Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks

Our work is motivated by a desire to study the theoretical underpinning for the convergence of stochastic gradient type algorithms widely used for non-convex learning tasks such as training of neural networks. The key insight, already observed in the works of Mei, Montanari and Nguyen (2018), Chizat and Bach (2018) as well as Rotskoff and Vanden-Eijnden (2018), is that a certain class of the finite-dimensional non-convex problems becomes convex when lifted to infinite-dimensional space of measures. We leverage this observation and show that the corresponding energy functional defined on the space of probability measures has a unique minimiser which can be characterised by a first-order condition using the notion of linear functional derivative. Next, we study the corresponding gradient flow structure in 2-Wasserstein metric, which we call Mean-Field Langevin Dynamics (MFLD), and show that the flow of marginal laws induced by the gradient flow converges to a stationary distribution, which is exactly the minimiser of the energy functional. We observe that this convergence is exponential under conditions that are satisfied for highly regularised learning tasks. Our proof of convergence to stationary probability measure is novel and it relies on a generalisation of LaSalle's invariance principle combined with HWI inequality. Importantly, we assume neither that interaction potential of MFLD is of convolution type nor that it has any particular symmetric structure. Furthermore, we allow for the general convex objective function, unlike, most papers in the literature that focus on quadratic loss. Finally, we show that the error between finite-dimensional optimisation problem and its infinite-dimensional limit is of order one over the number of parameters.Comment: 31 page

Incorporating social objectives in evaluating sustainable fisheries harvest strategy

Fisheries management must take account of environmental sustainability, economic profitability, and social benefits generated by the public resources. The traditional approach of maximum economic yield (MEY), however, is yet to consider social objectives in deriving quantitative quotes. Current MEY evaluation framework would be appropriate if the economic rent was distributed back to the public. If public resources are privatized as corporations, the rent largely flows to the owners of large capital in the fishing industry. This is in stark contrast to the aims of benefiting the community as a whole. In this short paper, we promote a socially responsible framework in decision-making of fisheries management. This approach is beyond the fleet-based MEY approach, for it incorporates fleet profitability, chain profitability, employment, environmental concerns, and broad social benefits, in strict accordance with stock sustainability. Recognizing the needs of fishers, as well as the interests of chain sectors and the broader community, is a vital part of ensuring responsible fishery management and a viable future for Australian fisheries. The established framework will provide open view scenarios and enrich the MEY approaches in fisheries management

Impact of central venous pressure on the mortality of patients with sepsis-related acute kidney injury: a propensity score-matched analysis based on the MIMIC IV database

Central venous pressure (CVP); Database; MortalityPressió venosa central (PVC); Base de dades; MortalitatPresión venosa central (PVC); Base de datos; MortalidadBackground: Sepsis has long been a life-threatening organ dysfunction. Sepsis associated acute kidney injury (SA-AKI) is an important complication of sepsis, as an important hemodynamic index, the impact of central venous pressure (CVP) on sepsis patients needs to be explored. Thus this study aimed to investigate the relationship between CVP and the mortality of SA-AKI. Methods: Clinical data of adult patients with sepsis-related acute kidney injury, defined as met both the Sepsis 3.0 criteria and the Kidney Disease Improving Global Outcomes Clinical Practice Guideline (KDIGO) criteria, were obtained from the Medical Information Mart for Intensive Care-IV (MIMIC-IV) database. The included cohort was divided into a high CVP and a low CVP group were determined based on the cuf-off value from receiver operating characteristic curve, with propensity score-matched analysis of the 28-day mortality for both groups and sensitivity analysis using inverse the probability-weighting model, multifactorial regression, and doubly robust estimation, patients acquired chronic coronary syndrome (CCS) and diabetes were also taken into consideration. Results: Of 1,377 patients with sepsis-related acute kidney injury, low CVP group (<13 mmHg) was 67.4% (n=928) and high CVP group (≥13 mmHg) was 32.6% (n=449). The two groups were matched 1:1 by propensity score to obtain a matched cohort (n=288). The mortality rates in the low versus high CVP group (19.4% vs. 34.7%) were statistically difference (odds ratio OR: 0.454; 95% confidence interval 0.263, 0.771). Moreover, the bistable analysis of logistic regression of the matched cohort (OR: 0.434; 95% CI: 0.244, 0.757), propensity score inverse probability weighting (IPW) (OR: 0.547; 95% CI: 0.454, 0.658), and multifactorial logistic regression (OR: 0.352; 95% CI: 0.127, 0.932) all yielded the same results. Conclusions: In patients with sepsis-related acute kidney injury, a lower CVP level (<13 mmHg) is an independent variable associated with decreased mortality. The threshold of CVP needs to be controlled in clinical work to improve the prognosis of patients with SA-AKI

Application of thermosensitive-hydrogel combined with dental pulp stem cells on the injured fallopian tube mucosa in an animal model

Objectives: Fallopian tube (FT) injury is an important factor that can lead to tubal infertility. Stem-cell-based therapy shows great potential for the treatment of injured fallopian tube. However, little research has shown that mesenchymal stem cells (MSCs) can be used to treat fallopian tube damage by in situ injection. In this study, we in situ transplanted PF127 hydrogel encapsulating dental pulp stem cells (DPSCs) into the injured sites to promote the repair and regeneration of fallopian tube injury.Materials and methods: The properties of dental pulp stem cells were evaluated by flow cytometry, immunofluorescence analysis, and multi-differentiation detection. The immunomodulatory and angiogenic characteristics of dental pulp stem cells were analyzed on the basis of the detection of inflammatory factor expression and the formation of capillary-like structures, respectively. The biocompatibility of PF127 hydrogel was evaluated by using Live/Dead and CCK-8 assays. The effects of PF127 hydrogel containing dental pulp stem cells on the repair and regeneration of fallopian tube injury were evaluated by histological analysis [e.g., hematoxylin and eosin (H&amp;E) and Masson’s trichrome staining, TUNEL staining, immunofluorescence staining, and immunohistochemistry], Enzyme-linked immunosorbent assay (ELISA), and RT-PCR detections.Results: Dental pulp stem cells had MSC-like characteristics and great immunomodulatory and angiogenic properties. PF127 hydrogel had a thermosensitive feature and great cytocompatibility with dental pulp stem cells. In addition, our results indicated that PF127 hydrogel containing dental pulp stem cells could promote the repair and regeneration of fallopian tube damage by inhibiting cell apoptosis, stimulating the secretion of angiogenic factors, promoting cell proliferation, modulating the secretion of inflammatory factors, and restoring the secretion of epithelial cells.Conclusion: In this study, our results reported that in situ injection of PF127 hydrogel encapsulating dental pulp stem cells into the injured sites could provide an attractive strategy for the future treatment of fallopian tube injury in clinical settings

Knowledge and attitudes of healthcare workers in Chinese intensive care units regarding 2009 H1N1 influenza pandemic

<p>Abstract</p> <p>Background</p> <p>To describe the knowledge and attitudes of critical care clinicians during the 2009 H1N1 influenza pandemic.</p> <p>Methods</p> <p>A survey conducted in 21 intensive care units in 17 provinces in China.</p> <p>Results</p> <p>Out of 733 questionnaires distributed, 695 were completed. Three hundred and fifty-six respondents (51.2%) reported their experience of caring for H1N1 patients. Despite the fact that 88.5% of all respondents ultimately finished an H1N1 training program, only 41.9% admitted that they had the knowledge of 2009 H1N1 influenza. A total of 572 respondents (82.3%) expressed willingness to care for H1N1 patients. Independent variables associated with increasing likelihood to care for patients in the logistic regression analysis were physicians or nurses rather than other professionals (odds ratio 4.056 and 3.235, p = 0.002 and 0.007, respectively), knowledge training prior to patient care (odds ratio 1.531, p = 0.044), and the confidence to know how to protect themselves and their patients (odds ratio 2.109, p = 0.001).</p> <p>Conclusion</p> <p>Critical care clinicians reported poor knowledge of H1N1 influenza, even though most finished a relevant knowledge training program. Implementation of appropriate education program might improve compliance to infection control measures, and willingness to work in a pandemic.</p

Evidences for pressure-induced two-phase superconductivity and mixed structures of NiTe₂ and NiTe in type-II Dirac semimetal NiTe_(2-x) (x = 0.38 ± 0.09) single crystals

Bulk NiTe₂ is a type-II Dirac semimetal with non-trivial Berry phases associated with the Dirac fermions. Theory suggests that monolayer NiTe₂ is a two-gap superconductor, whereas experimental investigation of bulk NiTe_(1.98) for pressures (P) up to 71.2 GPa do not reveal any superconductivity. Here we report experimental evidences for pressure-induced two-phase superconductivity as well as mixed structures of NiTe₂ and NiTe in Te-deficient NiTe_(2-x) (x = 0.38±0.09) single crystals. Hole-dominant multi-band superconductivity with the P3M1 hexagonal-symmetry structure of NiTe₂ appears at P ≥ 0.5 GPa, whereas electron-dominant single-band superconductivity with the P2/m monoclinic-symmetry structure of NiTe emerges at 14.5 GPa < P < 18.4 GPa. The coexistence of hexagonal and monoclinic structures and two-phase superconductivity is accompanied by a zero Hall coefficient up to ∼ 40 GPa, and the second superconducting phase prevails above 40 GPa, reaching a maximum T_c = 7.8 K and persisting up to 52.8 GPa. Our findings suggest the critical role of Te-vacancies in the occurrence of superconductivity and potentially nontrivial topological properties in NiTe_(2-x)

Mean-field Langevin System, Optimal Control and Deep Neural Networks

In this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introduce a system of mean-field Langevin equations, the invariant measure of which is shown to be the optimal control of the initial problem under mild conditions. Therefore, this system of processes can be viewed as a continuous-time numerical algorithm for computing the optimal control. As an application, this result endorses the solvability of the stochastic gradient descent algorithm for a wide class of deep neural networks

Principal-agent problem with multiple principals

We consider a moral hazard problem with multiple principals in a continuous-time model. The agent can only work exclusively for one principal at a given time, so faces an optimal switching problem. Using a randomized formulation, we manage to represent the agent's value function and his optimal effort by an Itô process. This representation further helps to solve the principals' problem in case we have infinite number of principals in the sense of mean field game. Finally the mean field formulation is justified by an argument of propagation of chaos

Continuous-Time Principal-Agent Problem in Degenerate Systems

25 pagesIn this paper we present a variational calculus approach to Principal-Agent problem with a lump-sum payment on finite horizon in degenerate stochastic systems, such as filtered partially observed linear systems. Our work extends the existing methodologies in the Principal-Agent literature using dynamic programming and BSDE representation of the contracts in the non-degenerate controlled stochastic systems. We first solve the Principal's problem in an enlarged set of contracts defined by a forward-backward SDE system given by the first order condition of the Agent's problem using variational calculus. Then we use the sufficient condition of the Agent's problem to verify that the optimal contract that we obtain by solving the Principal's problem is indeed implementable (i.e. belonging to the admissible contract set). Importantly we consider the control problem in a weak formulation. Finally, we give explicit solution of the Principal-Agent problem in partially observed linear systems and extend our results to some mean field interacting Agents case