Counting Real Connected Components of Trinomial Curve Intersections and m-nomial Hypersurfaces

We prove that any pair of bivariate trinomials has at most 5 isolated roots in the positive quadrant. The best previous upper bounds independent of the polynomial degrees were much larger, e.g., 248832 (for just the non-degenerate roots) via a famous general result of Khovanski. Our bound is sharp, allows real exponents, allows degeneracies, and extends to certain systems of n-variate fewnomials, giving improvements over earlier bounds by a factor exponential in the number of monomials. We also derive analogous sharpened bounds on the number of connected components of the real zero set of a single n-variate m-nomial.Comment: 27 pages, 2 figures. Extensive revision of math.CO/0008069. To appear in Discrete and Computational Geometry. Technique from main theorem (Theorem 1) now pushed as far as it will go. In particular, Theorem 1 now covers certain fewnomial systems of type (n+1,...,n+1,m) and certain non-sparse fewnomial systems. Also, a new result on counting non-compact connected components of fewnomial hypersurfaces (Theorem 3) has been adde

Immersive Demonstrations are the Key to Imitation Learning

Achieving successful robotic manipulation is an essential step towards robots being widely used in industry and home settings. Recently, many learning-based methods have been proposed to tackle this challenge, with imitation learning showing great promise. However, imperfect demonstrations and a lack of feedback from teleoperation systems may lead to poor or even unsafe results. In this work we explore the effect of demonstrator force feedback on imitation learning, using a feedback glove and a robot arm to render fingertip-level and palm-level forces, respectively. 10 participants recorded 5 demonstrations of a pick-and-place task with 3 grippers, under conditions with no force feedback, fingertip force feedback, and fingertip and palm force feedback. Results show that force feedback significantly reduces demonstrator fingertip and palm forces, leads to a lower variation in demonstrator forces, and recorded trajectories that a quicker to execute. Using behavioral cloning, we find that agents trained to imitate these trajectories mirror these benefits, even though agents have no force data shown to them during training. We conclude that immersive demonstrations, achieved with force feedback, may be the key to unlocking safer, quicker to execute dexterous manipulation policies.Comment: This paper is accepted to be presented on IEEE International Conference on Robotics and Automation (ICRA) 202

Promoting tau secretion and propagation by hyperactive p300/CBP via autophagy-lysosomal pathway in tauopathy.

BackgroundThe trans-neuronal propagation of tau has been implicated in the progression of tau-mediated neurodegeneration. There is critical knowledge gap in understanding how tau is released and transmitted, and how that is dysregulated in diseases. Previously, we reported that lysine acetyltransferase p300/CBP acetylates tau and regulates its degradation and toxicity. However, whether p300/CBP is involved in regulation of tau secretion and propagation is unknown.MethodWe investigated the relationship between p300/CBP activity, the autophagy-lysosomal pathway (ALP) and tau secretion in mouse models of tauopathy and in cultured rodent and human neurons. Through a high-through-put compound screen, we identified a new p300 inhibitor that promotes autophagic flux and reduces tau secretion. Using fibril-induced tau spreading models in vitro and in vivo, we examined how p300/CBP regulates tau propagation.ResultsIncreased p300/CBP activity was associated with aberrant accumulation of ALP markers in a tau transgenic mouse model. p300/CBP hyperactivation blocked autophagic flux and increased tau secretion in neurons. Conversely, inhibiting p300/CBP promoted autophagic flux, reduced tau secretion, and reduced tau propagation in fibril-induced tau spreading models in vitro and in vivo.ConclusionsWe report that p300/CBP, a lysine acetyltransferase aberrantly activated in tauopathies, causes impairment in ALP, leading to excess tau secretion. This effect, together with increased intracellular tau accumulation, contributes to enhanced spreading of tau. Our findings suggest that inhibition of p300/CBP as a novel approach to correct ALP dysfunction and block disease progression in tauopathy

Take one for the team: on the time efficiency of application-level buffer-aided relaying in edge cloud communication

[Abstract] Background Adding buffers to networks is part of the fundamental advance in data communication. Since edge cloud computing is based on the heterogeneous collaboration network model in a federated environment, it is natural to consider buffer-aided data communication for edge cloud applications. However, the existing studies generally pursue the beneficial features of buffering at a cost of time, not to mention that many investigations are focused on lower-layer data packets rather than application-level communication transactions. Aims Driven by our argument against the claim that buffers “can introduce additional delay to the communication between the source and destination”, this research aims to investigate whether or not (and if yes, to what extent) the application-level buffering mechanism can improve the time efficiency in edge-cloud data transmissions. Method To collect empirical evidence for the theoretical discussion, we built up a testbed to simulate a remote health monitoring system, and conducted both experimental and modeling investigations into the first-in-first-served (FIFS) and buffer-aided data transmissions at a relay node in the system. Results An empirical inequality system is established for revealing the time efficiency of buffer-aided edge cloud communication. For example, given the reference of transmitting the 11th data entity in the FIFS manner, the inequality system suggests buffering up to 50 data entities into one transmission transaction on our testbed. Conclusions Despite the trade-off benefits (e.g., energy efficiency and fault tolerance) of buffering data, our investigation argues that the buffering mechanism can also speed up data transmission under certain circumstances, and thus it would be worth taking data buffering into account when designing and developing edge cloud applications even in the time-critical context.Chilean National Research and Development Agency; 11180905Ministerio de Ciencia e Innovación de España e European Regional Development Fund; RTC-2017-5908-7Ministerio de Ciencia e Innovación de España e European Regional Development Fund; PID2019-105221RB-C41Xunta de Galicia e European Regional Development Fund; ED431C 2017/58Xunta de Galicia e European Regional Development Fund; ED431G 2019/0

The HMW effect in Noncommutative Quantum Mechanics

The HMW effect in non-commutative quantum mechanics is studied. By solving the Dirac equations on non-commutative (NC) space and non-commutative phase space, we obtain topological HMW phase on NC space and NC phase space respectively, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly.Comment: 8 Latex page

A framework for the production of small area official statistics

Small area estimation is a research area in official and survey statistics of great practical relevance for National Statistical Institutes and related organisations. Despite rapid developments in methodology and software, researchers and users would benefit from having practical guidelines that assist the process of small area estimation. In this paper we propose a general framework for the production of small area statistics that is based on three broadly defined stages namely, Specification, Analysis/Adaptation and Evaluation. The corner stone of the proposed framework is the principle of parsimony. Emphasis is given on the interaction between a user and a methodologist for specifying the target geography and parameters in light of the available data. Model-free and model-dependent methods are described with focus on model selection and testing, model diagnostics and adaptations e.g. use of data transformations. The use of uncertainty measures and model and design-based simulations for method evaluation are also at the centre of the paper. We illustrate each stage of the process both theoretically and by using real data for estimating a simple and complex (non-linear) indicators