Random singlets and permutation symmetry in the disordered spin-2 Heisenberg chain: A tensor network renormalization group study

We use a tensor network renormalization group method to study random $S=2$ antiferromagnetic Heisenberg chains with alternating bond strength distributions. In the absence of randomness, bond alternation induces two quantum critical points between the $S=2$ Haldane phase, a partially dimerized phase and a fully dimerized phase, depending on the strength of dimerization. These three phases, called ($\sigma$,$4-\sigma$)=(2,2), (3,1) and (4,0) phases, are valence-bond solid (VBS) states characterized by $\sigma$ valence bonds forming across even links and $4-\sigma$ valence bonds on odd links. Here we study the effects of bond randomness on the ground states of the dimerized spin chain, calculating disorder-averaged twist order parameters and spin correlations. We classify the types of random VBS phases depending on strength of bond randomness $R$ and the dimerization $D$ using the twist order parameter, which has a negative/positive sign for a VBS phase with odd/even $\sigma$. Our results demonstrate the existence of a multicritical point in the intermediate disorder regime with finite dimerization, where (2,2), (3,1) and (4,0) phases meet. This multicritical point is at the junction of three phase boundaries in the $R$-$D$ plane: the (2,2)-(3,1) and (3,1)-(4,0) boundaries that extend to zero randomness, and the (2,2)-(4,0) phase boundary that connects another multicritical point in the undimerized limit. The undimerized multicritical point separates a gapless Haldane phase and an infinite-randomness critical line with the diverging dynamic critical exponent in the large $R$ limit at $D=0$. Furthermore, we identify the (3,1)-(4,0) phase boundary as an infinite-randomness critical line even at small $R$, and find the signature of infinite randomness at the (2,2)-(3,1) phase boundary only in the vicinity of the multicritical point.Comment: 13 pages, 14 figure

The use of multiple molecular markers as predictors of the clinical prognosis of patients with colorectal cancer

AbstractSerum carcinoembryonic antigen (CEA) is most commonly used as a prognostic biomarker for evaluating curatively resected colorectal cancer (CRC) patients, but it has a low sensitivity and specificity. The aim of this study was to evaluate potential genetic markers in CRC patients using membrane array. Fifty CRC patients were enrolled and mRNA expression in their tissues were analyzed using membrane array analysis. Seven genes were analyzed in this study, including ATP2A2, GLUT1, MMP13, MAGE-A2, MAGE-A7, MAGE-A8, and MAGE-A12. Correlations between the results of the membrane array and the clinicopathological features of these CRC patients were then evaluated. The results show that the overexpression of any three or four of these seven genes is correlated with tumor invasion depth, lymphatic invasion, advanced stage, and postoperative recurrence (all p < 0.005). Furthermore, the expression of any four genes was more significantly correlated with clinicopathological characteristics than the expression of only two or three genes. The combination of multiple molecular markers and the membrane array method might be useful for predicting postoperative relapse in CRC patients

Plasticity changes in forebrain activity and functional connectivity during neuropathic pain development in rats with sciatic spared nerve injury

Abstract Neuropathic pain is a major worldwide health problem. Although central sensitization has been reported in well-established neuropathic conditions, information on the acute brain activation patterns in response to peripheral nerve injury is lacking. This study first mapped the brain activity in rats immediately following spared nerve injury (SNI) of the sciatic nerve. Using blood-oxygenation-level-dependent functional magnetic resonance imaging (BOLD-fMRI), we observed sustained activation in the bilateral insular cortices (ICs), primary somatosensory cortex (S1), and cingulate cortex. Second, this study sought to link this sustained activation pattern with brain sensitization. Using manganese-enhanced magnetic resonance imaging (MEMRI), we observed enhanced activity in the ipsilateral anterior IC (AIC) in free-moving SNI rats on Days 1 and 8 post-SNI. Furthermore, enhanced functional connectivity between the ipsilateral AIC, bilateral rostral AIC, and S1 was observed on Day 8 post-SNI. Chronic electrophysiological recording experiments were conducted to confirm the tonic neuronal activation in selected brain regions. Our data provide evidence of tonic activation-dependent brain sensitization during neuropathic pain development and offer evidence that the plasticity changes in the IC and S1 may contribute to neuropathic pain development

Plasticity of cerebellar Purkinje cells in behavioral training of body balance control

Neural responses to sensory inputs caused by self-generated movements (reafference) and external passive stimulation (exafference) differ in various brain regions. The ability to differentiate such sensory information can lead to movement execution with better accuracy. However, how sensory responses are adjusted in regard to this distinguishability during motor learning is still poorly understood. The cerebellum has been hypothesized to analyze the functional significance of sensory information during motor learning, and is thought to be a key region of reafference computation in the vestibular system. In this study, we investigated Purkinje cell (PC) spike trains as cerebellar cortical output when rats learned to balance on a suspended dowel. Rats progressively reduced the amplitude of body swing and made fewer foot slips during a 5-min balancing task. Both PC simple (SSs; 17 of 26) and complex spikes (CSs; 7 of 12) were found to code initially on the angle of the heads with respect to a fixed reference. Using periods with comparable degrees of movement, we found that such SS coding of information in most PCs (10 of 17) decreased rapidly during balance learning. In response to unexpected perturbations and under anesthesia, SS coding capability of these PCs recovered. By plotting SS and CS firing frequencies over 15-s time windows in double-logarithmic plots, a negative correlation between SS and CS was found in awake, but not anesthetized, rats. PCs with prominent SS coding attenuation during motor learning showed weaker SS-CS correlation. Hence, we demonstrate that neural plasticity for filtering out sensory reafference from active motion occurs in the cerebellar cortex in rats during balance learning. SS-CS interaction may contribute to this rapid plasticity as a form of receptive field plasticity in the cerebellar cortex between two receptive maps of sensory inputs from the external world and of efference copies from the will center for volitional movements

Distributed Training Large-Scale Deep Architectures

Scale of data and scale of computation infrastructures together enable the current deep learning renaissance. However, training large-scale deep architectures demands both algorithmic improvement and careful system configuration. In this paper, we focus on employing the system approach to speed up large-scale training. Via lessons learned from our routine benchmarking effort, we first identify bottlenecks and overheads that hinter data parallelism. We then devise guidelines that help practitioners to configure an effective system and fine-tune parameters to achieve desired speedup. Specifically, we develop a procedure for setting minibatch size and choosing computation algorithms. We also derive lemmas for determining the quantity of key components such as the number of GPUs and parameter servers. Experiments and examples show that these guidelines help effectively speed up large-scale deep learning training

Derivative-free tree optimization for complex systems

A tremendous range of design tasks in materials, physics, and biology can be formulated as finding the optimum of an objective function depending on many parameters without knowing its closed-form expression or the derivative. Traditional derivative-free optimization techniques often rely on strong assumptions about objective functions, thereby failing at optimizing non-convex systems beyond 100 dimensions. Here, we present a tree search method for derivative-free optimization that enables accelerated optimal design of high-dimensional complex systems. Specifically, we introduce stochastic tree expansion, dynamic upper confidence bound, and short-range backpropagation mechanism to evade local optimum, iteratively approximating the global optimum using machine learning models. This development effectively confronts the dimensionally challenging problems, achieving convergence to global optima across various benchmark functions up to 2,000 dimensions, surpassing the existing methods by 10- to 20-fold. Our method demonstrates wide applicability to a wide range of real-world complex systems spanning materials, physics, and biology, considerably outperforming state-of-the-art algorithms. This enables efficient autonomous knowledge discovery and facilitates self-driving virtual laboratories. Although we focus on problems within the realm of natural science, the advancements in optimization techniques achieved herein are applicable to a broader spectrum of challenges across all quantitative disciplines.Comment: 39 pages, 3 figure