one of the 10,000 iterations, values for parameters were randomly selected from their probability distributions and results showed in 97% of the iterations, IEV was a dominant strategy. In other words, IEV was estimated to have a lower cost and greater QALYs than ESHAP. In addition, maximum willingness to pay (threshold) was calculated based on WHO method (three times of Gross Domestic Product per capita,$9395.4) (25).

Figure 3. Results of Probabilistic Sensitivity Analysis (Each Point Indicates the Differences in Costs and QALYs for IEV vs. ESHAP)

### 5. Discussion

The costs and consequences of interventions and programs are compared in economic evaluation for the optimal use of scarce resources. Therefore, the aim of this study was to perform a cost-utility analysis of IEV versus ESHAP in patients with lymphoma. To our knowledge, this is the first full economic evaluation study in patients with lymphoma in Iran. Because lymphoma is among the ten most common cancers and also cancer is the third leading cause of death in Iran; besides, IEV and ESHAP medication regimens are common drugs in the treatment of lymphoma, the discussion about the effectiveness and costs associated with them is of great importance.

The findings of this study showed that the average direct cost of treatment in IEV and ESHAP arms were 119,1.1 and 181,9.57 dollars respectively and the difference was significant (P value = 0.0001). However, a significant difference was not observed between the mean of non-medical direct costs and indirect costs in two arms. Also, the mean cost of chemotherapy was 866.92 dollars in the ESHAP arm; it is 47.7% of medical direct costs. However, the mean cost of chemotherapy was 866.92 dollars in the IEV arm, which is 41.04% of direct costs. In addition, the mean length of stay for each period of chemotherapy was 3 days in the IEV arm and 5 days in the ESHAP arm. These results could be due to the higher cost of chemotherapy in the ESHAP and probably a lengthier stay would lead to more paraclinical costs. Hackshaw et al. (26), Woronoff-Lemsi et al. (27), Johnston et al. (28), Leese et al. (29), Ray et al. (30) and Kuderer et al. (31) in their study concluded that the main cost drivers were medical direct costs especially chemotherapy drugs and medical direct costs were higher because of the higher cost of chemotherapy. Also, earlier discharge of patients with lymphoma would lead to reducing the length of stay and the medical direct costs.

Based on the results of this study, the means of QALY’s were 0.3676 and 0.3029 in the IEV and ESHAP arms, respectively. In the meantime, the mean of QALY in patients with Hodgkin’s lymphoma was 0.3712 and 0.3065, and in patients with non-Hodgkin’s lymphoma it was 0.362 and 0.295 for the IEV and ESHAP arms, respectively. Based on the findings of this study, it can be stated that quality of life of patients who had received ESHAP is lower than those who had received IEV. This could be because of the lengthier stay for these patients, having a more negative impact on quality of life or may be due to the appropriate dose in the IEV than ESHAP. Hjermstad et al. (32) in their study concluded that the length of stay has much impact on activities including work, family and social and daily activities, affecting their quality of life. So they will have a better quality in functional and emotional dimensions if their length of stay is shorter. Also, Hasanpoor et al. indicated that there was a significant relationship between quality of life and type of cancer (33). Also, Mols et al. (34), Webster and Cella (35) and van Dis et al. (36) indicated that patients who received chemotherapy reported lower overall health-related quality of life scores compared with patients who did not receive chemotherapy.

Based on the results of the study, ESHAP not cost-effective as compared to IEV and it is dominated because the expected cost was 20952.93 dollars and the expected QALY was 3.89 in the IEV arm whereas the expected cost was 31691.74 dollars and the expected QALY was 3.86 in the ESHAP arm. It can be stated that patients who had used the ESHAP had higher medical direct costs because of expensive chemotherapy and the higher mean of length of stay (5 days versus. 3 days) than IEV. Based on the results of the sensitivity analysis, the ICER was highly sensitive to QALY of patients who did not respond to ESHAP and less sensitive to the cost of patients who did not respond to IEV. Overall, the results showed that IEV versus ESHAP was dominant in the treatment of patients with lymphoma. Also, ICER was -379463.42 dollars (using IEV saves 379,463.42 dollars per each additional QALY). Therefore, it is recommended that oncologists should use IEV instead of ESHAP in the treatment of these patients. In addition, the results of the one-way and probabilistic sensitivity analysis powerfully support the conclusion that IEV regimen is a cost-effective option to ESHAP regimen.

As to the generalizability of these findings, we can generalize these results to other Iranian hospitals, because of using IEV and ESHAP in the treatment of lymphoma therein. However, we cannot generalize these results to other countries certainly due to differences in the costs covered by insurance organizations, the patients’ ability to pay, the incidence and prevalence of disease, difference in clinical guidelines, relative prices , payment system and ceiling ratio.

This study had several limitations: first, due to time limits all patients were studied during a course of treatment. Probably, different results would have been obtained if it had been done in a longer time period. Second, due to lack of studies in this field, using Markov models was not possible. Third, drug prices varied during the study so in relation with this case, the average prices were used. Fourth, due to the sensitivity of cancer patients about their disease, using the gentle way to communicate with them is essential. In addition, in this study we used the weighted scores of European quality of life questionnaire for measuring the utility of two regimens (IEV and ESHAP); therefore, the limitation of this questionnaire for Iranian setting must be considered and in future studies, it is suggested that researchers estimate these weighted scores for Iran.

Given the result of this study, it is suggested that IEV drugs be covered by insurance because of high costs of cancer patients or IEV drug costs be paid in health sectors. When developing clinical guidelines for the treatment of lymphoma, the government and the Ministry of Health should consider using IEV method by oncologists to reduce costs.

### References

• 1.

Stewart BW, Wild CP. World Cancer Report 2014. 2014;

• 2.

Thun MJ, DeLancey JO, Center MM, Jemal A, Ward EM. The global burden of cancer: priorities for prevention. Carcinogenesis. 2010; 31(1) : 100 -10 [DOI][PubMed]

• 3.

• 4.

Altekruse S, Kosary C, Krapcho M, Neyman N, Aminou R, Waldron W. SEER Cancer Statistics Review, 1975-2007. 2010;

• 5.

Bray F, Jemal A, Grey N, Ferlay J, Forman D. Global cancer transitions according to the Human Development Index (2008–2030): a population-based study. Lancet Oncol. 2012; 13(8) : 790 -801 [DOI]

• 6.

Jaffe E, Harris N, Stein H, Vardiman J. WHO classification: Pathology and genetics of tumors of haematopoietic and lymphoid tissues. Ann Oncol. 2001; 13(3) : 490 -1 [DOI]

• 7.

Townsend W, Linch D. Hodgkin's lymphoma in adults. Lancet. 2012; 380(9844) : 836 -47 [DOI]

• 8.

Mousavi S. Executive Guideline for Registering and Reporting Cancer Cases. 2007; : 22

• 9.

Iranian National Cancer . Iranian national cancer registration report, 2010. 2010;

• 10.

The GlobalBurden of Disease. 2008;

• 11.

Khajedaluee M, Dadgarmoghaddam M, Saeedi R, Izadi-Mood Z, Abrishami M, Zamani M. Mortality, Morbidity, Survival, and Burden of Top 9 Cancers in a Developing Country. Razavi Int J Med. 2014; 2(3)

• 12.

Murray CJ, Vos T, Lozano R, Naghavi M, Flaxman AD, Michaud C, et al. Disability-adjusted life years (DALYs) for 291 diseases and injuries in 21 regions, 1990–2010: a systematic analysis for the Global Burden of Disease Study 2010. Lancet. 2012; 380(9859) : 2197 -223 [DOI]

• 13.

Department of Human Services . Victorian burden of disease study, Mortality and morbidity in 2001. 2005; : 228

• 14.

Mousavi Jarrahi Y, Mousavi Jarrahi A, Mohagheghi MA. The indirect cost of cancer in Tehran, preliminary report. Cancer Bullet. 2010; 2 : 60 -4

• 15.

Atlanta G. Cancer Facts & Figures 2010. 2010;

• 16.

Davari M, Yazdanpanah F, Aslani A, Hosseini M, Nazari AR, Mokarian F. The Direct Medical Costs of Breast Cancer in Iran: Analyzing the Patient's Level Data from a Cancer Specific Hospital in Isfahan. Int J Prev Med. 2013; 4(7) : 748 -54 [PubMed]

• 17.

Wright MJ, Galea V, Barr RD. Proficiency of balance in children and youth who have had acute lymphoblastic leukemia. Phys Ther. 2005; 85(8) : 782 -90 [PubMed]

• 18.

Canellos GP, Anderson JR, Propert KJ, Nissen N, Cooper MR, Henderson ES, et al. Chemotherapy of advanced Hodgkin's disease with MOPP, ABVD, or MOPP alternating with ABVD. N Engl J Med. 1992; 327(21) : 1478 -84 [DOI][PubMed]

• 19.

Choi CW, Paek CW, Seo JH, Kim BS, Shin SW, Kim YH, et al. ESHAP salvage therapy for relapsed or refractory non-Hodgkin's lymphoma. J Korean Med Sci. 2002; 17(5) : 621 -4 [PubMed]

• 20.

Velasquez WS, McLaughlin P, Tucker S, Hagemeister FB, Swan F, Rodriguez MA, et al. ESHAP--an effective chemotherapy regimen in refractory and relapsing lymphoma: a 4-year follow-up study. J Clin Oncol. 1994; 12(6) : 1169 -76 [PubMed]

• 21.

Zinzani PL, Tani M, Molinari AL, Stefoni V, Zuffa E, Alinari L, et al. Ifosfamide, epirubicin and etoposide regimen as salvage and mobilizing therapy for relapsed/refractory lymphoma patients. Haematologica. 2002; 87(8) : 816 -21

• 22.

Zinzani PL, Barbieri E, Visani G, Gherlinzoni F, Perini F, Neri S, et al. Ifosfamide, epirubicin and etoposide (IEV) therapy in relapsed and refractory high-grade non-Hodgkin's lymphoma and Hodgkin's disease. Haematologica. 1994; 79(6) : 508 -12 [PubMed]

• 23.

Aaronson NK, Ahmedzai S, Bergman B, Bullinger M, Cull A, Duez NJ, et al. The European Organization for Research and Treatment of Cancer QLQ-C30: a quality-of-life instrument for use in international clinical trials in oncology. J Natl Cancer Inst. 1993; 85(5) : 365 -76 [PubMed]

• 24.

Taylor M. What is sensitivity analysis? 2009;

• 25.

Hutubessy R, Chisholm D, Edejer TT. Generalized cost-effectiveness analysis for national-level priority-setting in the health sector. Cost Eff Resour Alloc. 2003; 1(1) : 8 [DOI][PubMed]

• 26.

Hackshaw A, Sweetenham J, Knight A. Are prophylactic haematopoietic growth factors of value in the management of patients with aggressive non-Hodgkin's lymphoma? Br J Cancer. 2004; 90(7) : 1302 -5 [DOI][PubMed]

• 27.

Woronoff-Lemsi MC, Arveux P, Limat S, Deconinck E, Morel P, Cahn JY. Cost comparative study of autologous peripheral blood progenitor cells (PBPC) and bone marrow (ABM) transplantations for non-Hodgkin's lymphoma patients. Bone Marrow Transplant. 1997; 20(11) : 975 -82 [DOI][PubMed]

• 28.

Johnston KM, Marra CA, Connors JM, Najafzadeh M, Sehn L, Peacock SJ. Cost-effectiveness of the addition of rituximab to CHOP chemotherapy in first-line treatment for diffuse large B-cell lymphoma in a population-based observational cohort in British Columbia, Canada. Value Health. 2010; 13(6) : 703 -11 [DOI][PubMed]

• 29.

Leese B, Collin R, Clark DJ. The costs of treating febrile neutropenia in patients with malignant blood disorders. Pharmacoeconomics. 1994; 6(3) : 233 -9 [PubMed]

• 30.

Ray JA, Carr E, Lewis G, Marcus R. An evaluation of the cost-effectiveness of rituximab in combination with chemotherapy for the first-line treatment of follicular non-Hodgkin's lymphoma in the UK. Value Health. 2010; 13(4) : 346 -57 [DOI][PubMed]

• 31.

Kuderer NM, Dale DC, Crawford J, Cosler LE, Lyman GH. Mortality, morbidity, and cost associated with febrile neutropenia in adult cancer patients. Cancer. 2006; 106(10) : 2258 -66 [DOI][PubMed]

• 32.

Hjermstad MJ, Oldervoll L, Fossa SD, Holte H, Jacobsen AB, Loge JH. Quality of life in long-term Hodgkin's disease survivors with chronic fatigue. Eur J Cancer. 2006; 42(3) : 327 -33 [DOI][PubMed]

• 33.

Hasanpour Dehkordi A, Shaaban M. Relationship between cancer characteristics and quality of life in the cancer patients under chemotherapy referred to selected clinic of Tehran university of medical sciences. J Shahrekord Univ Med Sci. 2005; 6(4) : 63 -71

• 34.

Mols F, Aaronson NK, Vingerhoets AJ, Coebergh JW, Vreugdenhil G, Lybeert ML, et al. Quality of life among long-term non-Hodgkin lymphoma survivors: a population-based study. Cancer. 2007; 109(8) : 1659 -67 [DOI][PubMed]

• 35.

Webster K, Cella D. Quality of life in patients with low-grade non-Hodgkin's lymphoma. Oncology (Williston Park, NY). 1998; 12(5) : 697 -714

• 36.

van Dis FW, Mols F, Vingerhoets AJ, Ferrell B, van de Poll-Franse LV. A validation study of the Dutch version of the Quality of Life-Cancer Survivor (QOL-CS) questionnaire in a group of prostate cancer survivors. Qual Life Res. 2006; 15(10) : 1607 -12 [DOI][PubMed]


text:
# Equivalence of ComplexExpand and assuming real arguments

I am wondering why this simplification does not work,

FullSimplify[Im[1/Sin[a]], Assumptions -> Element[a, Reals]]
(*Out[1]= Im(csc(a))*)

while this does:

FullSimplify[ComplexExpand[Im[1/Sin[a]]]]
(*Out[2]= 0*)

I would think the two lines are equivalent? I understand of course that the denominator can become zero, but that does not create an imaginary part... In this particular case I can of course simply use the second version, but I have a problem where ComplexExpand takes very long, so I would like to avoid it. (Mathematica version: 11.1.0.0 for Linux)

• The implicit assumption of real values in ComplexExpand does not carry over to the outside function FullSimplify. Not sure if that answers your question though. – Daniel Lichtblau Mar 8 '18 at 16:58

FullSimplify[Im[1/Sin[a]], Assumptions -> {Element[a, Reals], Sin[a] != 0}]

0

Note that there is a pole in 1/Sin[a], which FullSimplify will not automatically discard. Since the pole is indeterminate, there's no actual guarantee that it doesn't have an imaginary part.

I am not entirely sure why ComplexExpand discards the pole.

• As I said, I understand that there's a pole. I would have thought that the inverse of a real number is real, and ComplexExpand seems to think so, too. Explicitly excluding 0 for the denominator is of course an option, I was hoping for something more general (since there might be many explicit exclusions I'd have to make). – Martin J. Mar 8 '18 at 16:09
• @MartinJ Infinity isn't exactly a real number, so division isn't closed within the reals if the denominator is 0. While it's perfectly reasonable in almost all cases to assume that the division of a real number by a real number is real, it's not actually the case. Add in that division by 0 isn't clear on which infinity it implies (if any), and there's a whole host of issues that result in FullSimplify leaving it alone. ComplexExpand is a little bit looser with its assumptions. – eyorble Mar 8 '18 at 16:15

Mathematica is not so careful with Conjugate, so you could do:

Block[{Im = (#-Conjugate[#])/(2I)&},
FullSimplify[Im[1/Sin[a]], Assumptions->Element[a,Reals]]
]

0

On the other hand, I'm surprised that ComplexExpand is slow, I would have expected the FullSimplify of the ComplexExpand output to be slow.


text:
# zbMATH — the first resource for mathematics

Théorie des noeuds et calcul formel. (Knot theory and computer algebra). (French) Zbl 0731.57005
The article describes some knot- resp. link-invariants such as Alexander polynomial, Jones polynomial, Milnor invariant, Seifert matrix. The appendix contains some hints how these invariants can be explicitly computed using the PROLOG programming language.
##### MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010) 57-04 Software, source code, etc. for problems pertaining to manifolds and cell complexes