"Glorious" Lovecraftian Horror Film (July/August 2022) and the Voronoi Pattern in the Liver

“Ghatanothoa clarifies that “satisfaction” means it needs Wes to offer it a piece of his liver, not sex, and passes him a shard of broken glass. With the Ghatanothoa’s father in sight, Wes cuts a hole in his abdomen, and allows Ghatanothoa to pull his liver out.”

In this brand new Lovecraftian horror film – hallmarked by magenta (and a whole lot of BLOOD) – the main character has to sacrifice his liver to the primordial being (etheric entity). He has to offer it via a glory hole – a portal. The metaphysical processing requires his LIVER.

Why the liver???

3d voronoi style


Architecture of Hepatic Tissue

The liver is covered with a connective tissue capsule that branches and extends throughout the substance of the liver as septae. This connective tissue tree provides a scaffolding of support and the highway which along which afferent blood vessels, lymphatic vessels and bile ducts traverse the liver. Additionally, the sheets of connective tissue divide the parenchyma of the liver into very small units called lobules.

The hepatic lobule is the structural unit of the liver. It consists of a roughly hexagonal arrangement of plates of hepatocytes radiating outward from a central vein in the center. At the vertices of the lobule are regularly distributed portal triads, containing a bile duct and a terminal branch of the hepatic artery and portal vein. Lobules are particularly easy to see in pig liver because in that species they are well deliniated by connective tissue septae that invaginate from the capsule.



Hidden Patterns: The Voronoi Theory of the Normal Liver Lobular Architecture and its Applicability in
Hepatic Zonation

Chun Lau

Rutgers, The State University of New Jersey

Bahman Kalantari

Rutgers, The State University of New Jersey

Kenneth Batts

Allina Health

Linda Ferrell

University of California, San Francisco

Scott Nyberg

Mayo Clinic

Rondell Graham

Mayo Clinic

Roger Moreira (  moreira.roger@mayo.edu )

Mayo Clinic

Research Article

Keywords: lobular architecture, Voronoi diagrams, hepatic zonation

DOI: Hidden Patterns: The Voronoi Theory of the Normal Liver Lobular Architecture and its Applicability in Hepatic Zonation. | Research Square


The precise characterization of the lobular architecture of the liver has been subject of investigation since

the earliest historical publications, but an accurate model to describe the hepatic lobular microanatomy is

yet to be proposed. Our aim was to evaluate whether Voronoi diagrams can be used to describe the

classic liver lobular architecture. We examined the histology of normal porcine and human livers and

analyzed the geometric relationships of various microanatomic structures utilizing digital tools. The

Voronoi diagram model described the organization of the hepatic classic lobules with overall accuracy

nearly 90% based on known histologic landmarks. We have also designed a Voronoi-based algorithm of

hepatic zonation, which also showed an overall zonal accuracy of nearly 90%. Therefore, we have

presented evidence that Voronoi diagrams represent the basis of the two-dimensional organization of the

normal liver and that this concept may have wide applicability in liver pathology and research.


Chapter 8 The Liver in Thalassaemia

Under normal circumstances, about one-third of storage iron (ferritin and haemosiderin) in the body is found in the liver. Approximately 98% of hepatic iron is found in hepatocytes, which make up 80% of total liver mass; the remaining 1.5-2% of total liver iron is found in reticuloendothelial cells, endothelial cells, bile ductular cells and fibroblasts. Iron that enters the cell in excess of that required accumulates in the major storage forms of iron, ferritin, and haemosiderin. Progressive accumulation of storage iron is associated with cellular toxicity, although the specific pathophysiologic mechanisms for hepatocytes injury and liver fibrosis are not entirely understood. These include lipid peroxidation of organelle membranes, increased lysosomal fragility and decreased mitochondrial oxidative metabolism. Iron also has a direct effect on collagen synthesis and/or degradation, and alterations in microsomal enzymes.

The liver plays a central role in iron homeostasis. In addition to iron released from transfused red cells, an enhanced rate of gastrointestinal iron absorption has been suggested. This excess iron is initially confined to the Kupffer cells but when transfusion requirements produce massive iron overload, spillover to hepatic parenchyma cells quickly occurs, with the risk of late development of fibrosis and cirrhosis. In patients with β-thalassaemia, in absence of co-factors, the threshold hepatic iron concentration for the development of fibrosis is about 16 mg/g dry weight liver (Angelucci, 2002). Clinical studies suggest a relationship between hepatic iron concentration and the development of iron-induced hepatotoxicity.

Hepatic iron concentration (HIC) is the gold standard for the measurement of body iron overload (HIC in mg/g dry weight × 10.6 = whole body iron store in mg/kg) (Angelucci, 2000). Non-invasive techniques used to assess hepatic iron include computed tomography, biomagnetic liver susceptometry (SQUID) and magnetic resonance imaging (MRI). Of these, relaxation rates R2 (1/T2) and R2 (1/T2*) measured by MRI appear to be the most promising and accurate (Wood, 2005).*

J Magn Reson Imaging

. 2014 Apr;39(4):1007-11.

doi: 10.1002/jmri.24216. Epub 2013 Oct 7.

FerriScan imaging can be utilized to determine hepatic iron concentration (HIC) . . .


R2* as a surrogate measure of ferriscan iron quantification in thalassemia

Wesley C Chan 1, Zahra Tejani, Faisal Budhani, Christine Massey, Masoom A Haider

Affiliations expand


Purpose: To determine whether R2* values are a consistent predictor of hepatic iron concentration (HIC) in thalassemia patients by demonstrating a correlation between R2* relaxation rates and FerriScan-determined HIC.

Materials and methods: Eighty-eight patients with thalassemia major were retrospectively evaluated. All patients underwent FerriScan imaging and multiecho gradient echo imaging. The results from FerriScan analysis were fitted against R2* estimates using linear regression.

Results: There was a very strong linear correlation between R2* values and FerriScan-determined HIC (Spearman correlation of 0.976; 95% confidence interval [CI]: 0.963, 0.984).

Conclusion: R2* values can predict HIC determined by FerriScan using a linear calibration curve. This technique may provide a potentially cost-saving alternative for hepatic iron determination and improve acceptance by referring physicians.

Keywords: iron overload; liver; magnetic resonance imaging; thalassemia.

Some background on one of the co-authors – Christine Massey – of the 2014 hepatic iron concentration study linked above (involving the voronoi-patterned liver and FerriScan):

I, Christine of the Massey family who’s red thumbprint affixed of a flesh and blood living woman, live in the City of Peterborough [Peterborough County], Ontario, Canada, and am competent to testify as an expert to the facts and matters set forth herein.

My statements herein are based upon direct knowledge, unless I state same to be based upon information and belief, in which case I will set forth the source of same, which I verily believe to be true.

I am trained and have worked professionally in the past as a biostatistician, with a master’s degree in biostatistics from the Dalla Lana School of Public Health, University of Toronto, Ontario, Canada.

In May of 2020, I began submitting “freedom of information” requests to Canadian health and science institutions, asking for all studies/reports in the possession/custody/control of each institution that describe the purification of the alleged “COVID-19 virus”, also referred to as “SARS-COV-2”, directly from a sample taken from a diseased human, where the patient sample was not first combined with any other source of genetic material. (my emphasis)


## 2 Delaunay Triangulation#

The second step is to construct a Delaunay Triangulation on these points on a sphere. A standard Delaunay library works on points in a 2D plane. Surprisingly, we can use existing 2D Delaunay libraries to run on points on a sphere. The key idea is to transform the data before running the algorithm.

1. Project the points from the sphere onto an infinite plane using a stereographic projection. This maps the northern hemisphere onto points inside the unit circle, and the southern hemisphere onto points outside the unit circle. There’s a proof that this projection produces a correct Delaunay Triangulation on a sphere; links at the end of the page.
2. Run the unmodified Delaunay triangulation library on the points on the infinite plane. This general idea is useful — instead of modifying an algorithm, you can often modify the input data, run an unmodified algorithm, and then modify the output data.
3. Wrap the results from the infinite plane back onto the sphere.

There will be a hole left over. The outer boundary of the Delaunay Triangulation is the convex hull of those points. That convex hull ends up wrapping into a small polygon near the south pole of the sphere. See this animation I made (also available in animated GIF and Quicktime movieformats).

The convex hull will wrap into a hole at the south pole:

We need to complete the mesh in this hole. It turns out I already implemented this for my dual-mesh library, for different reasons, and I reused that code here. Place a new point on the south pole, then add triangles to connect the edges of the hole to the new point:

This works but it ends up with one extra point that wasn’t in the original set. An improvement, which I haven’t implemented yet, would be to instead reuse an existing point:

1. Rotate all the points so that the last point in the array is on the south pole. (see stackoverflow for math details)
2. Run Delaunay without that point, because the stereographic projection will project that point out to infinity.
3. Stitch that point back in as shown above.

When they speak of this “hole” left over and needing to complete the mesh in said hole (see first image below) – I thought it evocative of both “holes” featured in the film, Glorious . . . the glory hole (see magenta image below) created by the primordial entity and the hole in Wes’s abdomen – one to pull out the liver, and the other to submit/transmit the liver (potentially conveying the transmission of Voronoi as the mesh substrate to seal the hole) . . .

About the Dalla Lana School of Public Health: The Dalla Lana School of Public Health is a Faculty of the University of Toronto that originated as one of the Schools of Hygiene begun by the Rockefeller Foundation in 1927. The School went through a dramatic renaissance after the 2003 SARS crisis and it is now the largest public health school in Canada, with over 800 faculty, 850 students, and research and training partnerships with institutions throughout Toronto and the world. With $33.5-million in research funding per year, the School supports discovery in global health, tobacco impacts on health, occupational disease and disability, air pollution, inner city and Indigenous health, among many other areas. (my emphasis)

In February 2020, I sent myself the following link (which is no longer active), but I had downloaded the information (RE: One Health Initiative Advisory Board – Dalla Lana School of Public Health being on the list, c/o David N. Fisman, scroll down below):


One Health Initiative Website Advisory Board (Hon.)

Established: December 1, 2010

Larry R. Anderson, DVM, MD - Sumner County Family Care Center, PA, Wellington, Kansas (USA)

Steven W. Atwood, VMD, MRCVS, MD, MPH – Animal Health Care Associates, West Tisbury, MA (USA)

B. Sonny Bal, MD, JD, MBA - Associate Professor, Department of Orthopaedic Surgery, University of Missouri School of Medicine (USA)

Donald S. Burke, MD - Dean, Graduate School of Public Health, University of Pittsburgh (USA)

Carina Blackmore, DVM, PhD – State Public Health Veterinarian, Florida Department of Health (USA)

Craig N. Carter, DVM, PhD – Director, University of Kentucky, Veterinary Diagnostic Laboratory (USA)

Nancy Chaney, RN, MS – Environmental Science– Past President, Association of Idaho Cities and Board member, National League of Cities, former mayor, City of Moscow Idaho (USA)

Helena J. Chapman, MD, MPH, PhD – Currently, American Association for the Advancement of Science (AAAS) fellowship, National Aeronautics and Space Administration (NASA) Earth Science Division, Washington, DC (USA)

James L. Cook, DVM, PhD, Diplomate ACVS - William & Kathryn Allen Distinguished Professor in Orthopaedic Surgery, Director, Comparative Orthopaedic Laboratory, University of Missouri (USA)

Virginia M. Dato, MD, MPH - Past President and webmaster American Association of Public Health Physicians (USA)

Peter C. Doherty, BVSc, MVSc, PhD – Nobel Laureate Professor Department of Microbiology and Immunology University of Melbourne, Australia, faculty member University of Tennessee Health Science Center through the College of Medicine and conducts research at St. Jude Children’s Research Hospital, Memphis, Tennessee (USA)

Bernadette Dunham, DVM, PhD - Former Director, Center for Veterinary Medicine, U.S. Food and Drug Administration, Rockville, MD. Currently, Professorial Lecturer, The Milken Institute School of Public Health, George Washington University, Washington, DC (USA)

Mary Echols, DVM, MPH – Former Editor, One Health Newsletter and current Public Health Veterinarian, Palm Beach County (FL) Health Department (USA)

David N. Fisman, MD, MPH – Dalla Lana School of Public Health, University of Toronto and Department of Medicine, North York General Hospital (Canada).

James G. Fox, DVM, MS, DACLAM, FIDSA - Professor and Director of the Division of Comparative Medicine and Professor in the Department of Biological Engineering, Massachusetts Institute of Technology (USA)

Kathleen F. Gensheimer, MD, MPH - Former State Epidemiologist, Maine Center for Disease Control, Department of Health and Human Services, Augusta, ME (USA)

Greg Gray, MD, MPH, FIDSA - Professor, Duke University School of Medicine, Duke Infectious Diseases & Duke Global Health Institute, Durham, North Carolina (USA) and Program in Emerging Infectious Diseases Duke-NUS Graduate Medical School Singapore. Formerly, Director, One Health Center of Excellence for Research & Training, Professor Department of Environmental and Global Health, College of Public Health and Health Professions, and Infectious Diseases and Pathology, College of Veterinary Medicine, University of Florida (USA).

Eleanor M. Green, DVM, DACVIM, DABVP- Carl B. King Dean of Veterinary Medicine, College of Veterinary Medicine & Biomedical Sciences, Texas A&M University, College Station, TX (USA)

John C. Hagan III, MD, FACS, FAAO - Editor, Missouri Medicine: The Journal of the Missouri Medical Association and an ophthalmologist, Kansas City, MO (USA)

*D.A. Henderson, MD, MPH - Professor, Department of Medicine, School of Medicine; Resident Scholar at the Center for Biosecurity of the University of Pittsburgh Medical Center; former Dean of Johns Hopkins School of Public Health from 1977 to 1990; Directed WHO global smallpox eradication program 1966-1977 (USA)

Joan C. Hendricks, VMD, PhD – Former Gilbert S. Kahn Dean, School of Veterinary Medicine, University of Pennsylvania, Philadelphia, PA (USA)

David L. Heymann, MD – Editor, Control of Communicable Diseases Manual and Director, U.K. Health Protection Agency (United Kingdom)

James M. Hughes, MD - Professor of Medicine and Public Health, Emory University (USA)

Martyn H. Jeggo, BVetMed, PhD – Director, Geelong Centre for Emerging Infectious Diseases, Deakin University Medical School, Melbourne, Australia.

Lawrence C. Madoff, MD - Editor, ProMED-mail, Professor of Medicine at the University of Massachusetts Medical School and an infectious disease public health physician (USA).

Indu Mani, DVM, DSc - Editor, Clinician’s Brief, the North American Veterinary Conference’s (NAVC) official small animal veterinary medical journal (USA)

Lonnie J. King, DVM, MP, MPA - Former director of the U.S. Centers for Disease Control’s (CDC) new National Center for Zoonotic, Vector-Borne and Enteric Diseases (NCZVED) and past dean of the College of Veterinary Medicine, Professor of Preventive Medicine and current Interim Vice President for Agriculture and Dean for the College of Food, Agricultural, and Environmental Sciences at Ohio State University (USA)

Roger K. Mahr, DVM – Past President, American Veterinary Medical Association (AVMA) and former Chief Executive Officer of the One Health Commission (USA)

Garth Manning, MB BCh BAO, DRCOG, DAvMed, MRCGP, FRCGP - Chief Executive Officer (CEO) World Organization of Family Doctors [physicians] (WONCA), (Thailand)

Frederick A. Murphy, DVM, PhD - Professor, University of Texas Medical Branch, Department of Pathology, Galveston, TX 77555-0609 (USA)

Björn Olsen, MD - Professor, Senior Physician Infectious Diseases Uppsala University and University Hospital (Sweden)

Michael T. Osterholm, PhD, MPH – Director, Center for Infectious Disease Research & Policy (CIDRAP) Academic Health Center—University of Minnesota (USA)

Peter M. Rabinowitz, MD, MPH – Associate Professor, Department of Environmental and Occupational Health Sciences, Department of Global Health, Department of Family Medicine, Division of Allergy and Infectious Disease (adjunct) University of Washington, School of Public Health, School of Medicine, Director, Center for One Health Research (USA)

Ralph C. Richardson, DVM, Diplomate ACVIM (Oncology, Internal Med) - CEO and Dean, K-State Olathe. Former Dean, College of Veterinary Medicine, Kansas State University (USA)

Kevin M. Sherin, MD, MPH, FACPM, FAAFP - Health Officer and Director of the Florida Department of Health in Orange County, Orlando, Florida (USA)

Gary Simpson, PhD, MD, MSc, MPH – College Master-Paul L. Foster School of Medicine - Texas Tech University Health Science Center, Professor of Infectious Diseases in Medical Education (USA)

*James H. Steele, DVM, MPH – Professor Emeritus, University of Texas School of Public Health (USA)

Cecil B. Wilson, MD, MACP – Practicing internist from Winter Park, Florida (USA), past president of the American Medical Association and past president of the World Medical Association.


Christine Massey

Department of Biostatistics at University Health Network

Christine Massey is a [sic] Department of Biostatistics at University Health Network based in Toronto, Ontario.

(Note: As per Forum guidelines, I cannot publish contact information, but you can search this information online)

Any chance the UHN logo invokes the Ghatanothoa archetype featured in the film, Glorious? See my previous deconstruction of imagery depicting the Ghatanothoa for some context:


August 23, 2022 at 7:15 pm

RE: Lovecraft and Magenta – again:

Presently, there is another Lovecraftian horror film featuring a heavy dose of magenta light (recall Lovecraft claimed – in the context of the Nicholas Cage film, Color out of Space – that magenta did not exist within our visible light spectrum).

Here is a review of the film: GLORIOUS Movie Review **SPOILER ALERT** - YouTube.

Following is a written analysis: 'Glorious' Review: Ryan Kwanten Finds Salvation in Haunted Glory Hole - Variety.

The August 2022 film features Lovecraft’s mythical figure – the Ghatanothoa:


Interestingly, I saw the trailer to this film yesterday, and a couple hours later, I read an article at Super Torch Ritual (behind a paywall – and completely un-related to the film) that featured the Sicilian flag – which can be seen here: What does Sicilian flag really symbolize? - Sicilian Post. I was not previously familiar with the Sicilian flag, but it seems to invoke the Greek mythical beasts – the Gorgons (Medusa, Stheno and Euryale): Medusa, Stheno and Euryale: The Gorgons - Mythological Bestiary #08 See U in History - YouTube. The depiction of Gorgons reminds me a whole lot of Lovecraft’s Ghatanothoa.

I also recall the poster of Everything Everywhere All at Once evoking Lovecraft’s Ghatanothoa in numerous ways (see all of the eyes in the image, and the consistent depiction of appendages – in a circular manner). {Also, since I had previously forgotten, I have been meaning to mention the pineal gland symbolism, and that in the center of the circle is a stylized depiction of an hourglass – denoting time, or perhaps, no time at the very core of the circle.}

Note: Following is an image created by Goro at Super Torch Ritual (STR) that seems significant in terms of symbology (hexagrams, temporal windows, and kicks – as in the film, Inception – kicks imply waking from the dream within a dream), and just happens to be signaling today’s date (August 23, 2022):

Goro’s description: As we discussed previously, Sicily’s flag is a set of hexagonally arranged legs, in effect “kicking” Hex Apex windows including the current one. (Ironically – the stylized image represents the juxtaposition of magenta and green; the original image on the Sicilian flag is red and yellow)




August 25, 2022 at 12:34 pm

On Lovecraft and the Kardashians . . .

Does Kim Kardashian look a bit “Lovecraftian” in this photo? (Refer to images above of the Ghatanothoa)

Source: Kim Kardashian Now Has a Millennial Side Part—See Photos | Glamour

Or does she more closely resemble this image from my comment above?

Some additional archetypal images invoking the same motif:

Interestingly (and very relatedly), following is an ad that appears in the Kim K. article above – ARCHETYPES. This is precisely what I am attempting to reveal – Lovecraftian archetypes, which indeed trace back to more ancient mythos/lore (Celtic, Greek, etc) – and thus, deeply ingrained templates/archetypes that continually floodour unconscious mind:

Addition: Does the tall boot motif in the Kim K. photo look familiar (returning again to the new Lovecraft-inspired film, Glorious)?

Additional studies co-authored by Christine Massey – I suggest they are worthy of exploration . . .







About Princess Margaret Cancer Centre

The Princess Margaret Cancer Centre has 12 site groups and 26 specialty clinics, and more than 3,000 staff who see over 400,000 patient visits every year. 850,000 square feet of clinical space house 202 inpatient beds, 16 linear accelerators, a state-of-the-art Magnetic Resonance-guided Radiation Therapy (MRgRT) suite, and two Leksell Gamma Knife Perfexion units, making it one of the largest comprehensive cancer treatment facilities in the world and the largest radiation treatment centre in Canada.

Princess Margaret sees over 1,000 patients every day and has the capacity to deliver diagnostic, treatment, and follow-up care to close to 200,000 patients and their families every year. In 2016, we saw 17,751 new patients. Among the services provided this past year, we delivered 6,031 cancer surgeries, as well as 37,754 system therapy visits, 91,517 radiation visits, and 428 stem cell transplants.

Through ongoing research, education and innovation, Princess Margaret continues to be on the frontiers of medical, surgical and radiation oncology, embracing the latest technology and international best-practices and setting standards for patient care. (my emphasis)

1 Like

That’s funny, I made a joke on yesterday’s live stream about a “portal potty” and now you post about this film Glorious.

Is it me or that image of H.P. Lovecraft look a bit like Mark Suckerberg?


Every single time I look at the Lovecraft photos, I see Zuckerberg. Every time. The resemblance (facial structure) is so apparent and striking to me.

FYI - Do not ever google “glory hole” – you do not want to know what pops up on your screen – just a ton of disgusting pornographic imagery.

I am only one hour into yesterday’s live stream . . . will look out for your “portal potty” mention. :slight_smile:


Voronoi, Cancer, and Game Theory . . .

VORONOI – 27 Oct 18


보로노이는 카이네이스(Kinase) 표적치료제 신약개발 전문기업입니다. 정밀의학 표적치료제와 Target Protein Degrader(TPD) 개발에 집중하여 암 및 난치성 질환의 극복을 위해 나아가고 있습니다.

Dana-Farber Cancer Institute visits VORONOI…“Strengthening partnerships by strengthening joint research, etc.” … Introducing Voronoi Bio. Dr. Son has developed compounds licensed out to global pharmaceuticals, and now introduces Voronoi Bio. People Sunghwan Kim, PhD (Korean) 보로노이는 글로벌 제약사와 견줄 수 있는 …

Department Affiliations

Department of Biology

External Affiliations

Huck Institutes of the Life Sciences


Game Theory

Evolutionary Genetics

Dynamics of Cancer


Marco Archetti

Teaching Fall 2022

Advanced Genetics (BIOL 422)

Evolutionary Game Theory (BIOL 497) PSU231x73

Defective interfering viruses


Evolutionary Dynamics of Cancer [more…]

Growth Factors and Cell Therapy

156x207 Game theory of cancer

PNAS99x132 Game theory of growth factor production in pancreatic cancer In the way cancer cells work together, a possible tool for their demise nytimes87x87

Warburg Effect

Evolutionary Game Theory

Public goods



Marriage systems

Evolutionary Genetics

Intragenomic conflict

Genetic robustness

[Autumn Colours] (Marco Archetti - Autumn Colors)[ more…[]](Marco Archetti - Autumn Colors)
Experiments and data

Reviews and comments

Naut83x83 nytimes78x78 NG76x65

The hidden warning of fall colors Those brilliant fall outfits may be saving trees Are red autumn leaves a warning sign to insects?



Statistical Game Theory

Game theory and statistics are two huge scientific disciplines that have in turn played a significant role in the development of a wide variety of fields, including computer science, natural sciences, and social sciences. Traditionally, game theory has been used for decision- making in strategic environments where multiple agents interact with each other. For example, in economics, it is often used for designing auctions and for decision-making in competitive markets. In computer science, it has found applications in numerous sub-fields such as distributed computing, network security, robotics, self-driving cars, and in general where multiple self-interested parties interact with each other.

Unlike game theory, statistics has traditionally been used for reasoning in non-strategic and non-adversarial environments. In particular, statistics is concerned with the analysis and interpretation of data generated by some stationary non-reactive source. For exam- ple, in numerous fields such as astronomy, biostatistics, business analytics, epidemiology, finance, statistical analysis, and estimation is often performed on data generated from non- reactive sources. Due to the contrasting settings in which game theory and statistics are often studied, these two disciplines have traditionally been regarded as disparate research areas. However, there is a great degree of commonality between the two fields. A surprising range of developments in classical and modern statistics have a game theoretic component to them:

Classical Developments. Classically, the mathematical philosophy of statistics, in particular frequentist statistics, was concerned about strategic considerations. It posits that the source of samples seen by the statistician is potentially adversarial. This re- sulted in the rich theory of minimax statistical estimation and games [Wal49]. In these games, statistical estimation problems are framed as two-player games in which nature adversarially selects a distribution that makes it difficult for a statistician to perform the estimation. Boosting algorithms, which are often regarded as best off-the-shelf classifiers, can be viewed as playing a zero-sum game against a weak learner [FS96].

Modern Developments. Modern statistical and machine learning applications are increasingly moving towards multi-agent learning as illustrated by the following exam- ples. To allow for various departures of “test environment” from “train environments”, the emerging field of robust machine learning allows for adversarial manipulation of the train or test environments [Pra+20; Sze+13]. An emerging class of density estimators in mod- ern machine learning use an adversarial “critic” of the density estimator to improve the final density estimation [Goo+14]. Finally, approaches for algorithmic fairness [Has+18; DN18], uncertainty quantification (e.g., calibration, prediction intervals) [Gup+21], can be framed as finding the equilibrium of two-player games.

The common theme among these classical and modern developments is an interplay be- tween statistical estimation and two-player games. Moving beyond two-player games, sev- eral emerging problems in statistics and machine learning naturally lead to multi-player games. Due to various privacy concerns, data used in many modern statistical applications in healthcare and advertising is often collected in a decentralized manner by multiple local actors, each with their own self-interests. Statistical inference in such scenarios naturally leads to an interplay with multi-player game theory. All these examples show that the intersection of statistics and game theory is becoming an increasingly relevant sub-field.

In this thesis, we aim to bring together statistics and game theory and study the interplay between the two fields. In particular, we are interested in studying statistical problems from a game theoretic perspective and understand how game theory can advance statistics. Despite the many commonalities between the two fields, the game theoretic perspective of many statistical problems is often ignored due to various analytical and computational reasons…

Voronoi and void statistics for superhomogeneous point processes

Andrea Gabrielli and Salvatore Torquato

“E. Fermi” Center for Research and Studies, Via Panisperna 89A, Compendio del Viminale, 00184 Rome, Italy

Department of Chemistry and Materials Institute, Princeton University, Princeton, New Jersey 08544

(Received 30 April 2004; published 27 October 2004)

We study the Voronoi and void statistics of superhomogeneous (or hyperuniform) point patterns in which the infinite-wavelength density fluctuations vanish. Superhomogeneous or hyperuniform point patterns arise in one-component plasmas, primordial density fluctuations in the Universe, and jammed hard-particle packings. We specifically analyze a certain one-dimensional model by studying size fluctuations and correlations of the associated Voronoi cells. We derive exact results for the complete joint statistics of the size of two Voronoi cells. We also provide a sum rule that the correlation matrix for the Voronoi cells must obey in any space dimension. In contrast to the conventional picture of superhomogeneous systems, we show that infinitely large Voronoi cells or voids can exist in superhomogeneous point processes in any dimension. We also present two heuristic conditions to identify and classify any superhomogeneous point process in terms of the asymptotic behavior of the void size distribution.

Salvatore Torquato is an American theoretical scientist born in Falerna, Italy. His research work has impacted a variety of fields, including physics,[6] chemistry,[7] applied and pure mathematics,[8] materials science,[9] engineering,[10] and biological physics. He is the Lewis Bernard Professor of Natural Sciences in the Department of Chemistry and Princeton Institute for the Science and Technology of Materials at Princeton University. He has been a Senior Faculty Fellow in the Princeton Center for Theoretical Science, an enterprise dedicated to exploring frontiers across the theoretical natural sciences. He is also an Associated Faculty Member in three departments or programs at Princeton University: Physics, Program in Applied and Computational Mathematics, and Mechanical & Aerospace Engineering. On multiple occasions, he was a Member of the School of Mathematics as well as the School of Natural Sciences at the Institute for Advanced Study, Princeton, New Jersey.


Professor Salvatore Torquato, (https://torquatocpanel.deptcpanel.princeton.edu/salvatore/) Lewis Bernard Professor of Natural Sciences, is the Director of the Complex Materials Theory Group. Our research group is based at Princeton University in the Department of Chemistry, the Princeton Institute of Materials, and the Princeton Center for Theoretical Science. We also have affiliations with three other departments/programs: Physics, Applied and Computational Mathematics, and Mechanical & Aerospace Engineering. Research work in the group is centered in statistical mechanics and soft condensed matter theory.

Our current research topics of interest include unusual low-temperature states of matter, packing problems, structure and bulk properties of colloids, liquids, glasses, quasicrystals and crystals, hyperuniformity, novel photonic materials, discrete geometry, self-assembly theory, disordered heterogeneous materials, optimization in materials science, cancer modeling, and biophysics. For more information, please see our News page. (my emphasis)

Some takeaway images from the film, Glorious (please excuse my highly amateur screenshots!) – primarily evoking the Voronoi (polygon) template (in 3D) . . .

Compare images in the film to this image . . .

Additional significant images from the movie – invoking the vagina dentata, the birth canal, and magenta plasma . . .