Statistical Optimality of Deep Wide Neural Networks

In this paper, we consider the generalization ability of deep wide feedforward ReLU neural networks defined on a bounded domain $\mathcal X \subset \mathbb R^{d}$. We first demonstrate that the generalization ability of the neural network can be fully characterized by that of the corresponding deep neural tangent kernel (NTK) regression. We then investigate on the spectral properties of the deep NTK and show that the deep NTK is positive definite on $\mathcal{X}$ and its eigenvalue decay rate is $(d+1)/d$. Thanks to the well established theories in kernel regression, we then conclude that multilayer wide neural networks trained by gradient descent with proper early stopping achieve the minimax rate, provided that the regression function lies in the reproducing kernel Hilbert space (RKHS) associated with the corresponding NTK. Finally, we illustrate that the overfitted multilayer wide neural networks can not generalize well on $\mathbb S^{d}$. We believe our technical contributions in determining the eigenvalue decay rate of NTK on $\mathbb R^{d}$ might be of independent interests

Therapeutic targeting of replicative immortality

One of the hallmarks of malignant cell populations is the ability to undergo continuous proliferation. This property allows clonal lineages to acquire sequential aberrations that can fuel increasingly autonomous growth, invasiveness, and therapeutic resistance. Innate cellular mechanisms have evolved to regulate replicative potential as a hedge against malignant progression. When activated in the absence of normal terminal differentiation cues, these mechanisms can result in a state of persistent cytostasis. This state, termed “senescence,” can be triggered by intrinsic cellular processes such as telomere dysfunction and oncogene expression, and by exogenous factors such as DNA damaging agents or oxidative environments. Despite differences in upstream signaling, senescence often involves convergent interdependent activation of tumor suppressors p53 and p16/pRB, but can be induced, albeit with reduced sensitivity, when these suppressors are compromised. Doses of conventional genotoxic drugs required to achieve cancer cell senescence are often much lower than doses required to achieve outright cell death. Additional therapies, such as those targeting cyclin dependent kinases or components of the PI3K signaling pathway, may induce senescence specifically in cancer cells by circumventing defects in tumor suppressor pathways or exploiting cancer cells’ heightened requirements for telomerase. Such treatments sufficient to induce cancer cell senescence could provide increased patient survival with fewer and less severe side effects than conventional cytotoxic regimens. This positive aspect is countered by important caveats regarding senescence reversibility, genomic instability, and paracrine effects that may increase heterogeneity and adaptive resistance of surviving cancer cells. Nevertheless, agents that effectively disrupt replicative immortality will likely be valuable components of new combinatorial approaches to cancer therapy

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Post-capitalist property

When writing about property and property rights in his imagined post-capitalist society of the future, Marx seemed to envisage ‘individual property’ co-existing with ‘socialized property’ in the means of production. As the social and political consequences of faltering growth and increasing inequality, debt and insecurity gradually manifest themselves, and with automation and artificial intelligence lurking in the wings, the future of capitalism, at least in its current form, looks increasingly uncertain. With this, the question of what property and property rights might look like in the future, in a potentially post-capitalist society, is becoming ever more pertinent. Is the choice simply between private property and markets, and public (state-owned) property and planning? Or can individual and social property in the (same) means of production co-exist, as Marx suggested? This paper explores ways in which they might, through an examination of the Chinese household responsibility system (HRS) and the ‘fuzzy’ and seemingly confusing regime of land ownership that it instituted. It examines the HRS against the backdrop of Marx’s ideas about property and subsequent (post-Marx) theorizing about the legal nature of property in which property has come widely to be conceptualized not as a single, unitary ‘ownership’ right to a thing (or, indeed, as the thing itself) but as a ‘bundle of rights’. The bundle-of-rights idea of property, it suggests, enables us to see not only that ‘individual’ and ‘socialized’ property’ in the (same) means of production might indeed co-exist, but that the range of institutional possibility is far greater than that between capitalism and socialism/communism as traditionally conceived

Characterization of Mycobacterium leprae RecA Intein, a LAGLIDADG Homing Endonuclease, Reveals a Unique Mode of DNA Binding, Helical Distortion, and Cleavage Compared with a Canonical LAGLIDADG Homing Endonuclease*

Mycobacterium leprae, which has undergone reductive evolution leaving behind a minimal set of essential genes, has retained intervening sequences in four of its genes implicating a vital role for them in the survival of the leprosy bacillus. A single in-frame intervening sequence has been found embedded within its recA gene. Comparison of the M. leprae recA intervening sequence with the known intervening sequences indicated that it has the consensus amino acid sequence necessary for being a LAGLIDADG-type homing endonuclease. In light of massive gene decay and function loss in the leprosy bacillus, we sought to investigate whether its recA intervening sequence encodes a catalytically active homing endonuclease. Here we show that the purified M. leprae RecA intein (PI-MleI) binds to cognate DNA and displays endonuclease activity in the presence of alternative divalent cations, Mg2+ or Mn2+. A combination of approaches, including four complementary footprinting assays such as DNase I, copper-phenanthroline, methylation protection, and KMnO4, enhancement of 2-aminopurine fluorescence, and mapping of the cleavage site revealed that PI-MleI binds to cognate DNA flanking its insertion site, induces helical distortion at the cleavage site, and generates two staggered double strand breaks. Taken together, these results implicate that PI-MleI possesses a modular structure with separate domains for DNA target recognition and cleavage, each with distinct sequence preferences. From a biological standpoint, it is tempting to speculate that our findings have implications for understanding the evolution of the LAGLIDADG family of homing endonucleases

Systemic administration of β(2)-adrenoceptor agonists, formoterol and salmeterol, elicit skeletal muscle hypertrophy in rats at micromolar doses

1. β(2)-Adrenoceptor agonists provide a potential therapy for muscle wasting and weakness, but their use may be limited by adverse effects on the heart, mediated in part, by β(1)-adrenoceptor activation. 2. Two β(2)-agonists, formoterol and salmeterol, are approved for treating asthma and have an extended duration of action and increased safety, associated with greater β(2)-adrenoceptor selectivity. 3. The pharmacological profiles of formoterol and salmeterol and their effects on skeletal and cardiac muscle mass were investigated in 12-week-old, male F344 rats. Formoterol and salmeterol were each administered via daily i.p. injection at one of seven doses (ranging from 1 to 2000 μg kg(−1) day(−1)), for 4 weeks. Rats were anaesthetised and the EDL and soleus muscles and the heart were excised and weighed. Dose–response curves were constructed based on skeletal and cardiac muscle hypertrophy. 4. Formoterol was more potent than salmeterol, with a significantly lower ED(50) in EDL muscles (1 and 130 μg kg(−1) day(−1), P <0.05), whereas salmeterol had greater intrinsic activity than formoterol in both EDL and soleus muscles (12% greater hypertrophy than formoterol). The drugs had similar potency and intrinsic activity in the heart, with a smaller leftward shift for formoterol than seen in skeletal muscle. A dose of 25 μg kg(−1) day(−1) of formoterol elicited greater EDL and soleus hypertrophy than salmeterol, but resulted in similar β-adrenoceptor downregulation. 5. These results show that doses as low as 1 μg kg(−1) day(−1) of formoterol can elicit significant muscle hypertrophy with minimal cardiac hypertrophy and provide important information regarding the potential therapeutic use of formoterol and salmeterol for muscle wasting