Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value functions, i.e., problems of the form min. In order to solve this stochastic composition problem, we propose a class of stochastic compositional gradient descent (SCGD) algorithms that can be viewed as stochastic versions of quasi-gradient method. SCGD update the solutions based on noisy sample gradients of f v , g w and use an auxiliary variable to track the unknown quantity E w [g w (x)]. We prove that the SCGD converge almost surely to an optimal solution for convex optimization problems, as long as such a solution exists. The convergence involves the interplay of two iterations with different time scales. For nonsmooth convex problems, the SCGD achieve a convergence rate of O(k −1/4 ) in the general case and O(k −2/3 ) in the strongly convex case, after taking k samples. For smooth convex problems, the SCGD can be accelerated to converge at a rate of O(k −2/7 ) in the general case and O(k −4/5 ) in the strongly convex case. For nonconvex problems, we prove that any limit point generated by SCGD is a stationary point, for which we also provide the convergence rate analysis. Indeed, the stochastic setting where one wants to optimize compositions of expected-value functions is very common in practice. The proposed SCGD methods find wide applications in learning, estimation, dynamic programming, etc.

A highly flexible Ag2Se based composite film on nylon with a record power factor is prepared for thermoelectric generators.

Modeling the processes of neuronal progenitor proliferation and differentiation to produce mature cortical neuron subtypes is essential for the study of human brain development and the search for potential cell therapies. We demonstrated a novel paradigm for the generation of vascularized organoids (vOrganoids) consisting of typical human cortical cell types and a vascular structure for over 200 days as a vascularized and functional brain organoid model. The observation of spontaneous excitatory postsynaptic currents (sEPSCs), spontaneous inhibitory postsynaptic currents (sIPSCs), and bidirectional electrical transmission indicated the presence of chemical and electrical synapses in vOrganoids. More importantly, singlecell RNA-sequencing analysis illustrated that vOrganoids exhibited robust neurogenesis and that cells of vOrganoids differentially expressed genes (DEGs) related to blood vessel morphogenesis. The transplantation of vOrganoids into the mouse S1 cortex resulted in the construction of functional human-mouse blood vessels in the grafts that promoted cell survival in the grafts. This vOrganoid culture method could not only serve as a model to study human cortical development and explore brain disease pathology but also provide potential prospects for new cell therapies for nervous system disorders and injury.

Surveying brain interneuron development As transient structures in early brain development, the ganglionic eminences generate dozens of different types of interneurons that go on to migrate throughout and weave together the developing brain. Shi et al . analyzed human fetal ganglionic eminences. Single-cell transcriptomics revealed unexpected diversity in the types of progenitor cells involved. The human ganglionic eminence depends more heavily on intermediate progenitor cells as workhorses than does the developing neocortex, with its greater reliance on radial glial cells. —PJH

The recent development of chemical and bio-conjugation techniques allows for the engineering of various protein polymers. However, most of the polymerization process is difficult to control. To meet this challenge, we develop an enzymatic procedure to build polyprotein using the combination of a strict protein ligase OaAEP1 ( Oldenlandia affinis asparaginyl endopeptidases 1) and a protease TEV (tobacco etch virus). We firstly demonstrate the use of OaAEP1-alone to build a sequence-uncontrolled ubiquitin polyprotein and covalently immobilize the coupled protein on the surface. Then, we construct a poly-metalloprotein, rubredoxin, from the purified monomer. Lastly, we show the feasibility of synthesizing protein polymers with rationally-controlled sequences by the synergy of the ligase and protease, which are verified by protein unfolding using atomic force microscopy-based single-molecule force spectroscopy (AFM-SMFS). Thus, this study provides a strategy for polyprotein engineering and immobilization.

Neurogenesis processes differ in different areas of the cortex in many species, including humans. Here, we performed single-cell transcriptome profiling of the four cortical lobes and pons during human embryonic and fetal development. We identified distinct subtypes of neural progenitor cells (NPCs) and their molecular signatures, including a group of previously unidentified transient NPCs. We specified the neurogenesis path and molecular regulations of the human deep-layer, upper-layer, and mature neurons. Neurons showed clear spatial and temporal distinctions, while glial cells of different origins showed development patterns similar to those of mice, and we captured the developmental trajectory of oligodendrocyte lineage cells until the human mid-fetal stage. Additionally, we verified region-specific characteristics of neurons in the cortex, including their distinct electrophysiological features. With systematic single-cell analysis, we decoded human neuronal development in temporal and spatial dimensions from GW7 to GW28, offering deeper insights into the molecular regulations underlying human neurogenesis and cortical development.

We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We propose a single time-scale stochastic approximation algorithm, which we call the Nested Averaged Stochastic Approximation (NASA), to find an approximate stationary point of the problem. The algorithm has two auxiliary averaged sequences (filters) which estimate the gradient of the composite objective function and the inner function value. By using a special Lyapunov function, we show that NASA achieves the sample complexity of O(1/ε 2 ) for finding an ε-approximate stationary point, thus outperforming all extant methods for nested stochastic approximation. Our method and its analysis are the same for both unconstrained and constrained problems, without any need of batch samples for constrained nonconvex stochastic optimization. We also present a simplified parameter-free variant of the NASA method for solving constrained single level stochastic optimization problems, and we prove the same complexity result for both unconstrained and constrained problems.

In this paper we provide faster algorithms for approximately solving discounted Markov decision processes in multiple parameter regimes. Given a discounted Markov decision process (DMDP) with |S| states, |A| actions, discount factor γ ∈ (0, 1), and rewards in the range [−M, M], we show how to compute an ϵ‐optimal policy, with probability 1 − δ in time (Note: We use trueO˜$$ \tilde{O} $$ to hide polylogarithmic factors in the input parameters, that is, trueO˜(f(x))=O(f(x)⋅logfalse(ffalse(xfalse)false)O(1))$$ \tilde{O}\left(f(x)\right)=O\left(f(x)\cdot \log {\left(f(x)\right)}^{O(1)}\right) $$.) trueO˜()()|S|2|A|+false|Sfalse‖Afalse|(1−γ)3log()Mϵlog()1δ.$$ \tilde{O}\left(\left({\left|S\right|}^2\mid A\mid +\frac{\mid S\Big\Vert A\mid }{{\left(1-\gamma \right)}^3}\right)\log \left(\frac{M}{\epsilon}\right)\log \left(\frac{1}{\delta}\right)\right). $$ This contribution reflects the first nearly linear time, nearly linearly convergent algorithm for solving DMDPs for intermediate values of γ. We also show how to obtain improved sublinear time algorithms provided we can sample from the transition function in O(1) time. Under this assumption we provide an algorithm which computes an ϵ‐optimal policy for ϵ∈(]0,M1−γ$$ \epsilon \in \left(0,\frac{M}{\sqrt{1-\gamma }}\right] $$ with probability 1 − δ in time trueO˜()false|Sfalse‖Afalse|M2false(1−γfalse)4ϵ2log()1δ.$$ \tilde{O}\left(\frac{\mid S\Big\Vert A\mid {M}^2}{{\left(1-\gamma \right)}^4{\epsilon}^2}\log \left(\frac{1}{\delta}\right)\right). $$ Furthermore, we extend both these algorithms to solve finite horizon MDPs. Our algorithms improve upon the previous best for approximately computing optimal policies for fixed‐horizon MDPs in multiple parameter regimes. Interestingly, we obtain our results by a careful modification of approximate value iteration. We show how to combine classic approximate value iteration analysis with new techniques in variance reduction. Our fastest algorithms leverage further insights to ensure that our algorithms make monotonic progress towards the optimal value. This paper is one of few instances in using sampling to obtain a linearly convergent linear programming algorithm and we hope that the analysis may be useful more broadly.