Analysis of Langevin Monte Carlo via convex optimization

In this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order $2$. Using this interpretation and techniques borrowed from convex optimization, we give a non-asymptotic analysis of this method to sample from logconcave smooth target distribution on $\mathbb{R}^d$. Based on this interpretation, we propose two new methods for sampling from a non-smooth target distribution, which we analyze as well. Besides, these new algorithms are natural extensions of the Stochastic Gradient Langevin Dynamics (SGLD) algorithm, which is a popular extension of the Unadjusted Langevin Algorithm. Similar to SGLD, they only rely on approximations of the gradient of the target log density and can be used for large-scale Bayesian inference

Siły okluzyjne generowane przez pacjentów bezzębnych z niekorzystnymi warunkami podłoża protetycznego użytkujących protezy całkowite wykonane według systemu biofunkcjonalnego

Głównym celem rehabilitacji protetycznej pacjentów bezzębnych jest przywrócenie warunków biomechanicznych narządu żucia poprzez zastosowanie rozwiązań konstrukcyjnych najbardziej sprzyjających realizacji tego celu. Cel badań. Celem badań była ocena: czy konstrukcja protez całkowitych ma wpływ na wartości i symetrię generowanych sił okluzyjnych oraz dynamiki zmian w zakresie generowanych sił okluzyjnych po zastosowaniu protez całkowitych wykonanych według systemu biofunkcjonalnego. Materiał i metody. Grupa 30 bezzębnych kobiet w przedziale wiekowym 65-80 lat, z niekorzystnymi warunkami podłoża protetycznego. W I etapie pacjentki zostały zaopatrzone protezami całkowitymi wykonanymi w trybie postępowania tradycyjnego (grupa K). Po 3-miesięcznym okresie użytkowania tych protez przeprowadzono instrumentalne pomiary wartości sił okluzyjnych (badanie I). W II etapie tej samej grupie pacjentek, zastosowano protezy wykonane według zasad biofunkcjonalnego systemu protetycznego (BPS) (grupa Z). Instrumentalne pomiary wielkości sił okluzyjnych przeprowadzano po 24 godzinach (badanie II), 1 tygodniu (badanie III) oraz 3 miesiącach użytkowania protez (badanie IV) za pomocą specjalnego przyrządu mierniczego. Uzyskane wyniki zostały opracowane przy zastosowaniu specjalistycznego pakietu programów komputerowych STATISTICA. Wyniki. Wielkości sił zgryzowych u osób użytkujących protezy całkowite wykonane metodą tradycyjną wynosiły w zakresie zębów siecznych 49,49N, w zakresie zębów trzonowych prawych 91,12N, a zębów lewych 75,95N. Zastosowanie uzupełnień protetycznych wykonanych w systemie biofunkcjonalnym, spowodowało wzrost sił okluzyjnych generowanych na poziomie zębów trzonowych prawych i lewych w kolejnych badaniach. W stosunku do wartości osiągniętych podczas użytkowania poprzednich protez uległy one zwiększeniu średnio o 30N. Różnice w wielkości generowanych sił były statystycznie istotne. Wnioski. 1. Konstrukcja protezy całkowitej ma istotny wpływ na wielkość generowanych sił okluzyjnych. 2. Generowanie większych sił okluzyjnych po zastosowaniu protez wykonanych wg systemu biofunkcjonalnego może wskazywać na ich dobre utrzymanie na podłożu. 3. Systematyczny wzrost sił zgryzowych oraz ich symetryczny rozkład na powierzchni okluzyjnej po zastosowaniu protez wykonanych według systemu biofunkcjonalnego może świadczyć, że uzupełnienia te stwarzają korzystniejsze warunki biomechaniczne dla pracy mięśni.The main aim of prosthetic rehabilitation of edentulous patients is to restore the biomechanical conditions of the masticatory system through the use of structural solutions that are most conducive to achieving this goal. Aim of the study. To evaluate whether the method of construction of full prostheses affects the magnitude and symmetry of the occlusal forces that are generated and to study the dynamics of changes in the occlusal forces that occur when using prostheses made according to the biofunctional system. Materials and methods. Thirty edentulous women aged 65–80 years with unfavourable prosthetic base conditions were included in the study. In the first stage, all patients were fitted with full prostheses constructed in accordance with traditional procedures (group K). After a three-month period of using these prostheses, instrumental measurements of the occlusal force were made (Test 1). In the second stage, the same patients were given prostheses constructed according to the principles of the biofunctional prosthetic system (BPS) (Group Z). Instrumental measurements of the occlusal forces thus generated were made after 24 hours (Test 2), one week (Test 3), and three months (Test 4) of use of these prostheses in order to assess their dynamics. The occlusal force measurements were carried out using a special measuring device that was inserted between the upper and lower incisors, then between the molars on the left and the right side. The measurements were processed using the Statistica software package. Results. The magnitude of the occlusal force in patients using the traditional full prostheses was 49.49 N at the incisors, 91.12 N at the right molars, and 75.95 N at the left molars. Replacing the prostheses with ones constructed according to the biofunctional system produced an increase in the occlusal force generated at the right and left molars; this force systematically increased in subsequent measurements – an average increase of 30 N over the forces produced with the traditional prostheses. These differences in the generated forces were statistically significant. Conclusions. 1. The method used to construct prostheses has a significant impact on the magnitude of the generated occlusal force. 2. The generation of larger occlusal forces with biofunctional prostheses may indicate that they have good retention in the prosthetic base. 3. When using a biofunctional prosthesis, a systematic increase in occlusal forces and their symmetric distribution across the occlusal surface can provide evidence that the prosthesis is creating favourable biomechanical conditions for muscle action

Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions

By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of complicated datasets and sampling from them. The proposed algorithm is based on a functional optimization problem, which aims at finding a measure that is close to the data distribution as much as possible and also expressive enough for generative modeling purposes. We formulate the problem as a gradient flow in the space of probability measures. The connections between gradient flows and stochastic differential equations let us develop a computationally efficient algorithm for solving the optimization problem. We provide formal theoretical analysis where we prove finite-time error guarantees for the proposed algorithm. To the best of our knowledge, the proposed algorithm is the first nonparametric IGM algorithm with explicit theoretical guarantees. Our experimental results support our theory and show that our algorithm is able to successfully capture the structure of different types of data distributions.Comment: Published at the International Conference on Machine Learning (ICML) 201

The Wasserstein Distance as a Dissimilarity Measure for Mass Spectra with Application to Spectral Deconvolution

We propose a new approach for the comparison of mass spectra using a metric known in the computer science under the name of Earth Mover\u27s Distance and in mathematics as the Wasserstein distance. We argue that this approach allows for natural and robust solutions to various problems in the analysis of mass spectra. In particular, we show an application to the problem of deconvolution, in which we infer proportions of several overlapping isotopic envelopes of similar compounds. Combined with the previously proposed generator of isotopic envelopes, IsoSpec, our approach works for a wide range of masses and charges in the presence of several types of measurement inaccuracies. To reduce the computational complexity of the solution, we derive an effective implementation of the Interior Point Method as the optimization procedure. The software for mass spectral comparison and deconvolution based on Wasserstein distance is available at https://github.com/mciach/wassersteinms

Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions

International audienceBy building upon the recent theory that estab- lished the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algo- rithm for learning the underlying distributions of complicated datasets and sampling from them. The proposed algorithm is based on a functional optimization problem, which aims at finding a measure that is close to the data distribution as much as possible and also expressive enough for generative modeling purposes. We formulate the problem as a gradient flow in the space of proba- bility measures. The connections between gradi- ent flows and stochastic differential equations let us develop a computationally efficient algorithm for solving the optimization problem. We provide formal theoretical analysis where we prove finite- time error guarantees for the proposed algorithm. To the best of our knowledge, the proposed algo- rithm is the first nonparametric IGM algorithm with explicit theoretical guarantees. Our experi- mental results support our theory and show that our algorithm is able to successfully capture the structure of different types of data distributions

TOF-PET detector concept based on organic scintillators

In this contribution we present a new concept of the large acceptance detector systems based on organic scintillators which may allow for simultaneous diagnostic of large fraction of the human body. Novelty of the concept lies in employing large blocks of polymer scintillators instead of crystals as detectors of annihilation quanta, and in using predominantly the timing of signals instead of their amplitudes

Strip- PET : a novel detector concept for the TOF-PET scanner

We briefly present a design of a new PET scanner based on strips of polymer scintillators arranged in a barrel constituting a large acceptance detector. The solution proposed is based on the superior timing properties of the polymer scintillators. The position and time of the reaction of the gamma quanta in the detector material will be determined based on the time of arrival of light signals to the edges of the scintillator strips

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements