Regression-based {Monte Carlo} integration

© Corentin Salaun, Adrien Gruson, Binh-Son Hua, Toshiya Hachisuka & Gurprit Singh | ACM, (2022). This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in ACM Transactions on Graphics, http://dx.doi.org/10.1145/3528223.3530095.Monte Carlo integration is typically interpreted as an estimator of the expected value using stochastic samples. There exists an alternative interpretation in calculus where Monte Carlo integration can be seen as estimating a constant function—from the stochastic evaluations of the integrand—that integrates to the original integral. The integral mean value theorem states that this constant function should be the mean (or expectation) of the integrand. Since both interpretations result in the same estimator, little attention has been devoted to the calculus-oriented interpretation. We show that the calculus-oriented interpretation actually implies the possibility of using a more complex function than a constant one to construct a more efficient estimator for Monte Carlo integration. We build a new estimator based on this interpretation and relate our estimator to control variates with least-squares regression on the stochastic samples of the integrand. Unlike prior work, our resulting estimator is provably better than or equal to the conventional Monte Carlo estimator. To demonstrate the strength of our approach, we introduce a practical estimator that can act as a simple drop-in replacement for conventional Monte Carlo integration. We experimentally validate our framework on various light transport integrals. The code is available at https://github.com/iribis/regressionmc

Myelofibrosis-Associated Lymphoproliferative Disease: Retrospective Study of 16 Cases and Literature Review

Background. To better describe the clinical, biological, and the outcome of non-Hodgkin's lymphoma (NHL) with, at the initial presentation, bone marrow fibrosis (MF). Patients and Methods. From January 2001 to January 2007, 16 eligible patients with NHL and MF were retrieved from the Pathology Department of the University hospital of Amiens. Median age of patients was 62 years (range 16–74) with a sex ratio male/female of 3. Results. MF is associated with all types of lymphoma predominantly with B-cell phenotype and it seems to be more associated with low-grade NHL. B-symptoms are more frequent at diagnosis and more patients presented with an elevated LDH level. JAK-2 was negative in the 10 patients analysed. Two patients presented with features of primary MF with no evidence of lymphoma. Overall response rate was 94% after the first line of therapy with regression or improvement of MF. Relapse occurred in 8 patients (47%) with recurrence of MF in all of them. After a median follow-up of 42 months, 12 patients were alive with an overall survival rate for the entire group of 75%. Conclusions. MF-associated NHL is a rare manifestation which may be associated with all types of NHL and its presence does not seem to confer a poor prognosis. A search for lymphoproliferation should be considered when the cause of MF is not apparent

Homological algebra for osp(1/2n)

We discuss several topics of homological algebra for the Lie superalgebra osp(1|2n). First we focus on Bott-Kostant cohomology, which yields classical results although the cohomology is not given by the kernel of the Kostant quabla operator. Based on this cohomology we can derive strong Bernstein-Gelfand-Gelfand resolutions for finite dimensional osp(1|2n)-modules. Then we state the Bott-Borel-Weil theorem which follows immediately from the Bott-Kostant cohomology by using the Peter-Weyl theorem for osp(1|2n). Finally we calculate the projective dimension of irreducible and Verma modules in the category O

Attosecond dynamics through a Fano resonance: Monitoring the birth of a photoelectron

This is the author’s version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science on 354, 11 november 2016, DOI: 10.1126/science.aah5188The dynamics of quantum systems are encoded in the amplitude and phase of wave packets. However, the rapidity of electron dynamics on the attosecond scale has precluded the complete characterization of electron wave packets in the time domain. Using spectrally resolved electron interferometry, we were able to measure the amplitude and phase of a photoelectron wave packet created through a Fano autoionizing resonance in helium. In our setup, replicas obtained by two-photon transitions interfere with reference wave packets that are formed through smooth continua, allowing the full temporal reconstruction, purely from experimental data, of the resonant wave packet released in the continuum. In turn, this resolves the buildup of the autoionizing resonance on an attosecond time scale. Our results, in excellent agreement with ab initio time-dependent calculations, raise prospects for detailed investigations of ultrafast photoemission dynamics governed by electron correlation, as well as coherent control over structured electron wave packetsWe thank S. Weber for crucial contributions to the PLFA attosecond beamline, D. Cubaynes, M. Meyer, F. Penent, J. Palaudoux, for setup and test of the electron spectrometer, and O. Smirnova, for fruitful discussions. Supported by ITN-MEDEA 641789, ANR-15-CE30-0001-01-CIMBAAD, ANR11-EQPX0005-ATTOLAB, the European Research Council Advanced Grant XCHEM no. 290853, the European COST Action XLIC CM1204, and the MINECO Project no. FIS2013-42002-R. We acknowledge allocation of computer time from CCC-UAM and Mare Nostrum BS

Lifting and restricting recollement data

We study the problem of lifting and restricting TTF triples (equivalently, recollement data) for a certain wide type of triangulated categories. This, together with the parametrizations of TTF triples given in "Parametrizing recollement data", allows us to show that many well-known recollements of right bounded derived categories of algebras are restrictions of recollements in the unbounded level, and leads to criteria to detect recollements of general right bounded derived categories. In particular, we give in Theorem 1 necessary and sufficient conditions for a 'right bounded' derived category of a differential graded(=dg) category to be a recollement of 'right bounded' derived categories of dg categories. In Theorem 2 we consider the particular case in which those dg categories are just ordinary algebras.Comment: 29 page

A Horizon Study for Cosmic Explorer: Science, Observatories, and Community

Gravitational-wave astronomy has revolutionized humanity's view of the universe. Investment in the field has rewarded the scientific community with the first direct detection of a binary black hole merger and the multimessenger observation of a neutron-star merger. Each of these was a watershed moment in astronomy, made possible because gravitational waves reveal the cosmos in a way that no other probe can. Since the first detection of gravitational waves in 2015, the National Science Foundation's LIGO and its partner observatory, the European Union's Virgo, have detected over fifty binary black hole mergers and a second neutron star merger -- a rate of discovery that has amazed even the most optimistic scientists.This Horizon Study describes a next-generation ground-based gravitational-wave observatory: Cosmic Explorer. With ten times the sensitivity of Advanced LIGO, Cosmic Explorer will push the gravitational-wave astronomy towards the edge of the observable universe ($z \sim 100$). This Horizon Study presents the science objective for Cosmic Explorer, and describes and evaluates its design concepts for. Cosmic Explorer will continue the United States' leadership in gravitational-wave astronomy in the international effort to build a "Third-Generation" (3G) observatory network that will make discoveries transformative across astronomy, physics, and cosmology