Two-Sided Random Matching Markets: Ex-Ante Equivalence of the Deferred Acceptance Procedures

Stable matching in a community consisting of N men and N women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal work by Gale and Shapley. When the input preference profile is generated from a distribution, we study the output distribution of two stable matching procedures: women-proposing-deferred-acceptance and men-proposing-deferred-acceptance. We show that the two procedures are ex-ante equivalent—that is, under certain conditions on the input distribution, their output distributions are identical. In terms of technical contributions, we generalize (to the non-uniform case) an integral formula, due to Knuth and Pittel, which gives the probability that a fixed matching is stable. Using an inclusion-exclusion principle on the set of rotations, we give a new formula that gives the probability that a fixed matching is the women/men-optimal stable matching.

Space, Matter and Interactions in a Quantum Early Universe. Part II: Superalgebras and Vertex Algebras

In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra gu that extends e9. It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn gu into a Lie superalgebra sgu with no superpartners, in order to comply with the Pauli exclusion principle. There is a natural action of the Poincaré group on sgu, which is an automorphism in the massive sector. We introduce a mechanism for scattering that includes decays as particular resonant scattering. Finally, we complete the model by merging the local sgu into a vertex-type algebra.

Symmetry Energy and the Pauli Exclusion Principle

In this article we present a classical potential that respects the Pauli exclusion principle and can be used to describe nucleon-nucleon interactions at intermediate energies. The potential depends on the relative momentum of the colliding nucleons and reduces interactions at low momentum transfer mimicking the Pauli exclusion principle. We use the potential with Metropolis Monte Carlo methods and study the formation of finite nuclei and infinite systems. We find good agreement in terms of the binding energies, radii, and internal nucleon distribution of finite nuclei, and the binding energy in nuclear matter and neutron star matter, as well as the formation of nuclear pastas, and the symmetry energy of neutron star matter.

Nonextensive Tsallis statistics in Unruh effect for Dirac neutrinos

Flavor mixing of quantum fields was found to be responsible for the breakdown of the thermality of Unruh effect. Recently, this result was revisited in the context of nonextensive Tsallis thermostatistics, showing that the emergent vacuum condensate can still be featured as a thermal-like bath, provided that the underlying statistics is assumed to obey Tsallis prescription. This was analyzed explicitly for bosons. Here we extend this study to Dirac fermions and in particular to neutrinos. Working in the relativistic approximation, we provide an effective description of the modified Unruh spectrum in terms of the q-generalized Tsallis statistics, the q-entropic index being dependent on the mixing parameters $$\sin \theta $$ sin θ and $$\Delta m$$ Δ m . As opposed to bosons, we find $$q>1$$ q > 1 , which is indicative of the subadditivity regime of Tsallis entropy. An intuitive understanding of this result is discussed in relation to the nontrivial entangled structure exhibited by the quantum vacuum for mixed fields, combined with the Pauli exclusion principle.

Exploring Better Strategies for RAS Mutation-Associated EGFR-Targeted Resistance in Colorectal Cancer: From the Perspective of Cancer Community Ecology

RAS is the most common mutated gene in colorectal cancer (CRC), and its occurrence is associated with primary and acquired resistance to anti-epidermal growth factor receptor (EGFR) blockade. Cancer community ecology, such as the competitive exclusion principle, is a valuable focus and would contribute to the understanding of drug resistance. We have presented several articles on RAS mutant clonal evolution monitoring during anti-EGFR treatment in CRC. In these articles, the availability of serially collected samples provided a unique opportunity to model the tumor evolutionary process from the perspective of cancer community ecology in those patients upon treatment. In this perspective article, we presented a theoretical basis and evidence from several experimental or phase II clinical trials for the contemporary application of ecological mechanisms in CRC treatment. In general, a reduction in targetable RAS wild-type cells to a maximum tolerated extent, such as continuous treatment, might lead to the competitive release of inextirpable RAS mutant cells and cancer progression. A full understanding of subclonal competition might be beneficial in managing CRC. Several ecological strategies, including anti-EGFR treatment reintroduced at an appropriate point of time for RAS mutant patients, intermittent treatment instead of continuous treatment, the appropriate sequence of nonselective targeted therapy, and combination therapy, were proposed.

Universal Evolutionary Model for Periodical Species

Real-world examples of periodical species range from cicadas, whose life cycles are large prime numbers, like 13 or 17, to bamboos, whose periods are large multiples of small primes, like 40 or even 120. The periodicity is caused by interaction of species, be it a predator-prey relationship, symbiosis, commensalism, or competition exclusion principle. We propose a simple mathematical model, which explains and models all those principles, including listed extremal cases. This rather universal, qualitative model is based on the concept of a local fitness function, where a randomly chosen new period is selected if the value of the global fitness function of the species increases. Arithmetically speaking, the different interactions are related to only four principles: given a couple of integer periods either (1) their greatest common divisor is one, (2) one of the periods is prime, (3) both periods are equal, or (4) one period is an integer multiple of the other.

How Quarks can be derived to Weak Interaction and Spin Classification with respect to the Pauli Exclusion

In this paper, we will strive to derive how quarks relate to spin classification and weak interactions with respect to the Pauli exclusion principle. Papers such as [2] and [3] inspired us to investigate quarks and their connections to weak interaction and spin classification. Being able to understand the inner workings of quarks would help scientists understand how physics work at the smallest level. By deriving it to contemporary physics concepts such as weak interaction, it would allow us to understand how very recent discoveries such as quarks work in the presence of interactions not designed for them. We will present research that attempt to construct how quarks work in weak interactions and prove how quarks play a crucial part in spin classification through using quark models that show why quarks are constrained by the Pauli exclusion principle and tables that show how they affect spin classification through their own properties and spin identifiers. Understanding these interactions will help contribute to every physicist always growing understanding of quarks and will help integrate modeling into the studying of quarks. Quarks are a crucial part of physics at the smallest level and this paper will contribute to knowledge already known and could be used to help other scientists learn more and publish new research about quarks.

Phytoplankton biodiversity and the inverted paradox

Earth’s aquatic food webs are overwhelmingly supported by planktonic microalgae that live in the sunlit water column where only a minimum number of physical niches are readily identifiable. Despite this paucity of environmental differentiation, these “phytoplankton” populations exhibit a rich biodiversity, an observation not easily reconciled with broadly accepted rules of resource-based competitive exclusion. This conundrum is referred to as the “Paradox of the Plankton”. Consideration of physical distancing between nutrient depletion zones around individual phytoplankton, however, suggests a competition-neutral resource landscape. Application of neutral theory to the sheer number of phytoplankton in physically-mixed water masses yields a prediction of astronomical biodiversity, suggesting the inverted paradox: Why are there so few phytoplankton species? Here, we introduce a trophic constraint on phytoplankton that, when combined with stochastic principals of ecological drift, predicts only modest levels of diversity in an otherwise competition-neutral landscape. Our “trophic exclusion” principle predicts diversity to be independent of population size and yields a species richness across cell-size classes that is consistent with broad oceanographic survey observations.

The Paradox of the Plankton: Coexistence of Structured Microbial Communities

In the framework of resource-competition models, it has been argued that the number of species stably coexisting in an ecosystem cannot exceed the number of shared resources. However, plankton seems to be an exception of this so-called "competitive-exclusion principle". In planktic ecosystems, a large number of different species stably coexist in an environment with limited resources. This contradiction between theoretical expectations and empirical observations is often referred to as "The Paradox of the Plankton". This project aims to investigate biophysical models that can account for the large biodiversity observed in real ecosystems in order to resolve this paradox. A model is proposed that combines classical resource competition models, metabolic trade-offs and stochastic ecosystem assembly. Simulations of the model match empirical observations, while relaxing some unrealistic assumptions from previous models.