More Like this

1. Equal area partitions of the sphere with diameter bounds, via optimal transport

   https://doi.org/10.1112/blms.70045  

   Kitagawa, Jun; Takatsu, Asuka (March 2025, Bulletin of the London Mathematical Society)

   Abstract We prove existence of equal area partitions of the unit sphere via optimal transport methods, accompanied by diameter bounds written in terms of Monge–Kantorovich distances. This can be used to obtain bounds on the expectation of the maximum diameter of partition sets, when points are uniformly sampled from the sphere. An application to the computation of sliced Monge–Kantorovich distances is also presented. 

   more » « less
2. Transport inequalities on Euclidean spaces for non-Euclidean metrics

   https://doi.org/10.1007/s00041-020-09766-2  

   Bobkov, S. G.; Ledoux, M. (January 2020, Journal of fourier analysis applications)

   null (Ed.)

   We explore upper bounds on Kantorovich transport distances between probability measures on the Euclidean spaces in terms of their Fourier-Stieltjes transforms, with focus on non-Euclidean metrics. The results are illustrated on empirical measures in the optimal matching problem on the real line. 

   more » « less
3. A pre-expectation calculus for probabilistic sensitivity

   https://doi.org/10.1145/3434333  

   Aguirre, Alejandro; Barthe, Gilles; Hsu, Justin; Kaminski, Benjamin Lucien; Katoen, Joost-Pieter; Matheja, Christoph (January 2021, Proceedings of the ACM on Programming Languages)

   null (Ed.)

   Sensitivity properties describe how changes to the input of a program affect the output, typically by upper bounding the distance between the outputs of two runs by a monotone function of the distance between the corresponding inputs. When programs are probabilistic, the distance between outputs is a distance between distributions. The Kantorovich lifting provides a general way of defining a distance between distributions by lifting the distance of the underlying sample space; by choosing an appropriate distance on the base space, one can recover other usual probabilistic distances, such as the Total Variation distance. We develop a relational pre-expectation calculus to upper bound the Kantorovich distance between two executions of a probabilistic program. We illustrate our methods by proving algorithmic stability of a machine learning algorithm, convergence of a reinforcement learning algorithm, and fast mixing for card shuffling algorithms. We also consider some extensions: using our calculus to show convergence of Markov chains to the uniform distribution over states and an asynchronous extension to reason about pairs of program executions with different control flow. 

   more » « less
4. Nucleon-level Effective Theory of μ→e Conversion

   https://doi.org/10.22323/1.413.0099  

   Rule, Evan (February 2024, Sissa Medialab)

   The Mu2E and COMET μ→e collaborations plan to advance branching ratio sensitivities by four orders of magnitude, further constraining new sources of charged lepton flavor violation (CLFV). We formulate a non-relativistic nucleon-level effective theory for this process, in order to clarify what can and cannot be learned about CLFV operator coefficients from elastic μ→e conversion. Utilizing state-of-the-art shell model wave functions, we derive bounds on operator coefficients from existing μ→e conversion results, and estimate the improvement in these bounds that will be possible if Mu2E and COMET reach their design goals. In the conversion process, we employ a treatment of the lepton Coulomb physics that is very accurate, yet yields transparent results and preserves connections to standard-model processes like β decay and μ capture. The formulation provides a bridge between the nuclear physics needed in form factor evaluations and the particle physics needed to relate low-energy constraints from μ→e conversion to UV sources of CLFV. 

   more » « less
5. Neutrino masses from low scale partial compositeness

   https://doi.org/10.1007/JHEP03(2021)112  

   Chacko, Zackaria; Fox, Patrick J.; Harnik, Roni; Liu, Zhen (March 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract We consider a class of models in which the neutrinos acquire Majorana masses through mixing with singlet neutrinos that emerge as composite states of a strongly coupled hidden sector. In this framework, the light neutrinos are partially composite particles that obtain their masses through the inverse seesaw mechanism. We focus on the scenario in which the strong dynamics is approximately conformal in the ultraviolet, and the compositeness scale lies at or below the weak scale. The small parameters in the Lagrangian necessary to realize the observed neutrino masses can naturally arise as a consequence of the scaling dimensions of operators in the conformal field theory. We show that this class of models has interesting implications for a wide variety of experiments, including colliders and beam dumps, searches for lepton flavor violation and neutrinoless double beta decay, and cosmological observations. At colliders and beam dumps, this scenario can give rise to striking signals involving multiple displaced vertices. The exchange of hidden sector states can lead to observable rates for flavor violating processes such as μ → eγ and μ → e conversion. If the compositeness scale lies at or below a hundred MeV, the rate for neutrinoless double beta decay is suppressed by form factors and may be reduced by an order of magnitude or more. The late decays of relic singlet neutrinos can give rise to spectral distortions in the cosmic microwave background that are large enough to be observed in future experiments. 

   more » « less