Stable Maps Research Articles

Computational case study on upward two-phase flow in vertical circular pipe based on CFD approach: Multidimensional flow instabilities investigation

In this paper, a numeric scheme made up of the three-dimensional (3-D) Two-Fluid Model (TFM) and the Rensselaer Polytechnic Institute (RPI) wall boiling model for two-phase flow instabilities simulation was validated by comparing its results with the flow boiling and instability experimental data. Then two-phase flow instabilities in a vertical circular channel were studied based on the validated numeric scheme. The flow instability was analyzed by both the Lumped Parameter Approach (LPA) and the Distributed Parameter Approach (DPA). The average parameter oscillation characteristics and local distributions were analyzed. The transient responses of the local conditions during the flow instability were discussed. Besides, the stability of the vertical circular tube channel flow boiling system was studied with the stable map based on the subcooling number (Nsub) versus the phase change number (Npch). This study provides a new feasible scheme for the simulation of flow instability which also actualizes an improved understanding of multidimensional flow and heat transfer characteristics in the flow instabilities phenomenon.

Genome-Wide Association Analysis of Stable Stripe Rust Resistance Loci in a Chinese Wheat Landrace Panel Using the 660K SNP Array.

Stripe rust (caused by Puccinia striiformis f. sp. tritici) is one of the most severe diseases affecting wheat production. The disease is best controlled by developing and growing resistant cultivars. Chinese wheat (Triticum aestivum) landraces have excellent resistance to stripe rust. The objectives of this study were to identify wheat landraces with stable resistance and map quantitative trait loci (QTL) for resistance to stripe rust from 271 Chinese wheat landraces using a genome-wide association study (GWAS) approach. The landraces were phenotyped for stripe rust responses at the seedling stage with two predominant Chinese races of P. striiformis f. sp. tritici in a greenhouse and the adult-plant stage in four field environments and genotyped using the 660K wheat single-nucleotide polymorphism (SNP) array. Thirteen landraces with stable resistance were identified, and 17 QTL, including eight associated to all-stage resistance and nine to adult-plant resistance, were mapped on chromosomes 1A, 1B, 2A, 2D, 3A, 3B, 5A, 5B, 6D, and 7A. These QTL explained 6.06–16.46% of the phenotypic variation. Five of the QTL, QYrCL.sicau-3AL, QYrCL.sicau-3B.4, QYrCL.sicau-3B.5, QYrCL.sicau-5AL.1 and QYrCL.sicau-7AL, were likely new. Five Kompetitive allele specific PCR (KASP) markers for four of the QTL were converted from the significant SNP markers. The identified wheat landraces with stable resistance to stripe rust, significant QTL, and KASP markers should be useful for breeding wheat cultivars with durable resistance to stripe rust.

The extra-nice dimensions

We define the extra-nice dimensions and prove that the subset of locally stable 1-parameter families in C^{infty }(Ntimes [0,1],P) is dense if and only if the pair of dimensions (dim N, dim P) is in the extra-nice dimensions. This result is parallel to Mather’s characterization of the nice dimensions as the pairs (n, p) for which stable maps are dense. The extra-nice dimensions are characterized by the property that discriminants of stable germs in one dimension higher have {mathscr {A}}_e-codimension 1 hyperplane sections. They are also related to the simplicity of {mathscr {A}}_e-codimension 2 germs. We give a sufficient condition for any {mathscr {A}}_e-codimension 2 germ to be simple and give an example of a corank 2 codimension 2 germ in the nice dimensions which is not simple. Then we establish the boundary of the extra-nice dimensions. Finally we answer a question posed by Wall about the codimension of non-simple maps.

Curve counting in genus one: Elliptic singularities and relative geometry

We construct and study the reduced, relative, genus one Gromov--Witten theory of very ample pairs. These invariants form the principal component contribution to relative Gromov--Witten theory in genus one and are relative versions of Zinger's reduced Gromov--Witten invariants. We relate the relative and absolute theories by degeneration of the tangency conditions, and the resulting formulas generalise a well-known recursive calculation scheme put forward by Gathmann in genus zero. The geometric input is a desingularisation of the principal component of the moduli space of genus one logarithmic stable maps to a very ample pair, using the geometry of elliptic singularities. Our study passes through general techniques for calculating integrals on logarithmic blowups of moduli spaces of stable maps, which may be of independent interest.

Reactivation predicts the consolidation of unbiased long-term cognitive maps.

Spatial memories that can last a lifetime are thought to be encoded during 'online' periods of exploration and subsequently consolidated into stable cognitive maps through their 'offline' reactivation. However, the mechanisms and computational principles by which offline reactivation stabilize long-lasting spatial representations remain poorly understood. Here, we employed simultaneous fast calcium imaging and electrophysiology to track hippocampal place cells over 2 weeks of online spatial reward learning behavior and offline resting. We describe that recruitment to persistent network-level offline reactivation of spatial experiences in mice predicts the future representational stability of place cells days in advance of their online reinstatement. Moreover, while representations of reward-adjacent locations are generally more stable across days, offline-reactivation-related stability is, conversely, most prominent for reward-distal locations. Thus, while occurring on the tens of milliseconds timescale, offline reactivation is uniquely associated with the stability of multiday representations that counterbalance the overall reward-adjacency bias, thereby predicting the stabilization of cognitive maps that comprehensively reflect entire underlying spatial contexts. These findings suggest that post-learning offline-related memory consolidation plays a complimentary and computationally distinct role in learning compared to online encoding.

The hippocampus converts dynamic entorhinal inputs into stable spatial maps

SummaryThe medial entorhinal cortex (MEC)-hippocampal network plays a key role in the processing, storage, and recall of spatial information. However, how the spatial code provided by MEC inputs relates to spatial representations generated by principal cell assemblies within hippocampal subfields remains enigmatic. To investigate this coding relationship, we employed two-photon calcium imaging in mice navigating through dissimilar virtual environments. Imaging large MEC bouton populations revealed spatially tuned activity patterns. MEC inputs drastically changed their preferred spatial field locations between environments, whereas hippocampal cells showed lower levels of place field reconfiguration. Decoding analysis indicated that higher place field reliability and larger context-dependent activity-rate differences allow low numbers of principal cells, particularly in the DG and CA1, to provide information about location and context more accurately and rapidly than MEC inputs. Thus, conversion of dynamic MEC inputs into stable spatial hippocampal maps may enable fast encoding and efficient recall of spatio-contextual information.

On stability of the fibres of Hopf surfaces as harmonic maps and minimal surfaces

We construct a family of Hermitian metrics on the Hopf surface S 3 × S 1 \mathbb {S}^3\times \mathbb {S}^1 , whose fundamental classes represent distinct cohomology classes in the Aeppli cohomology group. These metrics are locally conformally Kähler. Among the toric fibres of π : S 3 × S 1 → C P 1 \pi :\mathbb {S}^3\times \mathbb {S}^1\to \mathbb {C} P^1 two of them are stable minimal surfaces and each of the two has a neighbourhood so that fibres therein are given by stable harmonic maps from 2-torus and outside, far away from the two tori, there are unstable harmonic ones that are also unstable minimal surfaces. A similar result is true for S 2 n − 1 × S 1 \mathbb {S}^{2n-1}\times \mathbb {S}^{1} .

Data-Driven Mapping With Prediction Neural Network for the Future Wide-Swath Satellite Altimetry

Two-dimensional mapping of sea surface height (SSH) for future wide-swath satellite altimetry (WSA) is a challenge at present. So far, considering the utilization of data-driven methods is a new researching direction for SSH mapping. In general, the data-driven mapping methods rely on the spatial-temporal relationship of the observations. These methods require training in large volumes, and the time cost is high, especially for the WSA observations. This paper proposed the prediction neural networks for mapping (Mapping-PNN) method to improve the training efficiency and maintain stable data and mapping capabilities. By 10-year wide-swath satellite along track observing system simulation experiments (OSSEs) on the HYCOM data, the experiment results indicate that the method introduced in this paper can improve the training efficiency and meet the grid mapping expectations. Compared with other methods, the root mean squared error (RMSE) of the mapping-PNN method can be limited within the range of ~1.8 cm, and the new method can promote the observation of the ocean phenomena scale with < ~40 km, which reaches state of the art.

Indoor Positioning Using Magnetic Fingerprint Map Captured by Magnetic Sensor Array.

By collecting the magnetic field information of each spatial point, we can build a magnetic field fingerprint map. When the user is positioning, the magnetic field measured by the sensor is matched with the magnetic field fingerprint map to identify the user’s location. However, since the magnetic field is easily affected by external magnetic fields and magnetic storms, which can lead to “local temporal-spatial variation”, it is difficult to construct a stable and accurate magnetic field fingerprint map for indoor positioning. This research proposes a new magnetic indoor positioning method, which combines a magnetic sensor array composed of three magnetic sensors and a recurrent probabilistic neural network (RPNN) to realize a high-precision indoor positioning system. The magnetic sensor array can detect subtle magnetic anomalies and spatial variations to improve the stability and accuracy of magnetic field fingerprint maps, and the RPNN model is built for recognizing magnetic field fingerprint. We implement an embedded magnetic sensor array positioning system, which is evaluated in an experimental environment. Our method can reduce the noise caused by the spatial-temporal variation of the magnetic field, thus greatly improving the indoor positioning accuracy, reaching an average positioning accuracy of 0.78 m.

Mapping brain-behavior space relationships along the psychosis spectrum.

Difficulties in advancing effective patient-specific therapies for psychiatric disorders highlight a need to develop a stable neurobiologically grounded mapping between neural and symptom variation. This gap is particularly acute for psychosis-spectrum disorders (PSD). Here, in a sample of 436 PSD patients spanning several diagnoses, we derived and replicated a dimensionality-reduced symptom space across hallmark psychopathology symptoms and cognitive deficits. In turn, these symptom axes mapped onto distinct, reproducible brain maps. Critically, we found that multivariate brain-behavior mapping techniques (e.g. canonical correlation analysis) do not produce stable results with current sample sizes. However, we show that a univariate brain-behavioral space (BBS) can resolve stable individualized prediction. Finally, we show a proof-of-principle framework for relating personalized BBS metrics with molecular targets via serotonin and glutamate receptor manipulations and neural gene expression maps derived from the Allen Human Brain Atlas. Collectively, these results highlight a stable and data-driven BBS mapping across PSD, which offers an actionable path that can be iteratively optimized for personalized clinical biomarker endpoints.

Curve neighborhoods and minimal degrees in quantum products

Let G be a connected, simply connected, simple, complex, linear algebraic group. Let P be an arbitrary parabolic subgroup of G. Let be the G-homogeneous projective space attached to this situation. We consider the (small) quantum cohomology ring attached to X. Postnikov proved that any quantum product of two Schubert classes admits a unique minimal degree. In particular, this result implies that there exists a unique degree d which is minimal with the property that qd occurs with nonzero coefficient in the quantum product of two point classes. This unique minimal degree in is denoted by dX . We use the technique of curve neighborhoods by Buch-Mihalcea to compute dX explicitly in terms of Kostant’s cascade of orthogonal roots. Moreover, we prove orthogonality relations in greedy decompositions of minimal degrees. Such orthogonality relations can be seen as a generalization of the computation of dX from one minimal degree to every minimal degree, and were successfully applied to prove quasi-homogeneity of the moduli space of stable maps.

Sparse flow adversarial model for robust image compression

Existing learned-based image compression methods have shown impressive performance. However, they rely mostly on the consistent distribution between training and test images, which reduces the robustness of the training model. In this paper, we propose a novel compression method called sparse flow adversarial model (SFAM). SFAM employs a deep generative framework to learn a reversible and stable mapping between image distributions, thus it can work in varied scenes for robust compression. The mapping explores the sparsity of the image by combining linear and nonlinear transformations, rather than extracting the features of a particular dataset as is the case with other learning-based methods. Moreover, a sparse adversarial map is introduced into SFAM, to constrain the SFAM to generate sparser features for efficient compression. Extensive experiments are performed on different datasets, in which the effectiveness and robustness of the proposed method are verified. Meanwhile, SFAM is trained only once and it can work well on three different datasets, which also prove the robustness of the proposed SFAM.

Sheaves of maximal intersection and multiplicities of stable log maps

A great number of theoretical results are known about log Gromov–Witten invariants (Abramovich and Chen in Asian J Math 18:465–488, 2014; Chen in Ann Math (2) 180:455–521, 2014; Gross and Siebert J Am Math Soc 26: 451–510, 2013), but few calculations are worked out. In this paper we restrict to surfaces and to genus 0 stable log maps of maximal tangency. We ask how various natural components of the moduli space contribute to the log Gromov–Witten invariants. The first such calculation (Gross et al. in Duke Math J 153:297–362, 2010, Proposition 6.1) by Gross–Pandharipande–Siebert deals with multiple covers over rigid curves in the log Calabi–Yau setting. As a natural continuation, in this paper we compute the contributions of non-rigid irreducible curves in the log Calabi–Yau setting and that of the union of two rigid curves in general position. For the former, we construct and study a moduli space of “logarithmic” 1-dimensional sheaves and compare the resulting multiplicity with tropical multiplicity. For the latter, we explicitly describe the components of the moduli space and work out the logarithmic deformation theory in full, which we then compare with the deformation theory of the analogous relative stable maps.

WITHDRAWN: Category theory-based emotional intelligence mapping model for consumer-E-business to improve E-commerce

Economic growth, proliferation, and globalization of economic and trade policies have resulted in the rapid growth and development of e-commerce and e-business across different application domains. However, with this growing demand for e-business, there is also a significant need to develop stable business mapping models that can support the successful and sustained operation of e-business. As their complexity of running e-business increases, there is an equal demand to increase the employees' capability at work and meet the growing demands and evolving changes. It is mandatory to keep the employees motivated and in a good emotional state of mind to achieve quality work. At the same time, it is also highly essential to study the emotional intelligence and mind frame of the management and leaders and explore possible means to foster creative and innovative ideas that create a healthy atmosphere. Also, it is equally important to understand the significant need of customers to whom the e-business caters to. Studying the emotional intelligence part from the customer perspective is also highly needed for ensuring the growth, development, and important innovations in the e-business model. This work is motivated towards developing a Category Theory model that concentrates on understanding the emotional intelligence of managers and leaders and mapping them towards customer emotional intelligence so that the gaps and expectations can be narrowed down using emotional intelligence.

Weighted graphs and stable maps of 3-manifolds in R3

En el presente artículo se estudia el espacio de grafos con pesos, junto con dos operaciones entre estos grafos. Los resultados que se encuentran en este espacio son usados en el estudio de aplicaciones estables de 3-variedades en R3, en particular cuando la 3-variedad es Mn, donde esta variedad es la suma conexa de n-copias de S1×S2 con M0 = S3. Además, se prueban resultados importantes para la construcción de este tipo de aplicaciones.

Quantitative platform for accurate and reproducible assessment of transverse (T2) relaxation time

MRI's transverse relaxation time (T2) is sensitive to tissues' composition and pathological state. While variations in T2 values can be used as clinical biomarkers, it is challenging to quantify this parameter in vivo due to the complexity of the MRI signal model, differences in protocol implementations, and hardware imperfections. Herein, we provide a detailed analysis of the echo modulation curve (EMC) platform, offering accurate and reproducible mapping of T2 values, from 2D multi‐slice multi‐echo spin‐echo (MESE) protocols.Computer simulations of the full Bloch equations are used to generate an advanced signal model, which accounts for stimulated echoes and transmit field (B1+) inhomogeneities. In addition to quantifying T2 values, the EMC platform also provides proton density (PD) maps, and fat‐water fraction maps. The algorithm's accuracy, reproducibility, and insensitivity to T1 values are validated on a phantom constructed by the National Institute of Standards and Technology and on in vivo human brains.EMC‐derived T2 maps show excellent agreement with ground truth values for both in vitro and in vivo models. Quantitative values are accurate and stable across scan settings and for the physiological range of T2 values, while showing robustness to main field (B0) inhomogeneities, to variations in T1 relaxation time, and to magnetization transfer. Extension of the algorithm to two‐component fitting yields accurate fat and water T2 maps along with their relative fractions, similar to a reference three‐point Dixon technique.Overall, the EMC platform allows to generate accurate and stable T2 maps, with a full brain coverage using a standard MESE protocol and at feasible scan times. The utility of EMC‐based T2 maps was demonstrated on several clinical applications, showing robustness to variations in other magnetic properties. The algorithm is available online as a full stand‐alone package, including an intuitive graphical user interface.

The roles of the lateral intraparietal area and frontal eye field in guiding eye movements in free viewing search behavior.

The lateral intraparietal area (LIP) and frontal eye field (FEF) have been shown to play significant roles in oculomotor control, yet most studies have found that the two areas behave similarly. To identify the unique roles each area plays in guiding eye movements, we recorded 200 LIP neurons and 231 FEF neurons from four animals performing a free viewing visual foraging task. We analyzed how neuronal responses were modulated by stimulus identity and the animals' choice of where to make a saccade. We additionally analyzed the comodulation of the sensory signals and the choice signal to identify how the sensory signals drove the choice. We found a clearly defined division of labor: LIP provided a stable map integrating task rules and stimulus identity, whereas FEF responses were dynamic, representing more complex information and, just before the saccade, were integrated with task rules and stimulus identity to decide where to move the eye.NEW & NOTEWORTHY The lateral intrapareital area (LIP) and frontal eye field (FEF) are known to contribute to guiding eye movements, but little is known about the unique roles that each area plays. Using a free viewing visual search task, we found that LIP provides a stable map of the visual world, integrating task rules and stimulus identity. FEF activity is consistently modulated by more complex information but, just before the saccade, integrates all the information to make the final decision about where to move.

Linear logic in normed cones: probabilistic coherence spaces and beyond

Abstract Ehrhard et al. (2018. Proceedings of the ACM on Programming Languages, POPL 2, Article 59.) proposed a model of probabilistic functional programming in a category of normed positive cones and stable measurable cone maps, which can be seen as a coordinate-free generalization of probabilistic coherence spaces (PCSs). However, unlike the case of PCSs, it remained unclear if the model could be refined to a model of classical linear logic. In this work, we consider a somewhat similar category which gives indeed a coordinate-free model of full propositional linear logic with nondegenerate interpretation of additives and sound interpretation of exponentials. Objects are dual pairs of normed cones satisfying certain specific completeness properties, such as existence of norm-bounded monotone weak limits, and morphisms are bounded (adjointable) positive maps. Norms allow us a distinct interpretation of dual additive connectives as product and coproduct. Exponential connectives are modeled using real analytic functions and distributions that have representations as power series with positive coefficients. Unlike the familiar case of PCSs, there is no reference or need for a preferred basis; in this sense the model is invariant. PCSs form a full subcategory, whose objects, seen as posets, are lattices. Thus, we get a model fitting in the tradition of interpreting linear logic in a linear algebraic setting, which arguably is free from the drawbacks of its predecessors.

VLSI Design for High‐Precision Three‐Dimensional Depth Perception Chip

This paper presents a Very large scale integration (VLSI) design method for Three-dimensional (3D) depth perception chip based on infrared coding structure light. The primary sub-modules on the chip contain the speckle pattern preprocessing module, block-matching disparity estimation, depth mapping and post-processing. The chip employs pipelining technology, and after Application specific integrated circuit (ASIC) verification, it proves that our chip has more advantages in performance of depth precision (12bits, 1mm @ 1m), image resolution (1280×960), time delay (less than 17ms), range limit (0.4~6m). It also can generate more stable and smooth depth map in real-time, which can be used in 3D recognition, motion capture or scene perception.

Triangles and electrostatic ion traps

We consider the equilibrium points of the electrostatic potential of three mutually repelling point charges with Coulomb interaction placed at the vertices of a given triangle T. It is proven that for each point P inside the triangle T, there exists a unique collection of positive point charges, called stationary charges for P in T, such that P is a critical point of the electrostatic potential of these point charges placed at vertices of T in a fixed order. Explicit formulas for stationary charges are given, which are used to investigate the existence and geometry of stable equilibria arising in this setting. In particular, symbolic computations and computer experiments reveal that for an isosceles triangle T, the set S(T) of points P that are stable equilibria of their stationary charges is a non-empty open set containing the incenter of a triangle T. For a regular triangle, using symbolic computations, it appears possible to verify that the formulas for stationary charges define a stable mapping in the sense of Whitney having a deltoid caustic with three ordinary cusps. An interpretation of our results in terms of electrostatic ion traps is also given, and several plausible conjectures are presented.